Data commit

Task/Archimedean-spiral/00-META.yaml

@@ -0,0 +1,2 @@
+---
+from: http://rosettacode.org/wiki/Archimedean_spiral

Task/Archimedean-spiral/00-TASK.txt

@@ -0,0 +1,14 @@
+The [[wp:Archimedean_spiral|Archimedean spiral]] is a spiral named after the Greek mathematician Archimedes. 
+
+
+An Archimedean spiral can be described by the equation:
+
+:<big><math>\, r=a+b\theta</math></big>
+
+with real numbers ''a'' and ''b''.
+
+
+;Task
+Draw an Archimedean spiral.
+<br><br>
+

Task/Archimedean-spiral/ALGOL-W/archimedean-spiral.alg

@@ -0,0 +1,42 @@
+begin % draw an Archimedian spiral %
+      % Translation of AWK which was a trnslation of Applesoft Basic program %
+    integer procedure max ( integer x, y ) ; begin if x > y then x else y end;
+    integer procedure min ( integer x, y ) ; begin if x < y then x else y end;
+    integer x_min, y_min, x_max, y_max, a, b, x, y;
+    string(255) array arr ( 1 :: 255 );
+    real    h, w, m, s, t;
+    x_min := y_min := 9999;
+    x_max := y_max := 0;
+    h := 96;
+    w := h + h / 2;
+    a := 1;
+    b := 1;
+    m := 6 * PI;
+    s := .02;
+    t := s;
+    while t <= m do begin % build spiral %
+      real r;
+      r := a + b * t;
+      x := round(r * cos(t) + w);
+      y := round(r * sin(t) + h);
+      if x <= 0 or y <= 0 then begin end
+      else if x >= 280    then begin end
+      else if y >= 192    then begin end
+      else begin
+        arr( x )( y // 1 ) := "*";
+        x_min := min(x_min,x);
+        x_max := max(x_max,x);
+        y_min := min(y_min,y);
+        y_max := max(y_max,y);
+        t     := t + s
+      end if__various_x_and_y_values__
+    end while__t_le_m ;
+    for i := x_min until x_max do begin
+        for j := y_min until y_max do begin
+            string(1) c;
+            c := arr( i )( j // 1 );
+            writeon( c, c )
+        end for_j ;
+        write()
+    end for_i
+end.

Task/Archimedean-spiral/APL/archimedean-spiral.apl

@@ -0,0 +1,5 @@
+  'InitCauseway' 'View' ⎕CY 'sharpplot'
+  InitCauseway ⍬   ⍝ initialise current namespace
+  sp←⎕NEW Causeway.SharpPlot
+  sp.DrawPolarChart {⍵(360|⍵)}⌽⍳720
+      View sp

Task/Archimedean-spiral/AWK/archimedean-spiral.awk

@@ -0,0 +1,35 @@
+# syntax: GAWK -f ARCHIMEDEAN_SPIRAL.AWK
+# converted from Applesoft BASIC
+BEGIN {
+    x_min = y_min = 9999
+    x_max = y_max = 0
+    h = 96
+    w = h + h / 2
+    a = 1
+    b = 1
+    m = 6 * 3.1415926
+    step = .02
+    for (t=step; t<=m; t+=step) { # build spiral
+      r = a + b * t
+      x = int(r * cos(t) + w)
+      y = int(r * sin(t) + h)
+      if (x <= 0 || y <= 0) { continue }
+      if (x >= 280 ) { continue }
+      if (y >= 192) { continue }
+      arr[x,y] = "*"
+      x_min = min(x_min,x)
+      x_max = max(x_max,x)
+      y_min = min(y_min,y)
+      y_max = max(y_max,y)
+    }
+    for (i=x_min; i<=x_max; i++) { # print spiral
+      rec = ""
+      for (j=y_min; j<=y_max; j++) {
+        rec = sprintf("%s%1s",rec,arr[i,j])
+      }
+      printf("%s\n",rec)
+    }
+    exit(0)
+}
+function max(x,y) { return((x > y) ? x : y) }
+function min(x,y) { return((x < y) ? x : y) }

Task/Archimedean-spiral/Action-/archimedean-spiral.action

@@ -0,0 +1,51 @@
+INT ARRAY SinTab=[
+  0 4 9 13 18 22 27 31 36 40 44 49 53 58 62 66 71 75 79 83
+  88 92 96 100 104 108 112 116 120 124 128 132 136 139 143
+  147 150 154 158 161 165 168 171 175 178 181 184 187 190
+  193 196 199 202 204 207 210 212 215 217 219 222 224 226
+  228 230 232 234 236 237 239 241 242 243 245 246 247 248
+  249 250 251 252 253 254 254 255 255 255 256 256 256 256]
+
+INT FUNC Sin(INT a)
+  WHILE a<0 DO a==+360 OD
+  WHILE a>360 DO a==-360 OD
+  IF a<=90 THEN
+    RETURN (SinTab(a))
+  ELSEIF a<=180 THEN
+    RETURN (SinTab(180-a))
+  ELSEIF a<=270 THEN
+    RETURN (-SinTab(a-180))
+  ELSE
+    RETURN (-SinTab(360-a))
+  FI
+RETURN (0)
+
+INT FUNC Cos(INT a)
+RETURN (Sin(a-90))
+
+PROC DrawSpiral(INT x0,y0)
+  INT angle,radius,x,y
+
+  Plot(x0,y0)
+  FOR angle=0 TO 1800 STEP 5
+  DO
+    radius=angle/20
+    x=radius*Cos(angle)/256+x0
+    y=radius*Sin(angle)/256+y0
+    DrawTo(x,y)
+  OD
+RETURN
+
+PROC Main()
+  BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6
+
+  Graphics(8+16)
+  Color=1
+  COLOR1=$0C
+  COLOR2=$02
+
+  DrawSpiral(160,96)
+
+  DO UNTIL CH#$FF OD
+  CH=$FF
+RETURN

Task/Archimedean-spiral/Ada/archimedean-spiral.ada

@@ -0,0 +1,72 @@
+with Ada.Numerics.Elementary_Functions;
+
+with SDL.Video.Windows.Makers;
+with SDL.Video.Renderers.Makers;
+with SDL.Events.Events;
+
+procedure Archimedean_Spiral is
+
+   Width      : constant := 800;
+   Height     : constant := 800;
+   A          : constant := 4.2;
+   B          : constant := 3.2;
+   T_First    : constant := 4.0;
+   T_Last     : constant := 100.0;
+
+   Window   : SDL.Video.Windows.Window;
+   Renderer : SDL.Video.Renderers.Renderer;
+   Event    : SDL.Events.Events.Events;
+
+   procedure Draw_Archimedean_Spiral is
+      use type SDL.C.int;
+      use Ada.Numerics.Elementary_Functions;
+      Pi   : constant := Ada.Numerics.Pi;
+      Step : constant := 0.002;
+      T    : Float;
+      R    : Float;
+   begin
+      T := T_First;
+      loop
+         R := A + B * T;
+         Renderer.Draw
+           (Point => (X => Width  / 2 + SDL.C.int (R * Cos (T, 2.0 * Pi)),
+                      Y => Height / 2 - SDL.C.int (R * Sin (T, 2.0 * Pi))));
+         exit when T >= T_Last;
+         T := T + Step;
+      end loop;
+   end Draw_Archimedean_Spiral;
+
+   procedure Wait is
+      use type SDL.Events.Event_Types;
+   begin
+      loop
+         while SDL.Events.Events.Poll (Event) loop
+            if Event.Common.Event_Type = SDL.Events.Quit then
+               return;
+            end if;
+         end loop;
+      end loop;
+   end Wait;
+
+begin
+   if not SDL.Initialise (Flags => SDL.Enable_Screen) then
+      return;
+   end if;
+
+   SDL.Video.Windows.Makers.Create (Win      => Window,
+                                    Title    => "Archimedean spiral",
+                                    Position => SDL.Natural_Coordinates'(X => 10, Y => 10),
+                                    Size     => SDL.Positive_Sizes'(Width, Height),
+                                    Flags    => 0);
+   SDL.Video.Renderers.Makers.Create (Renderer, Window.Get_Surface);
+   Renderer.Set_Draw_Colour ((0, 0, 0, 255));
+   Renderer.Fill (Rectangle => (0, 0, Width, Height));
+   Renderer.Set_Draw_Colour ((0, 220, 0, 255));
+
+   Draw_Archimedean_Spiral;
+   Window.Update_Surface;
+
+   Wait;
+   Window.Finalize;
+   SDL.Finalise;
+end Archimedean_Spiral;

Task/Archimedean-spiral/Amazing-Hopper/archimedean-spiral.hopper

@@ -0,0 +1,37 @@
+#include <jambo.h>
+
+Main
+   Set break
+   a=1.5, b=1.5, r=0, origen x=200, origen y=105
+   total = 0, Let ( total := Mul(20, M_PI) )
+   Cls
+   Loop for ( t=0, var 't' Is less equal to 'total', Let (t := Add (t, 0.005)) )
+       #( r = a + b * t )
+       Set 'origen x, origen y', # ( 200 + (2*r*sin(t)) ) » 'origen x', #( 105 + (r*cos(t)) ) » 'origen y',
+       Gosub 'Dibuja un segmento'
+   Next
+   Pause
+End
+
+Subrutines
+
+Define (Dibuja un segmento, x1, y1, x2, y2)
+  dx=0, dy=0, paso=0, i=0, DX=0, DY=0
+
+  Sub(x2, x1), Sub (y2, y1), Move to ' dx, dy '
+
+  Let( paso := Get if( Greater equal ( Abs(dx) » (DX), Abs(dy)»(DY) ), DX, DY ) )
+
+  // incremento:
+  Div(dx, paso), Div(dy, paso), Move to ( dx, dy )
+
+  Color back (13)
+  // dibuja línea:
+  i = 0
+  Loop if ( Less equal (i, paso) )
+     Locate( y1, x1 ), Printnl( " " )
+     Add ( x1, dx), Add( y1, dy ), Move to ( x1, y1 )
+     ++i
+  Back
+  Printnl("\OFF")
+Return

Task/Archimedean-spiral/AmigaBASIC/archimedean-spiral.basic

@@ -0,0 +1,9 @@
+a=1.5
+b=1.5
+pi=3.141592
+
+PSET (320,100)
+FOR t=0 TO 40*pi STEP .1
+  r=a+b*t
+  LINE -(320+2*r*SIN(t),100+r*COS(t))
+NEXT

Task/Archimedean-spiral/Applesoft-BASIC/archimedean-spiral.basic

@@ -0,0 +1,19 @@
+110 LET H = 96
+120 LET W = H + H / 2
+130 HGR2
+140 HCOLOR= 3
+150 LET A = 1
+160 LET B = 9
+170 LET PI = 3.1415926535
+180 LET M = 10 * PI
+190 LET S = .02
+200 FOR T = S TO M STEP S
+210     LET R = A + B * T
+220     LET X = R *  COS (T) + W
+230     LET Y = R *  SIN (T) + H
+240     IF X < 0 THEN  290
+250     IF Y < 0 THEN  290
+260     IF X > 279 THEN  290
+270     IF Y > 191 THEN  290
+280     HPLOT X,Y
+290 NEXT

