September 2017 Update

Task/Sierpinski-carpet/AppleScript/sierpinski-carpet.applescript

@@ -1,14 +1,15 @@
--- CARPET MODEL
+-- CARPET MODEL --------------------------------------------------------------
 
 -- sierpinskiCarpet :: Int -> [[Bool]]
 on sierpinskiCarpet(n)
 
     -- rowStates :: Int -> [Bool]
     script rowStates
-        on lambda(x, _, xs)
+        on |λ|(x, _, xs)
 
             -- cellState :: Int -> Bool
             script cellState
+
                 -- inCarpet :: Int -> Int -> Bool
                 on inCarpet(x, y)
                     if (x = 0 or y = 0) then
@@ -20,63 +21,74 @@ on sierpinskiCarpet(n)
                     end if
                 end inCarpet
 
-                on lambda(y)
+                on |λ|(y)
                     inCarpet(x, y)
-                end lambda
+                end |λ|
             end script
 
             map(cellState, xs)
-        end lambda
+        end |λ|
     end script
 
-    map(rowStates, range(0, (3 ^ n) - 1))
+    map(rowStates, enumFromTo(0, (3 ^ n) - 1))
 end sierpinskiCarpet
 
 
--- TEST
-
+-- TEST ----------------------------------------------------------------------
 on run
     -- Carpets of orders 1, 2, 3
 
     set strCarpets to ¬
         intercalate(linefeed & linefeed, ¬
-            map(showCarpet, range(1, 3)))
+            map(showCarpet, enumFromTo(1, 3)))
 
     set the clipboard to strCarpets
 
     return strCarpets
 end run
 
-
--- CARPET DISPLAY
+-- CARPET DISPLAY ------------------------------------------------------------
 
 -- showCarpet :: Int -> String
 on showCarpet(n)
+
     -- showRow :: [Bool] -> String
     script showRow
         -- showBool :: Bool -> String
         script showBool
-            on lambda(bool)
+            on |λ|(bool)
                 if bool then
                     character id 9608
                 else
                     " "
                 end if
-            end lambda
+            end |λ|
         end script
 
-        on lambda(xs)
+        on |λ|(xs)
             intercalate("", map(my showBool, xs))
-        end lambda
+        end |λ|
     end script
 
     intercalate(linefeed, map(showRow, sierpinskiCarpet(n)))
 end showCarpet
 
 
----------------------------------------------------------------------------
+-- GENERIC FUNCTIONS ---------------------------------------------------------
 
--- GENERIC LIBRARY FUNCTIONS
+-- enumFromTo :: Int -> Int -> [Int]
+on enumFromTo(m, n)
+    if m > n then
+        set d to -1
+    else
+        set d to 1
+    end if
+    set lst to {}
+    repeat with i from m to n by d
+        set end of lst to i
+    end repeat
+    return lst
+end enumFromTo
 
 -- map :: (a -> b) -> [a] -> [b]
 on map(f, xs)
@@ -84,7 +96,7 @@ on map(f, xs)
         set lng to length of xs
         set lst to {}
         repeat with i from 1 to lng
-            set end of lst to lambda(item i of xs, i, xs)
+            set end of lst to |λ|(item i of xs, i, xs)
         end repeat
         return lst
     end tell
@@ -98,20 +110,6 @@ on intercalate(strText, lstText)
     return strJoined
 end intercalate
 
--- range :: Int -> Int -> [Int]
-on range(m, n)
-    if n < m then
-        set d to -1
-    else
-        set d to 1
-    end if
-    set lst to {}
-    repeat with i from m to n by d
-        set end of lst to i
-    end repeat
-    return lst
-end range
-
 -- Lift 2nd class handler function into 1st class script wrapper
 -- mReturn :: Handler -> Script
 on mReturn(f)
@@ -119,7 +117,7 @@ on mReturn(f)
         f
     else
         script
-            property lambda : f
+            property |λ| : f
         end script
     end if
 end mReturn

Task/Sierpinski-carpet/Gnuplot/sierpinski-carpet-1.gnuplot

@@ -0,0 +1,11 @@
+## SCff.gp 1/14/17 aev
+## Plotting Sierpinski carpet fractal.
+## dat-files are PARI/GP generated output files:
+## http://rosettacode.org/wiki/Sierpinski_carpet#PARI.2FGP
+#cd 'C:\gnupData'
+
+##SC5
+clr = '"green"'
+filename = "SC5gp1"
+ttl = "Sierpinski carpet fractal, v.#1"
+load "plotff.gp"