Task/Archimedean-spiral/AutoHotkey/archimedean-spiral.ahk

@@ -0,0 +1,51 @@
+if !pToken := Gdip_Startup()
+{
+	MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system
+	ExitApp
+}
+OnExit, Exit
+SysGet, MonitorPrimary, MonitorPrimary
+SysGet, WA, MonitorWorkArea, %MonitorPrimary%
+WAWidth	:= WARight-WALeft
+WAHeight := WABottom-WATop
+Gui, 1: -Caption +E0x80000 +LastFound +AlwaysOnTop +ToolWindow +OwnDialogs
+Gui, 1: Show, NA
+hwnd1 := WinExist()
+hbm := CreateDIBSection(WAWidth, WAHeight)
+hdc := CreateCompatibleDC()
+obm := SelectObject(hdc, hbm)
+G := Gdip_GraphicsFromHDC(hdc)
+Gdip_SetSmoothingMode(G, 4)
+pPen := Gdip_CreatePen(0xffff0000, 3)
+;--------------------------------
+a := 1, b := 4, th := 0.1, step := 0.1
+loop, 720
+{
+	th += step
+	r := a + b * th
+	x1 := r * Cos(th)
+	y1 := r * Sin(th)
+	x1 += A_ScreenWidth/2
+	y1 += A_ScreenHeight/2	
+	if (x2 && y2)
+		Gdip_DrawLine(G, pPen, x1, y1, x2, y2)
+	x2 := x1, 	y2 := y1
+	if GetKeyState("Esc", "P")
+		break
+	; next two lines are optional to watch it draw
+	; Sleep 10
+	; UpdateLayeredWindow(hwnd1, hdc, WALeft, WATop, WAWidth, WAHeight)
+}
+UpdateLayeredWindow(hwnd1, hdc, WALeft, WATop, WAWidth, WAHeight)
+;--------------------------------
+return
+
+Exit:
+Gdip_DeletePen(pPen)
+SelectObject(hdc, obm)
+DeleteObject(hbm)
+DeleteDC(hdc)
+Gdip_DeleteGraphics(G)
+Gdip_Shutdown(pToken)
+ExitApp
+Return

Task/Archimedean-spiral/BASIC256/archimedean-spiral.basic

@@ -0,0 +1,30 @@
+# Basic-256 ver 1.1.4
+# Archimedean Spiral
+
+width = 430 : height = 430
+graphsize width, height
+rect 0,0, graphwidth,graphheight
+penwidth 1
+color green
+
+x = width/2 : y = height/2            # Center of graphics window
+i = 1 : t = 0 : xn = 0 : yn = 0       # Initial values
+iter = 150 : q = 30
+
+line x,0,x,height
+line 0,y,width,y
+
+penwidth 2
+color red
+
+while i <= iter
+    t = i / q * pi
+    xn = (1 + (1 * t)) * cos(t) +x
+    yn = (1 + (1 * t)) * sin(t) +y
+    line x,y,xn,yn
+    x = xn : y = yn
+    print i + chr(9) + int(x) + chr(9) + int(y) + chr(9) + int(t)    # chr(9) = TAB
+    i += 1
+end while
+
+imgsave "spiral-Basic-256.png", "PNG"

Task/Archimedean-spiral/BQN/archimedean-spiral.bqn

@@ -0,0 +1 @@
+{(•math.Sin •Plot○(⊢×↕∘≠) •math.Cos) -(2×π) × 𝕩⥊(↕÷-⟜1)100}

Task/Archimedean-spiral/C++/archimedean-spiral.cpp

@@ -0,0 +1,110 @@
+#include <windows.h>
+#include <string>
+#include <iostream>
+
+const int BMP_SIZE = 600;
+
+class myBitmap {
+public:
+    myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {}
+    ~myBitmap() {
+        DeleteObject( pen ); DeleteObject( brush );
+        DeleteDC( hdc ); DeleteObject( bmp );
+    }
+    bool create( int w, int h ) {
+        BITMAPINFO bi;
+        ZeroMemory( &bi, sizeof( bi ) );
+        bi.bmiHeader.biSize        = sizeof( bi.bmiHeader );
+        bi.bmiHeader.biBitCount    = sizeof( DWORD ) * 8;
+        bi.bmiHeader.biCompression = BI_RGB;
+        bi.bmiHeader.biPlanes      = 1;
+        bi.bmiHeader.biWidth       =  w;
+        bi.bmiHeader.biHeight      = -h;
+        HDC dc = GetDC( GetConsoleWindow() );
+        bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
+        if( !bmp ) return false;
+        hdc = CreateCompatibleDC( dc );
+        SelectObject( hdc, bmp );
+        ReleaseDC( GetConsoleWindow(), dc );
+        width = w; height = h;
+        return true;
+    }
+    void clear( BYTE clr = 0 ) {
+        memset( pBits, clr, width * height * sizeof( DWORD ) );
+    }
+    void setBrushColor( DWORD bClr ) {
+        if( brush ) DeleteObject( brush );
+        brush = CreateSolidBrush( bClr );
+        SelectObject( hdc, brush );
+    }
+    void setPenColor( DWORD c ) {
+        clr = c; createPen();
+    }
+    void setPenWidth( int w ) {
+        wid = w; createPen();
+    }
+    void saveBitmap( std::string path ) {
+        BITMAPFILEHEADER fileheader;
+        BITMAPINFO       infoheader;
+        BITMAP           bitmap;
+        DWORD            wb;
+        GetObject( bmp, sizeof( bitmap ), &bitmap );
+        DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];
+        ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );
+        ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );
+        ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );
+        infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
+        infoheader.bmiHeader.biCompression = BI_RGB;
+        infoheader.bmiHeader.biPlanes = 1;
+        infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );
+        infoheader.bmiHeader.biHeight = bitmap.bmHeight;
+        infoheader.bmiHeader.biWidth = bitmap.bmWidth;
+        infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );
+        fileheader.bfType    = 0x4D42;
+        fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );
+        fileheader.bfSize    = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;
+        GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );
+        HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS,
+                                  FILE_ATTRIBUTE_NORMAL, NULL );
+        WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );
+        WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );
+        WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );
+        CloseHandle( file );
+        delete [] dwpBits;
+    }
+    HDC getDC() const     { return hdc; }
+    int getWidth() const  { return width; }
+    int getHeight() const { return height; }
+private:
+    void createPen() {
+        if( pen ) DeleteObject( pen );
+        pen = CreatePen( PS_SOLID, wid, clr );
+        SelectObject( hdc, pen );
+    }
+    HBITMAP bmp; HDC    hdc;
+    HPEN    pen; HBRUSH brush;
+    void    *pBits; int    width, height, wid;
+    DWORD    clr;
+};
+class spiral {
+public:
+    spiral() {
+        bmp.create( BMP_SIZE, BMP_SIZE );
+    }
+    void draw( int c, int s ) {
+        double a = .2, b = .3, r, x, y;
+        int w = BMP_SIZE >> 1;
+        HDC dc = bmp.getDC();
+        for( double d = 0; d < c * 6.28318530718; d += .002 ) {
+            r = a + b * d; x = r * cos( d ); y = r * sin( d );
+            SetPixel( dc, ( int )( s * x + w ), ( int )( s * y + w ), 255 );
+        }
+        // saves the bitmap
+        bmp.saveBitmap( "./spiral.bmp" );
+    }
+private:
+    myBitmap bmp;
+};
+int main(int argc, char* argv[]) {
+    spiral s; s.draw( 16, 8 ); return 0;
+}

Task/Archimedean-spiral/C-sharp/archimedean-spiral.cs

@@ -0,0 +1,39 @@
+using System;
+using System.Linq;
+using System.Drawing;
+using System.Diagnostics;
+using System.Drawing.Drawing2D;
+
+class Program
+{
+    const int width = 380;
+    const int height = 380;
+    static PointF archimedeanPoint(int degrees)
+    {
+        const double a = 1;
+        const double b = 9;
+        double t = degrees * Math.PI / 180;
+        double r = a + b * t;
+        return new PointF { X = (float)(width / 2 + r * Math.Cos(t)), Y = (float)(height / 2 + r * Math.Sin(t)) };
+    }
+
+    static void Main(string[] args)
+    {
+        var bm = new Bitmap(width, height);
+        var g = Graphics.FromImage(bm);
+        g.SmoothingMode = SmoothingMode.AntiAlias;
+        g.FillRectangle(new SolidBrush(Color.White), new Rectangle { X = 0, Y = 0, Width = width, Height = height });
+        var pen = new Pen(Color.OrangeRed, 1.5f);
+
+        var spiral = Enumerable.Range(0, 360 * 3).AsParallel().AsOrdered().Select(archimedeanPoint);
+        var p0 = new PointF(width / 2, height / 2);
+        foreach (var p1 in spiral)
+        {
+            g.DrawLine(pen, p0, p1);
+            p0 = p1;
+        }
+        g.Save(); // is this really necessary ?
+        bm.Save("archimedes-csharp.png");
+        Process.Start("archimedes-csharp.png"); // Launches default photo viewing app
+    }
+}

Task/Archimedean-spiral/C/archimedean-spiral.c

@@ -0,0 +1,32 @@
+#include<graphics.h>
+#include<stdio.h>
+#include<math.h>
+
+#define pi M_PI
+
+int main(){
+	double a,b,cycles,incr,i;
+	
+	int steps,x=500,y=500;
+	
+	printf("Enter the parameters a and b : ");
+	scanf("%lf%lf",&a,&b);
+	
+	printf("Enter cycles : ");
+	scanf("%lf",&cycles);
+	
+	printf("Enter divisional steps : ");
+	scanf("%d",&steps);
+	
+	incr = 1.0/steps;
+	
+	initwindow(1000,1000,"Archimedean Spiral");
+	
+	for(i=0;i<=cycles*pi;i+=incr){
+		putpixel(x + (a + b*i)*cos(i),x + (a + b*i)*sin(i),15);
+	}
+	
+	getch();
+	
+	closegraph();	
+}

Task/Archimedean-spiral/Chipmunk-Basic/archimedean-spiral.basic

@@ -0,0 +1,12 @@
+10 rem Archimedean spiral
+20 graphics 0
+30 graphics cls
+40 a = 3 : b = 1.4
+50 x0 = 320 : y0 = 200
+60 graphics moveto x0,y0
+70 for t = 0 to 40*pi step 0.2
+80 r = a+b*t
+90 x = r*cos(t)+320 : y = r*sin(t)+200
+100 graphics lineto x,y
+110 next t
+120 end

Task/Archimedean-spiral/Clojure/archimedean-spiral-1.clj

@@ -0,0 +1,14 @@
+(use '(incanter core stats charts io))
+
+(defn Arquimidean-function
+  [a b theta]
+  (+ a (* theta b)))
+
+(defn transform-pl-xy [r theta]
+  (let [x (* r (sin theta))
+        y (* r (cos theta))]
+    [x y]))
+
+(defn arq-spiral [t] (transform-pl-xy (Arquimidean-function 0 7 t) t))
+
+(view (parametric-plot arq-spiral 0 (* 10 Math/PI)))

Task/Archimedean-spiral/Clojure/archimedean-spiral-2.clj

@@ -0,0 +1,40 @@
+(let [panel (proxy [javax.swing.JPanel] []
+              (paintComponent [g]
+                (proxy-super paintComponent g)
+                (.setStroke g (java.awt.BasicStroke. 2))
+                (.setRenderingHint g java.awt.RenderingHints/KEY_ANTIALIASING
+                                   java.awt.RenderingHints/VALUE_ANTIALIAS_ON)
+                (let [[a b] [0 (/ 1 Math/PI)]
+                      [w h] [(.getWidth this) (.getHeight this)]
+                      [cx cy] [(/ w 2.0) (/ h 2.0)]
+                      margin 16
+                      [rotations point-n] [3 (quot (min w h) 2)]
+                      [ring-n line-n] [6 12]
+                      scale (/ (- (min w h) (* 2 margin)) (* 2.0 ring-n))]
+                  ;; Grid
+                  (.setColor g (java.awt.Color. 0xEEEEEE))
+                  (doseq [i (range 1 (inc ring-n))]
+                    (let [[posx posy] [(- cx (* i scale)) (- cy (* i scale))]]
+                      (.drawOval g posx posy (* 2 i scale) (* 2 i scale))))
+                  (dotimes [i line-n]
+                    (let [theta (* 2 Math/PI (/ i (double line-n)))
+                          [x y] [(+ cx (* scale ring-n (Math/cos theta)))
+                                 (+ cy (* scale ring-n (Math/sin theta)))]]
+                      (.drawLine g cx cy x y)))
+                  ;; Spiral
+                  (.setColor g (java.awt.Color. 0x202020))
+                  (loop [i 0 [x y] [(+ cx (* a scale)) cy]]
+                    (let [p (/ (inc i) (double point-n))
+                          theta (* rotations 2 Math/PI p)
+                          r (* scale (+ a (* b theta)))
+                          [x1 y1] [(+ cx (* r (Math/cos theta)))
+                                   (- cy (* r (Math/sin theta)))]]
+                      (.drawLine g x y x1 y1)
+                      (when (< i (dec point-n)) (recur (inc i) [x1 y1])))))))]
+  (doto (javax.swing.JFrame.)
+    (.add (doto panel
+            (.setPreferredSize (java.awt.Dimension. 640 640))
+            (.setBackground java.awt.Color/white))
+          java.awt.BorderLayout/CENTER)
+    (.pack)
+    (.setVisible true)))

Task/Archimedean-spiral/Commodore-BASIC/archimedean-spiral.basic

@@ -0,0 +1,15 @@
+1 REM       ARCHIMEDEAN SPIRAL
+2 REM   USING COMMODORE BASIC 7.0
+3 REM      OF THE COMMODORE 128
+4 REM **********************************
+10 GRAPHIC 1,1
+20 A = 1.5
+30 B = 0.7
+40 X0 = 160 : Y0 = 100
+50 FOR T = 0 TO 40*π STEP 0.2
+60 R = A+B*T
+70 X = R*COS(T)+160 : Y = R*SIN(T)+100
+80 DRAW 1,X0,Y0 TO X,Y
+90 X0 = X : Y0 = Y
+100 NEXT T
+110 GOTO 110

Task/Archimedean-spiral/Common-Lisp/archimedean-spiral.lisp

@@ -0,0 +1,67 @@
+(defun draw-coords-as-text (coords size fill-char)
+  (let* ((min-x (apply #'min (mapcar #'car coords)))
+         (min-y (apply #'min (mapcar #'cdr coords)))
+         (max-x (apply #'max (mapcar #'car coords)))
+         (max-y (apply #'max (mapcar #'cdr coords)))
+         (real-size (max (+ (abs min-x) (abs max-x)) ; bounding square
+                         (+ (abs min-y) (abs max-y))))
+         (scale-factor (* (1- size) (/ 1 real-size)))
+         (center-x (* scale-factor -1 min-x))
+         (center-y (* scale-factor -1 min-y))
+         (intermediate-result (make-array (list size size)
+                                          :element-type 'char
+                                          :initial-element #\space)))
+    (dolist (c coords)
+      (let ((final-x (floor (+ center-x (* scale-factor (car c)))))
+            (final-y (floor (+ center-y (* scale-factor (cdr c))))))
+        (setf (aref intermediate-result final-x final-y)
+              fill-char)))
+    ; print results to output
+    (loop for i below (array-total-size intermediate-result) do
+          (when (zerop (mod i size))
+            (terpri))
+          (princ (row-major-aref intermediate-result i)))))
+
+
+(defun spiral (a b step-resolution step-count)
+  "Returns a list of coordinates for r=a+b*theta stepping theta by step-resolution"
+  (loop for theta
+        from 0 upto (* step-count step-resolution)
+        by step-resolution
+        for r = (+ a (* b theta))
+        for x = (* r (cos theta))
+        for y = (* r (sin theta))
+        collect (cons x y)))
+
+(draw-coords-as-text (spiral 10 10 0.01 1500) 30 #\*)
+; Output:
+;
+;                         *
+;          ******          *
+;       ****    ***        **
+;     ***          **       *
+;    **             **       *
+;   **               **      *
+;   *                 **     **
+;  **                  *      *
+; **       ******      *      *
+; *       **    **     **     *
+; *      **      *      *     *
+; *     **       *      *     **
+; *     *        *      *     *
+; *     *     * **      *     *
+; *     *     ***      **     *
+; *     **             *      *
+; *      *            **      *
+; *      **          **      **
+; **      **        **       *
+;  *       **      **       **
+;  **       ********        *
+;   *                      **
+;   **                    **
+;    **                  **
+;     **               ***
+;       **            **
+;        ****      ***
+;           *******
+;

Task/Archimedean-spiral/Craft-Basic/archimedean-spiral.basic

@@ -0,0 +1,17 @@
+bgcolor 0, 0, 0
+cls
+fgcolor 255, 255, 0
+
+define pi = 3.14, size = 80
+define x = 250, y = 200
+define a = 1.5, b = .7
+
+for t = 0 to size * pi step .1
+
+	let r = a + b * t
+	dot r * cos(t) + x, r * sin(t) + y
+	wait
+
+next t
+
+end

Task/Archimedean-spiral/Delphi/archimedean-spiral.delphi

@@ -0,0 +1,23 @@
+procedure ArcSpiral(Image: TImage);
+var Radius,Theta: double;
+var X,Y: integer;
+var Center: TPoint;
+const Step = 0.2;
+const Offset = 3; Spacing = 1.4;
+begin
+Image.Canvas.Brush.Color:=clWhite;
+Image.Canvas.Rectangle(0,0,Image.Width,Image.Height);
+Center:=Point(Image.Width div 2, Image.Height div 2);
+Image.Canvas.MoveTo(Center.X,Center.Y);
+Theta:=0;
+while Theta<(40*Pi) do
+	begin
+	{Radius increases as theta increases}
+	Radius:=Offset+Spacing*Theta;
+	{Calculate position on circle}
+	X:=Trunc(Radius*Cos(Theta)+Center.X);
+	Y:=Trunc(Radius*sin(Theta)+Center.Y);
+	Image.Canvas.LineTo(X,Y);
+	Theta:=Theta+Step;
+	end;
+end;

Task/Archimedean-spiral/FOCAL/archimedean-spiral.focal

@@ -0,0 +1,17 @@
+1.1 S A=1.5
+1.2 S B=2
+1.3 S N=250
+1.4 F T=1,N; D 2
+1.5 X FSKP(2*N)
+1.6 Q
+
+2.1 S R=A+B*T; D 3
+2.2 X FPT(2*T,X1+512,Y1+390)
+2.3 S R=A+B*(T+1); D 4
+2.4 X FVEC(2*T+1,X2-X1,Y2-Y1)
+
+3.1 S X1=R*FSIN(.2*T)
+3.2 S Y1=R*FCOS(.2*T)
+
+4.1 S X2=R*FSIN(.2*(T+1))
+4.2 S Y2=R*FCOS(.2*(T+1))

Task/Archimedean-spiral/FreeBASIC/archimedean-spiral.basic

@@ -0,0 +1,25 @@
+' version 16-10-2016
+' compile with: fbc -s gui
+
+Const As double      deg2rad = Atn(1) * 4 / 180    ' pi = atn(1) * 4, pi/180
+
+Const As UInteger screensize = 600                 ' size of window in pixels
+Const As Double        turns = 5                   ' number of turns
+Const As UInteger   halfscrn = screensize \ 2
+Const As uinteger         sf = (turns * (screensize - 100)) / halfscrn
+
+ScreenRes screensize, screensize, 32   ' screen 600 * 600 pixels, 4 byte color
+
+Dim As Double r, x, y
+
+For r = 0 To turns * 360 Step 0.05
+  x = Cos(r * deg2rad) * r / sf
+  y = Sin(r * deg2rad) * r / sf
+  PSet(halfscrn + x, halfscrn - y), RGB(255, 255, 255)
+Next
+
+' empty keyboard buffer
+While InKey <> "" : Wend
+Print : Print "hit any key to end program"
+Sleep
+End

Task/Archimedean-spiral/Frege/archimedean-spiral.frege

@@ -0,0 +1,89 @@
+module Archimedean where
+
+import Java.IO
+import Prelude.Math
+
+data BufferedImage = native java.awt.image.BufferedImage where
+  pure native type_3byte_bgr "java.awt.image.BufferedImage.TYPE_3BYTE_BGR" :: Int
+  native new :: Int -> Int -> Int -> STMutable s BufferedImage
+  native createGraphics :: Mutable s BufferedImage -> STMutable s Graphics2D
+
+data Color = pure native java.awt.Color where
+  pure native orange "java.awt.Color.orange" :: Color
+  pure native white "java.awt.Color.white" :: Color
+  pure native new :: Int -> Color
+
+data BasicStroke = pure native java.awt.BasicStroke where
+  pure native new :: Float -> BasicStroke
+
+data RenderingHints = native java.awt.RenderingHints where
+  pure native key_antialiasing "java.awt.RenderingHints.KEY_ANTIALIASING" :: RenderingHints_Key
+  pure native value_antialias_on "java.awt.RenderingHints.VALUE_ANTIALIAS_ON" :: Object
+
+data RenderingHints_Key = pure native java.awt.RenderingHints.Key
+
+data Graphics2D = native java.awt.Graphics2D where
+  native drawLine :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
+  native drawOval :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
+  native fillRect :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
+  native setColor :: Mutable s Graphics2D -> Color -> ST s ()
+  native setRenderingHint :: Mutable s Graphics2D -> RenderingHints_Key -> Object -> ST s ()
+  native setStroke :: Mutable s Graphics2D -> BasicStroke -> ST s ()
+
+data ImageIO = mutable native javax.imageio.ImageIO where
+  native write "javax.imageio.ImageIO.write" :: MutableIO BufferedImage -> String -> MutableIO File -> IO Bool throws IOException
+
+width = 640
+center = width `div` 2
+
+roundi = fromIntegral . round
+
+drawGrid :: Mutable s Graphics2D -> ST s ()
+drawGrid g = do
+  g.setColor $ Color.new 0xEEEEEE
+  g.setStroke $ BasicStroke.new 2
+  let angle = toRadians 45
+      margin = 10
+      numRings = 8
+      spacing = (width - 2 * margin) `div` (numRings * 2)
+  forM_ [0 .. numRings-1] $ \i -> do
+    let pos = margin + i * spacing
+        size = width - (2 * margin + i * 2 * spacing)
+        ia = fromIntegral i * angle
+        multiplier = fromIntegral $ (width - 2 * margin) `div` 2
+        x2 = center + (roundi (cos ia * multiplier))
+        y2 = center - (roundi (sin ia * multiplier))
+    g.drawOval pos pos size size
+    g.drawLine center center x2 y2
+
+drawSpiral :: Mutable s Graphics2D -> ST s ()
+drawSpiral g = do
+  g.setStroke $ BasicStroke.new 2
+  g.setColor $ Color.orange
+  let degrees = toRadians 0.1
+      end = 360 * 2 * 10 * degrees
+      a = 0
+      b = 20
+      c = 1
+      drSp theta = do
+        let r = a + b * theta ** (1 / c)
+            x = r * cos theta
+            y = r * sin theta
+            theta' = theta + degrees
+        plot g (center + roundi x) (center - roundi y)
+        when (theta' < end) (drSp (theta' + degrees))
+  drSp 0
+
+plot :: Mutable s Graphics2D -> Int -> Int -> ST s ()
+plot g x y = g.drawOval x y 1 1
+
+main = do
+  buffy <- BufferedImage.new width width BufferedImage.type_3byte_bgr
+  g <- buffy.createGraphics
+  g.setRenderingHint RenderingHints.key_antialiasing RenderingHints.value_antialias_on
+  g.setColor Color.white
+  g.fillRect 0 0 width width
+  drawGrid g
+  drawSpiral g
+  f <- File.new "SpiralFrege.png"
+  void $ ImageIO.write buffy "png" f