Task/Sierpinski-carpet/Gnuplot/sierpinski-carpet-2.gnuplot

@@ -0,0 +1,20 @@
+## plotscf.gp 12/7/16 aev
+## Plotting a Sierpinski carpet fractal to the png-file.
+## Note: assign variables: ord (order), clr (color), filename and ttl (before using load command).
+## ord (order)  # a.k.a. level - defines size of fractal (also number of dots).
+reset
+set terminal png font arial 12 size 640,640
+ofn=filename.".png"
+set output ofn
+unset border; unset xtics; unset ytics; unset key;
+set title ttl font "Arial:Bold,12"
+set xrange [0:1]; set yrange [0:1];
+sc(n, x, y, d) = n >= ord ?  \
+  sprintf('set object rect from %f,%f to %f,%f fc rgb @clr fs solid;', x, y, x+d, y+d) : \
+  sc(n+1, x, y, d/3) . sc(n+1, x+d/3, y, d/3) . \
+  sc(n+1, x+2*d/3, y, d/3) . sc(n+1, x, y+d/3, d/3) . \
+  sc(n+1, x+2*d/3, y+d/3, d/3) . sc(n+1, x, y+2*d/3, d/3) . \
+  sc(n+1, x+d/3, y+2*d/3, d/3) . sc(n+1, x+2*d/3, y+2*d /3, d/3);
+eval(sc(0, 0.0, 0.0, 1.0))
+plot -100
+set output

Task/Sierpinski-carpet/Gnuplot/sierpinski-carpet-3.gnuplot

@@ -0,0 +1,27 @@
+## plotscf1.gp 12/7/16 aev
+## Plotting a Sierpinski carpet fractal to the png-file.
+## Note: assign variables: ord (order, just for title), clr (color), filename and ttl (before using load command).
+## In this version order is always 5.
+reset
+set terminal png font arial 12 size 640,640
+ofn=filename.".png"
+set output ofn
+unset border; unset xtics; unset ytics; unset key;
+set title ttl font "Arial:Bold,12"
+o=3
+sqr(x,y) = abs(x + y) + abs(x - y) - o
+f(x) = o*abs(x) - o
+c0(x,y) = abs(x + y) + abs(x - y) - 1
+c1(x,y) = c0(o*x,f(y)) * c0(f(x),o*y) * c0(f(x),f(y))
+c2(x,y) = c1(o*x,f(y)) * c1(f(x),o*y) * c1(f(x),f(y))
+c3(x,y) = c2(o*x,f(y)) * c2(f(x),o*y) * c2(f(x),f(y))
+c4(x,y) = c3(o*x,f(y)) * c3(f(x),o*y) * c3(f(x),f(y))
+sc(x,y) = sqr(x,y)>0 || c0(x,y)*c1(x,y)*c2(x,y)*c3(x,y)*c4(x,y)<0 ? 0:1
+set xrange [-1.5:1.5]; set yrange [-1.5:1.5];
+set pm3d map;
+set palette model RGB defined (0 "white", 1 @clr);
+set size ratio -1
+smp=640; set samples smp; set isosamples smp;
+unset colorbox
+splot sc(x,y)
+set output

Task/Sierpinski-carpet/Gnuplot/sierpinski-carpet-4.gnuplot

@@ -0,0 +1,20 @@
+## pSCF.gp 12/7/16 aev
+## Plotting Sierpinski carpet fractals.
+## Note: assign variables: ord (order), clr (color), filename and ttl (before using load command).
+## ord (order)  # a.k.a. level - defines size of fractal (also number of dots).
+#cd 'C:\gnupData'
+
+##SCF21
+ord=3; clr = '"red"';
+filename = "SCF21gp"; ttl = "Sierpinski carpet fractal #21, ord ".ord;
+load "plotscf.gp"
+
+##SCF22
+ord=5; clr = '"brown"';
+filename = "SCF22gp"; ttl = "Sierpinski carpet fractal #22, ord ".ord;
+load "plotscf.gp"
+
+##SCF31
+ord=5; clr = '"navy"';
+filename = "SCF31gp"; ttl = "Sierpinski carpet fractal #31, ord ".ord;
+load "plotscf1.gp"