Task/Archimedean-spiral/Frink/archimedean-spiral.frink

@@ -0,0 +1,15 @@
+p = new polyline
+g = new graphics
+a = 1
+b = 1
+for theta = 0 to 10 circle step 1 degree
+{
+   r = a + b theta
+   x = r cos[theta]
+   y = r sin[theta]
+   p.addPoint[x,-y]
+}
+
+g.add[p]
+g.show[]
+g.write["ArchimedeanSpiralFrink.svg",800,800]

Task/Archimedean-spiral/FutureBasic/archimedean-spiral.basic

@@ -0,0 +1,21 @@
+_maxPoints = 190
+
+void local fn DoIt
+  window 1, @"Archimedean Spiral", (0,0,500,500)
+  WindowSetBackgroundColor( 1, fn ColorBlack )
+  pen 3, fn ColorRed
+
+  float x, y, angle
+  long i, a = 10, b = 10, x1 = 250, y1 = 250
+  for i = 0 to _maxPoints - 1
+    angle = 0.1 * i
+    x = (a + b * angle) * cos(angle) + 250
+    y = (a + b * angle) * sin(angle) + 250
+    line x1,y1 to x,y
+    x1 = x : y1 = y
+  next
+end fn
+
+fn DoIt
+
+HandleEvents

Task/Archimedean-spiral/GW-BASIC/archimedean-spiral.basic

@@ -0,0 +1,12 @@
+10 A = 0
+20 B = 1
+30 SCREEN 1
+40 FOR THETA = 0 TO 160 STEP .01
+50 R = A + B*THETA
+60 X = R*COS(THETA)
+70 Y = R*SIN(THETA)
+80 PSET (160+X, 100-Y),3
+90 NEXT THETA
+100 IF INKEY$="" THEN GOTO 100
+110 SCREEN 2:SCREEN 0
+120 END

Task/Archimedean-spiral/Go/archimedean-spiral.go

@@ -0,0 +1,48 @@
+package main
+
+import (
+	"image"
+	"image/color"
+	"image/draw"
+	"image/png"
+	"log"
+	"math"
+	"os"
+)
+
+func main() {
+	const (
+		width, height = 600, 600
+		centre        = width / 2.0
+		degreesIncr   = 0.1 * math.Pi / 180
+		turns         = 2
+		stop          = 360 * turns * 10 * degreesIncr
+		fileName      = "spiral.png"
+	)
+
+	img := image.NewNRGBA(image.Rect(0, 0, width, height)) // create new image
+	bg := image.NewUniform(color.RGBA{255, 255, 255, 255}) // prepare white for background
+	draw.Draw(img, img.Bounds(), bg, image.ZP, draw.Src)   // fill the background
+	fgCol := color.RGBA{255, 0, 0, 255}                    // red plot
+
+	a := 1.0
+	b := 20.0
+
+	for theta := 0.0; theta < stop; theta += degreesIncr {
+		r := a + b*theta
+		x := r * math.Cos(theta)
+		y := r * math.Sin(theta)
+		img.Set(int(centre+x), int(centre-y), fgCol)
+	}
+
+	imgFile, err := os.Create(fileName)
+	if err != nil {
+		log.Fatal(err)
+	}
+	defer imgFile.Close()
+
+	if err := png.Encode(imgFile, img); err != nil {
+		imgFile.Close()
+		log.Fatal(err)
+	}
+}

Task/Archimedean-spiral/Haskell/archimedean-spiral.hs

@@ -0,0 +1,27 @@
+#!/usr/bin/env stack
+-- stack --resolver lts-7.0 --install-ghc runghc --package Rasterific --package JuicyPixels
+
+import Codec.Picture( PixelRGBA8( .. ), writePng )
+import Graphics.Rasterific
+import Graphics.Rasterific.Texture
+import Graphics.Rasterific.Transformations
+
+archimedeanPoint a b t = V2 x y
+  where r = a + b * t
+        x = r * cos t
+        y = r * sin t
+
+main :: IO ()
+main = do
+  let white = PixelRGBA8 255 255 255 255
+      drawColor = PixelRGBA8 0xFF 0x53 0x73 255
+      size = 800
+      points = map (archimedeanPoint 0 10) [0, 0.01 .. 60]
+      hSize = fromIntegral size / 2
+      img = renderDrawing size size white $
+            withTransformation (translate $ V2 hSize hSize) $
+            withTexture (uniformTexture drawColor) $
+            stroke 4 JoinRound (CapRound, CapRound) $
+            polyline points
+
+  writePng "SpiralHaskell.png" img

Task/Archimedean-spiral/IS-BASIC/archimedean-spiral.basic

@@ -0,0 +1,6 @@
+100 GRAPHICS LORES 2
+110 OPTION ANGLE DEGREES
+120 PLOT 640,360,ANGLE 90;
+130 FOR I=2 TO 33.2 STEP .05
+140   PLOT FORWARD I,LEFT 5;
+150 NEXT

Task/Archimedean-spiral/J/archimedean-spiral.j

@@ -0,0 +1,2 @@
+require'plot'
+'aspect 1' plot (*^)j.0.01*i.1400

Task/Archimedean-spiral/Java/archimedean-spiral.java

@@ -0,0 +1,84 @@
+import java.awt.*;
+import static java.lang.Math.*;
+import javax.swing.*;
+
+public class ArchimedeanSpiral extends JPanel {
+
+    public ArchimedeanSpiral() {
+        setPreferredSize(new Dimension(640, 640));
+        setBackground(Color.white);
+    }
+
+    void drawGrid(Graphics2D g) {
+        g.setColor(new Color(0xEEEEEE));
+        g.setStroke(new BasicStroke(2));
+
+        double angle = toRadians(45);
+
+        int w = getWidth();
+        int center = w / 2;
+        int margin = 10;
+        int numRings = 8;
+
+        int spacing = (w - 2 * margin) / (numRings * 2);
+
+        for (int i = 0; i < numRings; i++) {
+            int pos = margin + i * spacing;
+            int size = w - (2 * margin + i * 2 * spacing);
+            g.drawOval(pos, pos, size, size);
+
+            double ia = i * angle;
+            int x2 = center + (int) (cos(ia) * (w - 2 * margin) / 2);
+            int y2 = center - (int) (sin(ia) * (w - 2 * margin) / 2);
+
+            g.drawLine(center, center, x2, y2);
+        }
+    }
+
+    void drawSpiral(Graphics2D g) {
+        g.setStroke(new BasicStroke(2));
+        g.setColor(Color.orange);
+
+        double degrees = toRadians(0.1);
+        double center = getWidth() / 2;
+        double end = 360 * 2 * 10 * degrees;
+        double a = 0;
+        double b = 20;
+        double c = 1;
+
+        for (double theta = 0; theta < end; theta += degrees) {
+            double r = a + b * pow(theta, 1 / c);
+            double x = r * cos(theta);
+            double y = r * sin(theta);
+            plot(g, (int) (center + x), (int) (center - y));
+        }
+    }
+
+    void plot(Graphics2D g, int x, int y) {
+        g.drawOval(x, y, 1, 1);
+    }
+
+    @Override
+    public void paintComponent(Graphics gg) {
+        super.paintComponent(gg);
+        Graphics2D g = (Graphics2D) gg;
+        g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
+                RenderingHints.VALUE_ANTIALIAS_ON);
+
+        drawGrid(g);
+        drawSpiral(g);
+    }
+
+    public static void main(String[] args) {
+        SwingUtilities.invokeLater(() -> {
+            JFrame f = new JFrame();
+            f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
+            f.setTitle("Archimedean Spiral");
+            f.setResizable(false);
+            f.add(new ArchimedeanSpiral(), BorderLayout.CENTER);
+            f.pack();
+            f.setLocationRelativeTo(null);
+            f.setVisible(true);
+        });
+    }
+}

Task/Archimedean-spiral/JavaScript/archimedean-spiral-1.js

@@ -0,0 +1,24 @@
+<!-- ArchiSpiral.html -->
+<html>
+<head><title>Archimedean spiral</title></head>
+<body onload="pAS(35,'navy');">
+<h3>Archimedean spiral</h3> <p id=bo></p>
+<canvas id="canvId" width="640" height="640" style="border: 2px outset;"></canvas>
+<script>
+// Plotting Archimedean_spiral aev 3/17/17
+// lps - number of loops, clr - color.
+function pAS(lps,clr) {
+  var a=.0,ai=.1,r=.0,ri=.1,as=lps*2*Math.PI,n=as/ai;
+  var cvs=document.getElementById("canvId");
+  var ctx=cvs.getContext("2d");
+  ctx.fillStyle="white"; ctx.fillRect(0,0,cvs.width,cvs.height);
+  var x=y=0, s=cvs.width/2;
+  ctx.beginPath();
+  for (var i=1; i<n; i++) {
+    x=r*Math.cos(a), y=r*Math.sin(a);
+    ctx.lineTo(x+s,y+s);
+    r+=ri; a+=ai;
+  }//fend i
+  ctx.strokeStyle = clr; ctx.stroke();
+}
+</script></body></html>

Task/Archimedean-spiral/JavaScript/archimedean-spiral-2.js

@@ -0,0 +1,9 @@
+<html>
+<head>
+    <title>Archimedean spiral</title>
+    <style>h3 {font-family:sans-serif; color:gray;}</style>
+</head>
+<body onload="main('red')(15)">
+<h3>Archimedean spiral</h3></p>
+<canvas id="spiral" width="640" height="640" style="border: 2px outset;"></canvas>
+<script>

Task/Archimedean-spiral/JavaScript/archimedean-spiral-3.js

@@ -0,0 +1,33 @@
+const main = strColor => intCycles => {
+    const
+        ai = 0.05,
+        ri = 0.1,
+        cvs = document.getElementById('spiral'),
+        ctx = cvs.getContext('2d'),
+        s = cvs.width / 2,
+
+        points = enumFromTo(1)(
+            Math.PI * 2 * intCycles / ai
+        ).map(i => [Math.cos, Math.sin].map(
+            f => ri * i * f(ai * i) + s
+        ));
+
+    return (
+        console.log(points),
+        ctx.fillStyle = 'white',
+        ctx.fillRect(0, 0, cvs.width, cvs.height),
+        ctx.beginPath(),
+
+        points.forEach(xy => ctx.lineTo(...xy)),
+
+        ctx.strokeStyle = strColor,
+        ctx.stroke(),
+        points
+    );
+};
+
+// enumFromTo :: Int -> Int -> [Int]
+const enumFromTo = m => n =>
+    Array.from({
+        length: 1 + n - m
+    }, (_, i) => m + i);

Task/Archimedean-spiral/JavaScript/archimedean-spiral-4.js

@@ -0,0 +1 @@
+</script></body></html>

Task/Archimedean-spiral/Jq/archimedean-spiral-1.jq

@@ -0,0 +1,25 @@
+def spiral($zero; $turns; $step):
+
+  def pi: 1 | atan * 4;
+  def p2: (. * 100 | round) / 100;
+
+  def svg:
+    400 as $width
+    | 400 as $height
+    | 2 as $swidth # stroke
+    | "blue" as $stroke
+    | (range($zero; $turns * 2 * pi; $step) as $theta
+       | (((($theta)|cos) * 2 * $theta + ($width/2)) |p2) as $x
+       | (((($theta)|sin) * 2 * $theta + ($height/2))|p2) as $y
+       | if $theta == $zero
+         then "<path fill='transparent' style='stroke:\($stroke); stroke-width:\($swidth)' d='M \($x) \($y)"
+         else " L \($x) \($y)"
+         end),
+      "' />";
+
+  "<svg width='100%' height='100%'
+        xmlns='http://www.w3.org/2000/svg'>",
+        svg,
+  "</svg>" ;
+
+spiral(0; 10; 0.025)

Task/Archimedean-spiral/Jq/archimedean-spiral-2.jq

@@ -0,0 +1,31 @@
+def spiral($a; $b; $step; $h):
+  def min($x;$y): if $x <= $y then $x else $y end;
+  def max($x;$y): if $x <= $y then $y else $x end;
+  def pi: 1 | atan * 4;
+
+  (6 * pi) as $m
+  | ($h * 1.5) as $w
+  | { x_min: 9999, y_min: 9999,
+      x_max:    0, y_max:    0,
+      arr: [] }
+  | reduce range($step; $m+$step; $step) as $t (.;
+      .r = $a + $b * $t
+      | ((.r * ($t|cos) + $w) | round) as $x
+      | ((.r * ($t|sin) + $h) | round) as $y
+      | if   $x <= 0 or $y <= 0 then .
+        elif $x >= 280          then .
+        elif $y >= 192          then .
+        else .arr[$x][$y] = "*"
+        | .x_min = min(.x_min; $x)
+        | .x_max = max(.x_max; $x)
+        | .y_min = min(.y_min; $y)
+        | .y_max = max(.y_max; $y)
+	end )
+  # ... and print it
+  | .arr as $arr
+  | range(.x_min; .x_max + 1) as $i
+  | reduce range(.y_min; .y_max+1) as $j ( "";
+      . + ($arr[$i][$j] // " ") )
+  | "\(.)\n" ;
+
+spiral(1; 1; 0.02; 96)

Task/Archimedean-spiral/Julia/archimedean-spiral.julia

@@ -0,0 +1,6 @@
+using UnicodePlots
+
+spiral(θ, a=0, b=1) = @. b * θ * cos(θ + a), b * θ * sin(θ + a)
+
+x, y = spiral(1:0.1:10)
+println(lineplot(x, y))

Task/Archimedean-spiral/Kotlin/archimedean-spiral.kotlin

@@ -0,0 +1,76 @@
+// version 1.1.0
+
+import java.awt.*
+import javax.swing.*
+
+class ArchimedeanSpiral : JPanel() {
+    init {
+        preferredSize = Dimension(640, 640)
+        background = Color.white
+    }
+
+    private fun drawGrid(g: Graphics2D) {
+        g.color = Color(0xEEEEEE)
+        g.stroke = BasicStroke(2f)
+        val angle = Math.toRadians(45.0)
+        val w = width
+        val center = w / 2
+        val margin = 10
+        val numRings = 8
+        val spacing = (w - 2 * margin) / (numRings * 2)
+
+        for (i in 0 until numRings) {
+            val pos = margin + i * spacing
+            val size = w - (2 * margin + i * 2 * spacing)
+            g.drawOval(pos, pos, size, size)
+            val ia = i * angle
+            val x2 = center + (Math.cos(ia) * (w - 2 * margin) / 2).toInt()
+            val y2 = center - (Math.sin(ia) * (w - 2 * margin) / 2).toInt()
+            g.drawLine(center, center, x2, y2)
+        }
+    }
+
+    private fun drawSpiral(g: Graphics2D) {
+        g.stroke = BasicStroke(2f)
+        g.color = Color.magenta
+        val degrees = Math.toRadians(0.1)
+        val center = width / 2
+        val end = 360 * 2 * 10 * degrees
+        val a = 0.0
+        val b = 20.0
+        val c = 1.0
+        var theta = 0.0
+        while (theta < end) {
+            val r = a + b * Math.pow(theta, 1.0 / c)
+            val x = r * Math.cos(theta)
+            val y = r * Math.sin(theta)
+            plot(g, (center + x).toInt(), (center - y).toInt())
+            theta += degrees
+        }
+    }
+
+    private fun plot(g: Graphics2D, x: Int, y: Int) {
+        g.drawOval(x, y, 1, 1)
+    }
+
+    override fun paintComponent(gg: Graphics) {
+        super.paintComponent(gg)
+        val g = gg as Graphics2D
+        g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
+        drawGrid(g)
+        drawSpiral(g)
+    }
+}
+
+fun main(args: Array<String>) {
+    SwingUtilities.invokeLater {
+        val f = JFrame()
+        f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
+        f.title = "Archimedean Spiral"
+        f.isResizable = false
+        f.add(ArchimedeanSpiral(), BorderLayout.CENTER)
+        f.pack()
+        f.setLocationRelativeTo(null)
+        f.isVisible = true
+    }
+}

Task/Archimedean-spiral/Lambdatalk/archimedean-spiral.lambdatalk

@@ -0,0 +1,22 @@
+1) from polar to cartesian coordinates
+
+x = r*cos(t) = (a+b*t)*cos(t)
+y = r*sin(t) = (a+b*t)*sin(t)
+
+2) define the curve
+
+{def CURVE
+ {lambda {:a :b :t}
+  {* {+ :a {* :b :t}} {cos :t}}
+  {* {+ :a {* :b :t}} {sin :t}}
+}}
+-> CURVE
+
+3) and draw it using SVG
+
+{{SVG 580}
+ {g {AXES 580 580}
+  {polyline {@ points="{S.map {CURVE 5 4}
+                              {S.serie 0 {* 10 {PI}} 0.1}}"
+               {stroke red 3}}
+}}}

Task/Archimedean-spiral/Locomotive-Basic/archimedean-spiral.basic

@@ -0,0 +1,7 @@
+10 a=1.5:b=2
+20 mode 2:rad:move 320,200
+30 for t=0 to 40*pi step 0.2
+40 r=a+b*t
+50 draw r*sin(t)+320,r*cos(t)+200
+60 next
+70 while inkey$="":wend

Task/Archimedean-spiral/Lua/archimedean-spiral.lua

@@ -0,0 +1,20 @@
+a=1
+b=2
+cycles=40
+step=0.001
+x=0
+y=0
+
+function love.load()
+     x = love.graphics.getWidth()/2
+     y = love.graphics.getHeight()/2
+end
+
+function love.draw()
+     love.graphics.print("a="..a,16,16)
+     love.graphics.print("b="..b,16,32)
+
+     for i=0,cycles*math.pi,step do
+          love.graphics.points(x+(a + b*i)*math.cos(i),y+(a + b*i)*math.sin(i))
+     end
+end

Task/Archimedean-spiral/M2000-Interpreter/archimedean-spiral.m2000

@@ -0,0 +1,26 @@
+module Archimedean_spiral {
+	smooth on ' enable GDI+
+	def r(θ)=5+3*θ
+	cls #002222,0
+	pen #FFFF00
+	refresh 5000
+	every 1000 {
+		\\ redifine window (console width and height) and place it to center (symbol ;)
+		Window 12, random(10, 18)*1000, random(8, 12)*1000;
+		move scale.x/2, scale.y/2
+		let N=2, k1=pi/120, k=k1, op=5, op1=1
+		for i=1 to int(1200*min.data(scale.x, scale.y)/18000)
+			pen op
+			swap op, op1
+			Width 3 {draw angle k, r(k)*n}
+			k+=k1
+		next
+		refresh 5000
+		\\ press space to exit loop
+		if  keypress(32) then exit
+	}
+	pen 14
+	cls 5
+	refresh 50
+}
+Archimedean_spiral

Task/Archimedean-spiral/MATLAB/archimedean-spiral.m

@@ -0,0 +1,5 @@
+a = 1;
+b = 1;
+turns = 2;
+theta = 0:0.1:2*turns*pi;
+polarplot(theta, a + b*theta);

Task/Archimedean-spiral/Maple/archimedean-spiral.maple

@@ -0,0 +1 @@
+plots[polarplot](1+2*theta, theta = 0 .. 6*Pi)

Task/Archimedean-spiral/Mathematica/archimedean-spiral.math

@@ -0,0 +1 @@
+With[{a = 5, b = 4}, PolarPlot[a + b t, {t, 0, 10 Pi}]]

Task/Archimedean-spiral/Nim/archimedean-spiral.nim

@@ -0,0 +1,74 @@
+import math
+
+import gintro/[glib, gobject, gtk, gio, cairo]
+
+const
+
+  Width = 601
+  Height = 601
+
+  Limit = 12 * math.PI
+
+  Origin = (x: float(Width div 2), y: float(Height div 2))
+  B = floor((Width div 2) / Limit)
+
+#---------------------------------------------------------------------------------------------------
+
+proc draw(area: DrawingArea; context: Context) =
+  ## Draw the spiral.
+
+  var theta = 0.0
+  var delta = 0.01
+  var (prevx, prevy) = Origin
+
+  # Clear the region.
+  context.moveTo(0, 0)
+  context.setSource(0.0, 0.0, 0.0)
+  context.paint()
+
+  # Draw the spiral.
+  context.setSource(1.0, 1.0, 0.0)
+  context.moveTo(Origin.x, Origin.y)
+  while theta < Limit:
+    let r = B * theta
+    let x = Origin.x + r * cos(theta)   # X-coordinate on drawing area.
+    let y = Origin.y + r * sin(theta)   # Y-coordinate on drawing area.
+    context.lineTo(x, y)
+    context.stroke()
+    # Set data for next round.
+    context.moveTo(x, y)
+    prevx = x
+    prevy = y
+    theta += delta
+
+#---------------------------------------------------------------------------------------------------
+
+proc onDraw(area: DrawingArea; context: Context; data: pointer): bool =
+  ## Callback to draw/redraw the drawing area contents.
+
+  area.draw(context)
+  result = true
+
+#---------------------------------------------------------------------------------------------------
+
+proc activate(app: Application) =
+  ## Activate the application.
+
+  let window = app.newApplicationWindow()
+  window.setSizeRequest(Width, Height)
+  window.setTitle("Archimedean spiral")
+
+  # Create the drawing area.
+  let area = newDrawingArea()
+  window.add(area)
+
+  # Connect the "draw" event to the callback to draw the spiral.
+  discard area.connect("draw", ondraw, pointer(nil))
+
+  window.showAll()
+
+#———————————————————————————————————————————————————————————————————————————————————————————————————
+
+let app = newApplication(Application, "Rosetta.spiral")
+discard app.connect("activate", activate)
+discard app.run()