Task/Sierpinski-carpet/Kotlin/sierpinski-carpet-1.kotlin

@@ -0,0 +1,22 @@
+// version 1.1.2
+
+fun inCarpet(x: Int, y: Int): Boolean {
+    var xx = x
+    var yy = y
+    while (xx != 0 && yy != 0) {
+        if (xx % 3 == 1 && yy % 3 == 1) return false
+        xx /= 3
+        yy /= 3
+    }
+    return true
+}
+
+fun carpet(n: Int) {
+    val power = Math.pow(3.0, n.toDouble()).toInt()
+    for(i in 0 until power) {
+        for(j in 0 until power) print(if (inCarpet(i, j)) "*" else " ")
+        println()
+    }
+}
+
+fun main(args: Array<String>) = carpet(3)

Task/Sierpinski-carpet/Kotlin/sierpinski-carpet-2.kotlin

@@ -0,0 +1,57 @@
+// version 1.1.2
+
+import java.awt.*
+import javax.swing.*
+
+public class SierpinskiCarpet : JPanel() {
+    private val dim = 513
+    private val margin = 20
+    private var limit = dim
+
+    init {
+        val size = dim + 2 * margin
+        preferredSize = Dimension(size, size)
+        background = Color.blue
+        foreground = Color.yellow
+        Timer(2000) {
+            limit /= 3
+            if (limit <= 3) limit = dim
+            repaint()
+        }.start()
+    }
+
+    private fun drawCarpet(g: Graphics2D, x: Int, y: Int, s: Int) {
+        var size = s
+        if (s < limit) return
+        size /= 3
+        for (i in 0 until 9) {
+            if (i == 4) {
+                g.fillRect(x + size, y + size, size, size)
+            }
+            else {
+                drawCarpet(g, x + (i % 3) * size, y + (i / 3) * size, size)
+            }
+        }
+    }
+
+    override fun paintComponent(gg: Graphics) {
+        super.paintComponent(gg)
+        val g = gg as Graphics2D
+        g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
+        g.translate(margin, margin)
+        drawCarpet(g, 0, 0, dim)
+    }
+}
+
+fun main(args: Array<String>) {
+    SwingUtilities.invokeLater {
+        val f = JFrame()
+        f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
+        f.title = "Sierpinski Carpet"
+        f.isResizable = false
+        f.add(SierpinskiCarpet(), BorderLayout.CENTER)
+        f.pack()
+        f.setLocationRelativeTo(null)
+        f.isVisible = true
+    }
+}

Task/Sierpinski-carpet/MATLAB/sierpinski-carpet.m

@@ -0,0 +1,6 @@
+n = 3;
+c = string('#');
+for k = 1 : n
+  c = [c + c + c, c + c.replace('#', ' ') + c, c + c + c];
+end
+disp(c.join(char(10)))

Task/Sierpinski-carpet/PARI-GP/sierpinski-carpet-1.pari

@@ -0,0 +1,31 @@
+\\ Improved simple plotting using matrix mat (color and scaling added).
+\\ Matrix should be filled with 0/1. 7/6/16 aev
+iPlotmat(mat,clr)={
+  my(xz=#mat[1,],yz=#mat[,1],vx=List(),vy=vx,xmin,xmax,ymin,ymax,c=0.625);
+  for(i=1,yz, for(j=1,xz, if(mat[i,j]==0, next, listput(vx,i); listput(vy,j))));
+  xmin=listmin(vx); xmax=listmax(vx); ymin=listmin(vy); ymax=listmax(vy);
+  plotinit(0); plotcolor(0,clr);
+  plotscale(0, xmin,xmax,ymin,ymax);
+  plotpoints(0, Vec(vx)*c,Vec(vy));
+  plotdraw([0,xmin,ymin]);
+  print(" *** matrix: ",xz,"x",yz,", ",#vy," DOTS");
+}
+\\ iPlotV2(): Improved plotting from a file written by the wrtmat(). (color added)
+\\ Saving possibly huge generation time if re-plotting needed.
+iPlotV2(fn, clr)={
+  my(F,nf,vx=List(),vy=vx,Vr,xmin,xmax,ymin,ymax,c=0.625);
+  F=readstr(fn); nf=#F;
+  print(" *** Plotting from: ", fn, " - ", nf, " DOTS");
+  for(i=1,nf, Vr=stok(F[i]," "); listput(vx,eval(Vr[1])); listput(vy,eval(Vr[2])));
+  xmin=listmin(vx); xmax=listmax(vx); ymin=listmin(vy); ymax=listmax(vy);
+  plotinit(0); plotcolor(0,clr);
+  plotscale(0, xmin,xmax,ymin,ymax);
+  plotpoints(0, Vec(vx)*c,Vec(vy));
+  plotdraw([0,xmin,ymin]);
+}
+\\ Are x,y inside Sierpinski carpet? (1-yes, 0-no) 6/10/16 aev
+inSC(x,y)={
+  while(1, if(!x||!y,return(1));
+    if(x%3==1&&y%3==1, return(0));
+    x\=3; y\=3;);\\wend
+}