Task/Archimedean-spiral/PARI-GP/archimedean-spiral.parigp

@@ -0,0 +1,19 @@
+\\ The Archimedean spiral
+\\ ArchiSpiral() - Where: lps is a number of loops, c is a direction 0/1
+\\ (counter-clockwise/clockwise). 6/6/16 aev
+\\ Note: cartes2() can be found here on
+\\ http://rosettacode.org/wiki/Polyspiral#PARI.2FGP page.
+ArchiSpiral(size,lps,c=0)={
+my(a=.0,ai=.1,r=.0,ri=.1,as=lps*2*Pi,n=as/ai,x,y,vc,vx=List(.0),vy=vx);
+if(c<0||c>1, c=0); if(c, ai*=-1);
+print(" *** The Archimedean spiral: size=",size," loops=",lps," c=",c);
+for(i=1, n, vc=cartes2(r,a); x=vc[1]; y=vc[2];
+    listput(vx,x); listput(vy,y);
+    r+=ri; a+=ai;
+);\\fend i
+plothraw(Vec(vx),Vec(vy));
+}
+{\\ Executing:
+ArchiSpiral(640,5);   \\ArchiSpiral1.png
+ArchiSpiral(640,5,1); \\ArchiSpiral2.png
+}

Task/Archimedean-spiral/Perl/archimedean-spiral.pl

@@ -0,0 +1,13 @@
+use Imager;
+use constant PI => 3.14159265;
+
+my ($w, $h) = (400, 400);
+my $img = Imager->new(xsize => $w, ysize => $h);
+
+for ($theta = 0; $theta < 52*PI; $theta += 0.025) {
+    $x = $w/2 + $theta * cos($theta/PI);
+    $y = $h/2 + $theta * sin($theta/PI);
+    $img->setpixel(x => $x, y => $y, color => '#FF00FF');
+}
+
+$img->write(file => 'Archimedean-spiral.png');

Task/Archimedean-spiral/Phix/archimedean-spiral.phix

@@ -0,0 +1,50 @@
+(phixonline)-->
+ <span style="color: #000080;font-style:italic;">--
+ -- demo\rosetta\Archimedean_spiral.exw
+ -- ===================================
+ --</span>
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
+ <span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
+
+ <span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">canvas</span>
+ <span style="color: #004080;">cdCanvas</span> <span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cdcanvas</span>
+
+ <span style="color: #008080;">function</span> <span style="color: #000000;">redraw_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*ih*/</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGetIntInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"DRAWSIZE"</span><span style="color: #0000FF;">),</span>
+             <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">cy</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">cdCanvasActivate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">deg</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">360</span><span style="color: #0000FF;">*</span><span style="color: #000000;">7</span> <span style="color: #008080;">do</span>
+         <span style="color: #004080;">atom</span> <span style="color: #000000;">rad</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">deg</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">180</span><span style="color: #0000FF;">,</span>
+              <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rad</span><span style="color: #0000FF;">*</span><span style="color: #000000;">b</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">a</span>
+         <span style="color: #004080;">integer</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cx</span> <span style="color: #0000FF;">+</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rad</span><span style="color: #0000FF;">)),</span>
+                 <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cy</span> <span style="color: #0000FF;">+</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rad</span><span style="color: #0000FF;">))</span>
+         <span style="color: #7060A8;">cdCanvasPixel</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">#00FF00</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #7060A8;">cdCanvasFlush</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+
+ <span style="color: #008080;">function</span> <span style="color: #000000;">map_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">ih</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000000;">cdcanvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_IUP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ih</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000000;">cddbuffer</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_DBUFFER</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">cdCanvasSetBackground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_WHITE</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">cdCanvasSetForeground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cddbuffer</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_RED</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+
+ <span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
+     <span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>
+     <span style="color: #000000;">canvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupCanvas</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"RASTERSIZE=500x500"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- initial size</span>
+     <span style="color: #7060A8;">IupSetCallbacks</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"MAP_CB"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"map_cb"</span><span style="color: #0000FF;">),</span>
+                              <span style="color: #008000;">"ACTION"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"redraw_cb"</span><span style="color: #0000FF;">)})</span>
+     <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span><span style="color: #008000;">`TITLE="Archimedean spiral"`</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"RASTERSIZE"</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">NULL</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- release the minimum limitation</span>
+     <span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
+         <span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
+         <span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
+
+ <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
+<!--

Task/Archimedean-spiral/Processing-Python-mode/archimedean-spiral.processing-py

@@ -0,0 +1,18 @@
+theta = 0
+rotation = 0.1
+
+def setup():
+    size(300, 300)
+    background(255)
+
+def draw():
+    global theta
+    translate(width / 2.0, height / 2.0)
+    x = theta * cos(theta / PI)
+    y = theta * sin(theta / PI)
+    point(x, y)
+    theta = theta + rotation
+    # check restart
+    if x > width / 2.0:
+        background(255)
+        theta = 0

Task/Archimedean-spiral/Processing/archimedean-spiral-1.processing

@@ -0,0 +1,20 @@
+float x, y;
+float theta;
+float rotation;
+
+void setup() {
+  size(300, 300);
+  theta = 0;
+  rotation = 0.1;
+  background(255);
+}
+
+void draw() {
+  translate(width/2.0, height/2.0);
+  x = theta*cos(theta/PI);
+  y = theta*sin(theta/PI);
+  point(x, y);
+  theta = theta + rotation;
+  // check restart
+  if (x>width/2.0) frameCount=-1;
+}

Task/Archimedean-spiral/Processing/archimedean-spiral-2.processing

@@ -0,0 +1,18 @@
+float theta;
+float rotation;
+
+void setup() {
+  size(300, 300);
+  theta = 0;
+  rotation = 0.1;
+  background(255);
+}
+
+void draw() {
+  translate(width/2.0, height/2.0);
+  theta += rotation;
+  rotate(theta/PI);
+  point(theta, 0);
+  // check restart
+  if (theta>width/2.0) frameCount=-1;
+}

Task/Archimedean-spiral/Processing/archimedean-spiral-3.processing

@@ -0,0 +1,19 @@
+PVector pv;
+float rotation;
+
+void setup() {
+  size(300, 300);
+  rotation = 0.1;
+  pv = new PVector(rotation, 0);
+  background(255);
+}
+
+void draw() {
+  translate(width/2.0, height/2.0);
+  pv.setMag(pv.mag()+rotation);
+  println(pv.mag());
+  pv.rotate(rotation/PI);
+  point(pv.x, pv.y);
+  // check restart
+  if (pv.mag()>width/2.0) frameCount=-1;
+}

Task/Archimedean-spiral/Processing/archimedean-spiral-4.processing

@@ -0,0 +1,22 @@
+float px, py, x, y;
+float theta;
+float rotation;
+
+void setup() {
+  size(300, 300);
+  px = py = x = y = theta = 0;
+  rotation = 0.1;
+  background(255);
+}
+
+void draw() {
+  translate(width/2.0, height/2.0);
+  x = theta*cos(theta/PI);
+  y = (theta)*sin(theta/PI);
+  line(x, y, px, py);
+  theta = theta + rotation;
+  px = x;
+  py = y;
+  // check restart
+  if (px>width/2.0) frameCount=-1;
+}

Task/Archimedean-spiral/Processing/archimedean-spiral-5.processing

@@ -0,0 +1,26 @@
+float x, y, px, py;
+float theta;
+float rotation;
+
+void setup() {
+  size(300, 300);
+  x = y = px = py = theta = 0;
+  rotation = 0.1;
+  background(255);
+}
+
+void draw() {
+  // find coordinates with rotating reference frame
+  pushMatrix();
+  rotate(theta/PI);
+  x = screenX(theta, 0);
+  y = screenY(theta, 0);
+  popMatrix();
+
+  translate(width/2.0, height/2.0);
+  theta += rotation;
+  line(px, py, x, y);
+  px = x;
+  py = y;
+  if (theta>width/2.0) frameCount=-1; // start over
+}

Task/Archimedean-spiral/PureBasic/archimedean-spiral.basic

@@ -0,0 +1,22 @@
+#MAXLOOP  = 7*360
+#XCENTER  = 640/2
+#YCENTER  = 480/2
+#SCALAR   = 200
+
+If OpenWindow(0, 100, 200, 640, 480, "Archimedean spiral")
+  If CreateImage(0, 640, 480,24,RGB(255,255,255))
+    If StartDrawing(ImageOutput(0))
+      i.f=0.0
+      While i<=#MAXLOOP
+        x.f=#XCENTER+Cos(Radian(i))*#SCALAR*i/#MAXLOOP
+        y.f=#YCENTER+Sin(Radian(i))*#SCALAR*i/#MAXLOOP
+        Plot(x,y,RGB(50,50,50))
+        i+0.05
+      Wend
+      StopDrawing()
+    EndIf
+  EndIf
+  ImageGadget(0, 0, 0, 0, 0, ImageID(0))
+  Repeat : Event = WaitWindowEvent() : Until Event = #PB_Event_CloseWindow
+EndIf
+End

Task/Archimedean-spiral/Python/archimedean-spiral.py

@@ -0,0 +1,11 @@
+from turtle import *
+from math import *
+color("blue")
+down()
+for i in range(200):
+    t = i / 20 * pi
+    x = (1 + 5 * t) * cos(t)
+    y = (1 + 5 * t) * sin(t)
+    goto(x, y)
+up()
+done()

Task/Archimedean-spiral/QBasic/archimedean-spiral.basic

@@ -0,0 +1,12 @@
+SCREEN 12
+WINDOW (-2.67, -2!)-(2.67, 2!)
+PI = 4 * ATN(1)
+H = PI / 40
+A = .2: B = .05
+PSET (A, 0)
+FOR I = 0 TO 400
+    T = I * H
+    X = (A + B * T) * COS(T)
+    Y = (A + B * T) * SIN(T)
+    LINE -(X, Y)
+NEXT

Task/Archimedean-spiral/Quackery/archimedean-spiral.quackery

@@ -0,0 +1,10 @@
+  [ $ "turtleduck.qky" loadfile ] now!
+  turtle
+  20 frames
+  0 n->v
+  900 times
+    [ 2dup walk
+      1 20 v+
+      1 36 turn ]
+  2drop
+  1 frames

Task/Archimedean-spiral/R/archimedean-spiral.r

@@ -0,0 +1,2 @@
+with(list(s=seq(0, 10 * pi, length.out=500)),
+     plot((1 + s) * exp(1i * s), type="l"))