Task/Sierpinski-carpet/PARI-GP/sierpinski-carpet-2.pari

@@ -0,0 +1,19 @@
+\\ Sierpinski carpet fractal (n - order, clr - color, dfn - data file name)
+\\ 6/10/16, upgraded 11/29/16 aev
+pSierpinskiC(n, clr=5, dfn="")={
+  my(n3=3^n-1,M,pf=n>=5);
+  if(pf, M=matrix(n3+1,n3+1));
+  for(i=0,n3, for(j=0,n3,
+    if(inSC(i,j),
+      if(pf, M[i+1,j+1]=1, print1("* ")), if(!pf, print1("  ")));
+    ); if(!pf, print(""));
+  );\\fend i
+  if(!pf, return(0));
+  if(dfn=="", c, wrtmat(M, dfn));
+}
+{\\ Test:
+pSierpinskiC(3);
+pSierpinskiC(5,14); \\ SierpC5.png, color - navy
+}
+{pSierpinskiC(5,,"c:\\pariData\\SC5.dat");
+iPlotV2("c:\\pariData\\SC5.dat",10);} \\ SierpC5a.png, color - dark-green

Task/Sierpinski-carpet/PARI-GP/sierpinski-carpet.pari

@@ -1,23 +0,0 @@
-\\ Sierpinski carpet fractal
-\\ Note: plotmat() can be found here on
-\\ http://rosettacode.org/wiki/Brownian_tree#PARI.2FGP page.
-\\ 6/10/16 aev
-inSC(x,y)={
-while(1, if(!x||!y,return(1));
-         if(x%3==1&&y%3==1, return(0));
-         x\=3; y\=3;);\\wend
-}
-pSierpinskiC(n,pflg=0)={
-my(n3=3^n-1,M);
-if(pflg<0||pflg>1, pflg=0); if(pflg, M=matrix(n3+1,n3+1));
-for(i=0,n3, for(j=0,n3,
-    if(inSC(i,j),
-    if(pflg, M[i+1,j+1]=1, print1("* ")), if(!pflg, print1("  ")));
-   ); if(!pflg, print(""));
-   );\\fend i
-if(pflg, plotmat(M));
-}
-{\\ Test:
-pSierpinskiC(3);
-pSierpinskiC(5,1); \\ SierpC5.png
-}

Task/Sierpinski-carpet/R/sierpinski-carpet-1.r

@@ -0,0 +1,25 @@
+## Are x,y inside Sierpinski carpet (and where)? (1-yes, 0-no)
+inSC <- function(x, y) {
+  while(TRUE) {
+    if(!x||!y) {return(1)}
+    if(x%%3==1&&y%%3==1) {return(0)}
+    x=x%/%3; y=y%/%3;
+  } return(0);
+}
+## Plotting Sierpinski carpet fractal. aev 4/1/17
+## ord - order, fn - file name, ttl - plot title, clr - color
+pSierpinskiC <- function(ord, fn="", ttl="", clr="navy") {
+  m=640; abbr="SCR"; dftt="Sierpinski carpet fractal";
+  n=3^ord-1; M <- matrix(c(0), ncol=n, nrow=n, byrow=TRUE);
+  cat(" *** START", abbr, date(), "\n");
+  if(fn=="") {pf=paste0(abbr,"o", ord)} else {pf=paste0(fn, ".png")};
+  if(ttl!="") {dftt=ttl}; ttl=paste0(dftt,", order ", ord);
+  cat(" *** Plot file:", pf,".png", "title:", ttl, "\n");
+  for(i in 0:n) {
+    for(j in 0:n) {if(inSC(i,j)) {M[i,j]=1}
+  }}
+  plotmat(M, pf, clr, ttl);
+  cat(" *** END", abbr, date(), "\n");
+}
+## Executing:
+pSierpinskiC(5);