Task/Archimedean-spiral/REXX/archimedean-spiral.rexx

@@ -0,0 +1,42 @@
+/*REXX pgm plots several cycles (half a spiral) of the  Archimedean spiral (ASCII plot).*/
+parse arg cy a b inc chr .                       /*obtain optional arguments from the CL*/
+if  cy=='' |  cy==","   then  cy= 3              /*Not specified?  Then use the default.*/
+if   a=='' |   a==","   then   a= 1              /* "      "         "   "   "     "    */
+if   b=='' |   b==","   then   b= 9              /* "      "         "   "   "     "    */
+if inc=='' | inc==","   then inc= 0.02           /* "      "         "   "   "     "    */
+if chr=='' | chr==","   then chr= '∙'            /* "      "         "   "   "     "    */
+if length(chr)==3  then chr= d2c(chr)            /*plot character coded in     decimal? */
+if length(chr)==2  then chr= x2c(chr)            /*  "      "       "    " hexadecimal? */
+cy= max(2, cy);         LOx= .                   /*set the  LOx  variable (a semaphore).*/
+parse value scrsize()   with   sd  sw  .         /*get the size of the terminal screen. */
+w= sw - 1        ;      mw= w * (cy-1) * 4       /*set useable width; max width for calc*/
+h= sd - 1 + cy*10;      mh= h * (cy-1)           /* "     "    depth;  "  depth  "   "  */
+@.=                                              /*initialize the line based plot field.*/
+         do t=1  to pi()*cy  by inc              /*calc all the coördinates for spiral. */
+         r= a +  b*    t                         /*  "   "   "       R       "    "     */
+         x= w +  r*cos(t);     xx= x % 2         /*  "   "   "       X       "    "     */
+         y= h +  r*sin(t);     yy= y % 2         /*  "   "   "       Y       "    "     */
+         if x<0 | y<0 | x>mw | y>mh then iterate /*Is X or Y  out of bounds?  Then skip.*/
+         if LOx==.  then do;   LOx= xx;      HIx= xx;      LOy= yy;       HIy= yy
+                         end                     /* [↑]  find the minimums and maximums.*/
+         LOx= min(LOx, xx);    HIx= max(HIx, xx) /*determine the   X   MIN  and  MAX.   */
+         LOy= min(LOy, yy);    HIy= max(HIy, yy) /*    "      "    Y    "    "    "     */
+         @.yy= overlay(chr, @.yy, xx+1)          /*assign the plot character (glyph).   */
+         end   /*t*/
+call plot                                        /*invoke plotting subroutine (to term).*/
+exit                                             /*stick a fork in it,  we're all done. */
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+pi:   pi=3.1415926535897932384626433832795028841971693993751058209749445923078; return pi
+plot:      do row=HIy  to LOy  by -1;   say substr(@.row, LOx+1);   end;        return
+r2r:  return arg(1)  //  (pi() * 2)             /*normalize radians ───► a unit circle.*/
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+cos:  procedure; parse arg x;  x= r2r(x);  _= 1;  a= abs(x);    hpi= pi * .5
+      numeric fuzz  min(6, digits() - 3);         if a=pi       then return -1
+      if a=hpi | a=hpi*3  then return  0          if a=pi / 3   then return .5
+      if a=pi * 2 / 3     then return -.5;        q= x*x;       z= 1
+        do k=2  by 2  until p=z;   p= z;   _= -_ *q/(k*k-k);    z= z+_;   end;    return z
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+sin:  procedure; parse arg x;  x= r2r(x);  _= x;  numeric fuzz min(5, max(1, digits() -3))
+      if x=pi * .5         then return 1;         if x==pi*1.5  then return -1
+      if abs(x)=pi | x=0   then return 0;         q= x*x;       z= x
+        do k=2  by 2  until p=z;   p= z;   _= -_ *q/(k*k+k);    z= z+_;   end;    return z

Task/Archimedean-spiral/Racket/archimedean-spiral.rkt

@@ -0,0 +1,22 @@
+#lang racket/base
+(require plot
+         racket/math)
+
+;; x and y bounds set to centralise the circle
+(define (archemedian-spiral-renderer2d a b θ/τ-max
+                                       #:samples (samples (line-samples)))
+  (define (f θ) (+ a (* b θ)))
+  (define max-dim (+ a (* θ/τ-max 2 pi b)))
+  (polar f
+      0 (* θ/τ-max 2 pi)
+      #:x-min (- max-dim)
+      #:x-max max-dim
+      #:y-min (- max-dim)
+      #:y-max  max-dim
+      #:samples samples))
+
+(plot (list (archemedian-spiral-renderer2d 0.0 24  4)))
+
+;; writes to a file so hopefully, I can post it to RC...
+(plot-file (list (archemedian-spiral-renderer2d 0.0 24  4))
+           "images/archemidian-spiral-racket.png")

Task/Archimedean-spiral/Raku/archimedean-spiral.raku

@@ -0,0 +1,11 @@
+use Image::PNG::Portable;
+
+my ($w, $h) = (400, 400);
+
+my $png = Image::PNG::Portable.new: :width($w), :height($h);
+
+(0, .025 ... 52*π).race.map: -> \Θ {
+    $png.set: |((cis( Θ / π ) * Θ).reals »+« ($w/2, $h/2))».Int, 255, 0, 255;
+}
+
+$png.write: 'Archimedean-spiral-perl6.png';

Task/Archimedean-spiral/Ring/archimedean-spiral.ring

@@ -0,0 +1,104 @@
+/*
+ +---------------------------------------------------------------------------------------------------------
+ +     Program Name : Archimedean spiral
+ +---------------------------------------------------------------------------------------------------------
+*/
+Load "guilib.ring"
+
+horzSize  = 400
+vertSize  = 400
+
+counter     = 0  ### cycle thru colors
+colorRed    = new qcolor() { setrgb(255,000,000,255) }
+colorGreen  = new qcolor() { setrgb(000,255,000,255) }
+colorBlue   = new qcolor() { setrgb(000,000,255,255) }
+colorYellow = new qcolor() { setrgb(255,255,000,255) }
+
+penUseR = new qpen() { setcolor(colorRed)    setwidth(1) }
+penUseG = new qpen() { setcolor(colorGreen)  setwidth(1) }
+penUseB = new qpen() { setcolor(colorBlue)   setwidth(1) }
+penUseY = new qpen() { setcolor(colorYellow) setwidth(1) }
+
+        deg2rad    = atan(1) * 4 / 180
+        screensize = 600
+        turns      = 5
+        halfscrn   = screensize / 2
+        sf         = (turns * (screensize - 100)) / halfscrn
+        x = 1
+        y = 1
+        r = 0
+        inc = 0.50   ### control increment speed of r
+
+New qapp
+{
+   win1 =  new qwidget()
+    {
+        setwindowtitle("Draw Spiral")
+        setgeometry(100,100,600,600)
+
+       label1 = new qlabel(win1)
+       {
+           setgeometry(10,10,600,600)
+           settext("")
+       }
+
+
+       Canvas = new qlabel(win1)
+       {
+            MonaLisa = new qPixMap2( 600,600)
+            color    = new qcolor(){ setrgb(255,0,0,255) }
+
+            daVinci  = new qpainter()
+            {
+               begin(MonaLisa)
+               penUse = new qpen() { setcolor(colorRed) setwidth(1) }
+               setpen(penUseR)
+               #endpaint()      ### This will Stop the Painting
+            }
+
+            setpixmap(MonaLisa)
+       }
+
+        oTimer = new qTimer(win1)
+        {
+            setinterval(1)    ### 1 millisecond
+            settimeoutevent("DrawCounter()")
+            start()
+        }
+
+       show()   ### Will show Painting ONLY after exec
+    }
+   exec()
+}
+
+
+###====================================================
+
+Func DrawCounter()
+
+    x  = cos(r * deg2rad) * r / sf
+    y  = sin(r * deg2rad) * r / sf
+    r += inc   ###  0.20 fast, 0.90 slow
+
+        if r >= turns * 360
+            r = inc
+            x = 1
+            y = 1
+            counter++
+            whichColor = counter % 4
+            See  "whichColor: "+ whichColor +nl
+
+                if whichColor = 0 daVinci.setpen(penUseR)  ok
+                if whichColor = 1 daVinci.setpen(penUseG)  ok
+                if whichColor = 2 daVinci.setpen(penUseB)  ok
+                if whichColor = 3 daVinci.setpen(penUseY)  ok
+ ok
+
+    hpoint = halfscrn + x
+    ypoint = halfscrn - y
+
+    daVinci.drawpoint(hpoint, ypoint)
+    Canvas.setpixmap(MonaLisa)          ### Need this setpixmap to display imageLabel
+    win1.show()                         ### Need this show to display imageLabel
+
+return

Task/Archimedean-spiral/Ruby/archimedean-spiral.rb

@@ -0,0 +1,20 @@
+INCR = 0.1
+attr_reader :x, :theta
+
+def setup
+  sketch_title 'Archimedian Spiral'
+  @theta = 0
+  @x = 0
+  background(255)
+  translate(width / 2.0, height / 2.0)
+  begin_shape
+  (0..50*PI).step(INCR) do |theta|
+    @x = theta * cos(theta / PI)
+    curve_vertex(x, theta * sin(theta / PI))
+  end
+  end_shape
+end
+
+def settings
+  size(300, 300)
+end

Task/Archimedean-spiral/Run-BASIC/archimedean-spiral.basic

@@ -0,0 +1,27 @@
+    'archimedean spiral.bas
+    'runs in Run Basic
+    'Run Basic website http://www.runbasic.com
+    'From Rosettacode.org/wiki/ *** Liberty_BASIC
+
+  graphic #g, 300,300 'width and height - the center is 150
+  c = 255  '255 for white '0 for black
+  print "Welcome to the Arch-Spiral Program"
+
+  pi=acs(-1)
+  nLoops = 5
+   #g cls("blue") 'blue background color
+   #g color(c,c,c) 'set line color - see color above
+
+  for t=0 to 2*pi*nLoops step 0.01
+     'c = c - 1  'changes color parameter
+     x=100*t/(2*pi*nLoops)*cos(t)+150  '150x150 is the center
+     y=100*t/(2*pi*nLoops)*sin(t)+150
+     #g color(c,c,c)  'changes color
+     #g set(x,y)
+     'if c <1 then c=255
+  next
+    render #g
+
+  print "Thank you and Goodbye"
+  end
+End

Task/Archimedean-spiral/Rust/archimedean-spiral.rust

@@ -0,0 +1,32 @@
+#[macro_use(px)]
+extern crate bmp;
+
+use bmp::{Image, Pixel};
+use std::f64;
+
+fn main() {
+    let width = 600u32;
+    let half_width = (width / 2) as i32;
+    let mut img = Image::new(width, width);
+    let draw_color = px!(255, 128, 128);
+
+    // Constants defining the spiral size.
+    let a = 1.0_f64;
+    let b = 9.0_f64;
+
+    // max_angle = number of spirals * 2pi.
+    let max_angle = 5.0_f64 * 2.0_f64 * f64::consts::PI;
+
+    let mut theta = 0.0_f64;
+    while theta < max_angle {
+        theta = theta + 0.002_f64;
+
+        let r = a + b * theta;
+        let x = (r * theta.cos()) as i32 + half_width;
+        let y = (r * theta.sin()) as i32 + half_width;
+        img.set_pixel(x as u32, y as u32, draw_color);
+    }
+
+    // Save the image
+    let _ = img.save("archimedean_spiral.bmp").unwrap_or_else(|e| panic!("Failed to save: {}", e));
+}

Task/Archimedean-spiral/SAS/archimedean-spiral.sas

@@ -0,0 +1,14 @@
+data xy;
+h=constant('pi')/40;
+do i=0 to 400;
+    t=i*h;
+    x=(1+t)*cos(t);
+    y=(1+t)*sin(t);
+    output;
+end;
+keep x y;
+run;
+
+proc sgplot;
+series x=x y=y;
+run;

Task/Archimedean-spiral/Scala/archimedean-spiral.scala

@@ -0,0 +1,66 @@
+object ArchimedeanSpiral extends App {
+
+  SwingUtilities.invokeLater(() =>
+    new JFrame("Archimedean Spiral") {
+
+      class ArchimedeanSpiral extends JPanel {
+        setPreferredSize(new Dimension(640, 640))
+        setBackground(Color.white)
+
+        private def drawGrid(g: Graphics2D): Unit = {
+          val (angle, margin, numRings) = (toRadians(45), 10, 8)
+          val w = getWidth
+          val (center, spacing) = (w / 2, (w - 2 * margin) / (numRings * 2))
+
+          g.setColor(new Color(0xEEEEEE))
+          for (i <- 0 until numRings) {
+            val pos = margin + i * spacing
+            val size = w - (2 * margin + i * 2 * spacing)
+            g.drawOval(pos, pos, size, size)
+            val ia = i * angle
+            val x2 = center + (cos(ia) * (w - 2 * margin) / 2).toInt
+            val y2 = center - (sin(ia) * (w - 2 * margin) / 2).toInt
+            g.drawLine(center, center, x2, y2)
+          }
+        }
+
+        private def drawSpiral(g: Graphics2D): Unit = {
+          val (degrees: Double, center) = (toRadians(0.1), getWidth / 2)
+          val (a, b, c, end) = (0, 20, 1, 360 * 2 * 10 * degrees)
+
+          def plot(g: Graphics2D, x: Int, y: Int): Unit = g.drawOval(x, y, 1, 1)
+
+          def iter(theta: Double): Double = {
+            if (theta < end) {
+              val r = a + b * pow(theta, 1 / c)
+              val x = r * cos(theta)
+              val y = r * sin(theta)
+              plot(g, (center + x).toInt, (center - y).toInt)
+              iter(theta + degrees)
+            } else theta
+          }
+
+          g.setStroke(new BasicStroke(2))
+          g.setColor(Color.orange)
+          iter(0)
+        }
+
+        override def paintComponent(gg: Graphics): Unit = {
+          super.paintComponent(gg)
+          val g = gg.asInstanceOf[Graphics2D]
+          g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
+          drawGrid(g)
+          drawSpiral(g)
+        }
+      }
+
+      add(new ArchimedeanSpiral, BorderLayout.CENTER)
+      pack()
+      setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
+      setLocationRelativeTo(null)
+      setResizable(false)
+      setVisible(true)
+    }
+  )
+
+}

Task/Archimedean-spiral/Scheme/archimedean-spiral.ss

@@ -0,0 +1,34 @@
+(import (scheme base)
+        (scheme complex)
+        (rebottled pstk))
+
+; settings for spiral
+(define *resolution* 0.01)
+(define *count* 2000)
+(define *a* 10)
+(define *b* 10)
+(define *center*
+  (let ((size 200)) ; change this to alter size of display
+    (* size 1+i)))
+
+(define (draw-spiral canvas)
+  (define (coords theta)
+    (let ((r (+ *a* (* *b* theta))))
+      (make-polar r theta)))
+  ;
+  (do ((i 0 (+ i 1))) ; loop to draw spiral
+    ((= i *count*) )
+    (let ((c (+ (coords (* i *resolution*)) *center*)))
+      (canvas 'create 'line
+              (real-part c) (imag-part c)
+              (+ 1 (real-part c)) (imag-part c)))))
+
+(let ((tk (tk-start)))
+  (tk/wm 'title tk "Archimedean Spiral")
+  (let ((canvas (tk 'create-widget 'canvas)))
+    (tk/pack canvas)
+    (canvas 'configure
+            'height: (* 2 (real-part *center*))
+            'width: (* 2 (imag-part *center*)))
+    (draw-spiral canvas))
+  (tk-event-loop tk))

Task/Archimedean-spiral/Scilab/archimedean-spiral.scilab

@@ -0,0 +1,18 @@
+a = 3;
+b = 2;
+
+theta = linspace(0,10*%pi,1000);
+r = a + b .* theta;
+
+//1. Plot using polar coordinates
+scf(1);
+polarplot(theta,r);
+
+//2. Plot using rectangular coordinates
+//2.1 Convert coordinates using Euler's formula
+z = r .* exp(%i .* theta);
+x = real(z);
+y = imag(z);
+
+scf(2);
+plot2d(x,y);

Task/Archimedean-spiral/Seed7/archimedean-spiral.seed7

@@ -0,0 +1,27 @@
+$ include "seed7_05.s7i";
+  include "draw.s7i";
+  include "keybd.s7i";
+
+const proc: main is func
+  local
+    const float: xCenter is 117.0;
+    const float: yCenter is 139.0;
+    const float: maxTheta is 10.0 * PI;
+    const float: delta is 0.01;
+    const float: a is 1.0;
+    const float: b is 7.0;
+    var float: theta is 0.0;
+    var float: radius is 0.0;
+  begin
+    screen(256, 256);
+    clear(curr_win, black);
+    KEYBOARD := GRAPH_KEYBOARD;
+    while theta <= maxTheta do
+      radius := a + b * theta;
+      point(round(xCenter + radius * cos(theta)),
+            round(yCenter - radius * sin(theta)), white);
+      theta +:= delta;
+    end while;
+    DRAW_FLUSH;
+    ignore(getc(KEYBOARD));
+  end func;

Task/Archimedean-spiral/Sidef/archimedean-spiral.sidef

@@ -0,0 +1,15 @@
+require('Imager')
+define π = Num.pi
+
+var (w, h) = (400, 400)
+var img = %O<Imager>.new(xsize => w, ysize => h)
+
+for Θ in (0 .. 52*π -> by(0.025)) {
+    img.setpixel(
+        x => floor(cos(Θ / π)*Θ + w/2),
+        y => floor(sin(Θ / π)*Θ + h/2),
+        color => [255, 0, 0]
+    )
+}
+
+img.write(file => 'Archimedean_spiral.png')

Task/Archimedean-spiral/Sinclair-ZX81-BASIC/archimedean-spiral.basic

@@ -0,0 +1,6 @@
+10 LET A=1.5
+20 LET B=0.7
+30 FOR T=0 TO 7*PI STEP 0.05
+40 LET R=A+B*T
+50 PLOT R*COS T+32,R*SIN T+22
+60 NEXT T

Task/Archimedean-spiral/Stata/archimedean-spiral.stata

@@ -0,0 +1,7 @@
+clear all
+scalar h=_pi/40
+set obs 400
+gen t=_n*h
+gen x=(1+t)*cos(t)
+gen y=(1+t)*sin(t)
+line y x

Task/Archimedean-spiral/Tcl/archimedean-spiral.tcl

@@ -0,0 +1,65 @@
+package require Tk
+
+# create widgets
+canvas .canvas
+frame .controls
+
+ttk::label .legend -text " r = a + b θ "
+ttk::label .label_a -text "a ="
+ttk::entry .entry_a -textvariable a
+ttk::label .label_b -text "a ="
+ttk::entry .entry_b -textvariable b
+button .button -text "Redraw" -command draw
+
+# layout
+grid .canvas .controls -sticky nsew
+grid .legend - -sticky ns -in .controls
+grid .label_a .entry_a -sticky nsew -in .controls
+grid .label_b .entry_b -sticky nsew -in .controls
+grid .button - -sticky ns -in .controls
+
+# make the canvas resize with the window
+grid columnconfigure . 0 -weight 1
+grid rowconfigure . 0 -weight 1
+
+# spiral parameters:
+set a .2
+set b .05
+
+proc draw {} {
+    variable a
+    variable b
+
+    # make sure inputs are valid:
+    if {![string is double $a] || ![string is double $b]} return
+    if {$a == 0 || $b == 0} return
+
+    set w [winfo width .canvas]
+    set h [winfo height .canvas]
+    set r 0
+    set pi [expr {4*atan(1)}]
+    set step [expr {$pi / $w}]
+    for {set t 0} {$r < 2} {set t [expr {$t + $step}]} {
+        set r [expr {$a + $b * $t}]
+        set y [expr {sin($t) * $r}]
+        set x [expr {cos($t) * $r}]
+
+        # transform to canvas co-ordinates
+        set y [expr {entier((1+$y)*$h/2)}]
+        set x [expr {entier((1+$x)*$w/2)}]
+        lappend coords $x $y
+    }
+    .canvas delete all
+    set id [.canvas create line $coords -fill red]
+}
+
+# draw whenever parameters are changed
+# ";#" so extra trace arguments are ignored
+trace add variable a write {draw;#}
+trace add variable b write {draw;#}
+
+wm protocol . WM_DELETE_WINDOW exit ;# exit when window is closed
+
+update  ;# lay out widgets before trying to draw
+draw
+vwait forever ;# go into event loop until window is closed

Task/Archimedean-spiral/VBA/archimedean-spiral.vba

@@ -0,0 +1,23 @@
+Private Sub plot_coordinate_pairs(x As Variant, y As Variant)
+    Dim chrt As Chart
+    Set chrt = ActiveSheet.Shapes.AddChart.Chart
+    With chrt
+        .ChartType = xlXYScatter
+        .HasLegend = False
+        .SeriesCollection.NewSeries
+        .SeriesCollection.Item(1).XValues = x
+        .SeriesCollection.Item(1).Values = y
+    End With
+End Sub
+Public Sub main()
+    Dim x(1000) As Single, y(1000) As Single
+    a = 1
+    b = 9
+    For i = 0 To 1000
+        theta = i * WorksheetFunction.Pi() / 60
+        r = a + b * theta
+        x(i) = r * Cos(theta)
+        y(i) = r * Sin(theta)
+    Next i
+    plot_coordinate_pairs x, y
+End Sub

Task/Archimedean-spiral/Wren/archimedean-spiral.wren

@@ -0,0 +1,28 @@
+import "graphics" for Canvas, Color
+import "dome" for Window
+
+class Game {
+    static init() {
+        Window.title = "Archimedean Spiral"
+        __width = 400
+        __height = 400
+        Canvas.resize(__width, __height)
+        Window.resize(__width, __height)
+        var col = Color.red
+        spiral(col)
+    }
+
+    static spiral(col) {
+        var theta = 0
+        while (theta < 52 * Num.pi) {
+            var x = ((theta/Num.pi).cos * theta + __width/2).truncate
+            var y = ((theta/Num.pi).sin * theta + __height/2).truncate
+            Canvas.pset(x, y, col)
+            theta = theta + 0.025
+        }
+    }
+
+    static update() {}
+
+    static draw(dt) {}
+}

Task/Archimedean-spiral/XPL0/archimedean-spiral.xpl0

@@ -0,0 +1,10 @@
+real A, B, R, T, X, Y;
+[SetVid($12);           \set 640x480 graphics
+A:= 0.0;  B:= 3.0;  T:= 0.0;
+Move(320, 240);         \start at center of screen
+repeat  R:= A + B*T;
+        X:= R*Cos(T);  Y:= R*Sin(T);
+        Line(fix(X)+320, 240-fix(Y), 4\red\);
+        T:= T + 0.03;   \increase angle (Theta)
+until   T >= 314.159;   \50 revs
+]

Task/Archimedean-spiral/Yabasic/archimedean-spiral.basic

@@ -0,0 +1,7 @@
+5 OPEN WINDOW 320, 200 : WINDOW ORIGIN "CC"
+10 LET A=1.5
+20 LET B=0.7
+30 FOR T=0 TO 30*PI STEP 0.05
+40 LET R=A+B*T
+50 LINE TO R*COS(T),R*SIN(T)
+60 NEXT T

Task/Archimedean-spiral/Zkl/archimedean-spiral.zkl

@@ -0,0 +1,12 @@
+fcn archimedeanSpiral(a,b,circles){
+   w,h:=640,640; centerX,centerY:=w/2,h/2;
+   bitmap:=PPM(w+1,h+1,0xFF|FF|FF);  // White background
+
+   foreach deg in ([0.0 .. 360*circles]){
+      rad:=deg.toRad();
+      r:=rad*b + a;
+      x,y:=r.toRectangular(rad);
+      bitmap[centerX + x, centerY + y] = 0x00|FF|00;  // Green dot
+   }
+   bitmap.writeJPGFile("archimedeanSpiral.jpg");
+}(0,5,7);