Task/Sierpinski-carpet/R/sierpinski-carpet-2.r

@@ -0,0 +1,17 @@
+## Plotting Sierpinski carpet fractal v.2. aev 4/2/17
+## ord - order, fn - file name, ttl - plot title, clr - color
+pSierpinskiC2 <- function(ord, fn="", ttl="", clr="brown") {
+  m=640; abbr="SCR2"; dftt="Sierpinski carpet fractal v.2";
+  cat(" *** START", abbr, date(), "\n");
+  if(fn=="") {pf=paste0(abbr,"o", ord)} else {pf=paste0(fn, ".png")};
+  if(ttl!="") {dftt=ttl}; ttl=paste0(dftt,", order ", ord);
+  cat(" *** Plot file:", pf,".png", "title:", ttl, "\n");
+  S = matrix(1,1,1);
+  for (i in 1:ord) {
+    Q = cbind(S,S,S); R = cbind(S,0*S,S); S = rbind(Q,R,Q);
+  }
+  plotmat(S, pf, clr, ttl);
+  cat(" *** END", abbr, date(), "\n");
+}
+## Executing:
+pSierpinskiC2(5);

Task/Sierpinski-carpet/REXX/sierpinski-carpet.rexx

@@ -5,21 +5,20 @@ if char==''          then char="*"               /*use the default of an asteris
 if length(char)==2   then char=x2c(char)         /*it was specified in hexadecimal char.*/
 if length(char)==3   then char=d2c(char)         /* "  "      "      " decimal character*/
 width=linesize()                                 /*the width of the terminal screen.    */
-if N>18  then numeric digits 1000                /*just in case the user went  ka─razy. */
+if N>18  then numeric digits 100                 /*just in case the user went  ka─razy. */
 nnn=3**N                                         /* [↓]  NNN  is the  cube of  N.       */
 
   do   j=0  for nnn;   z=                        /*Z:    is the line to be displayed.   */
-    do k=0  for nnn;   jj=j;  kk=k;  xChar=char
-
+    do k=0  for nnn;   jj=j;   kk=k;   x=char
       do  while  jj\==0  &  kk\==0               /*one symbol for a  not (¬)  is a   \  */
-      if jj//3==1 & kk//3==1  then do            /*in REXX:    //  ≡  division remainder*/
-                                   xChar=' '     /*use a blank for this display line.   */
-                                   leave         /*LEAVE   terminates this   DO  WHILE. */
-                                   end
+      if jj//3==1  then if kk//3==1  then do     /*in REXX:    //  ≡  division remainder*/
+                                          x=' '  /*use a blank for this display line.   */
+                                          leave  /*LEAVE   terminates this   DO  WHILE. */
+                                          end
       jj=jj%3;      kk=kk%3                      /*in REXX:     %  ≡  integer division. */
       end   /*while*/
 
-    z=z || xChar                                 /*xChar  is either  black  or  white.  */
+    z=z || x                                     /*xChar  is either  black  or  white.  */
     end     /*k*/                                /* [↑]    "    "      "     "  blank.  */
 
   if length(z)<width  then say z                 /*display the line if it fits on screen*/

Task/Sierpinski-carpet/Run-BASIC/sierpinski-carpet.run

@@ -1,16 +0,0 @@
-dim c$(3)
-c$(1) = "# # #"
-c$(2) = "#   #"
-c$(3) = "# # #"
-
-for m = 1 to 6
- print "------ Order ";m;" ------------"
- for k = 1 to m
-  for i = 1 to 3
-   for j = 1 to m
-    print c$(i);
-   next j
-  print
-  next i
- next k
-next m

Task/Sierpinski-carpet/Sinclair-ZX81-BASIC/sierpinski-carpet.sinclair

@@ -0,0 +1,18 @@
+ 10 LET O=3
+ 20 LET S=3**O
+ 30 FOR I=0 TO S-1
+ 40 FOR J=0 TO S-1
+ 50 LET X=J
+ 60 LET Y=I
+ 70 GOSUB 120
+ 80 IF C THEN PLOT J,I
+ 90 NEXT J
+100 NEXT I
+110 GOTO 190
+120 LET C=0
+130 IF X-INT (X/3)*3=1 AND Y-INT (Y/3)*3=1 THEN RETURN
+140 LET X=INT (X/3)
+150 LET Y=INT (Y/3)
+160 IF X>0 OR Y>0 THEN GOTO 130
+170 LET C=1
+180 RETURN

Task/Sierpinski-carpet/Zkl/sierpinski-carpet-1.zkl

@@ -0,0 +1,8 @@
+fcn drawPat(x0,y0,s,img){  // Draw 3x3 pattern with hole in middle
+   foreach y,x in (3,3){
+      if(x.isEven or y.isEven){	// don't draw middle pattern
+	 if(s>1) self.fcn(x*s + x0, y*s + y0, s/3, img);	// recurse
+	 else img[x + x0, y + y0]=0xff0000; // red
+      }
+   }
+}

Task/Sierpinski-carpet/Zkl/sierpinski-carpet-2.zkl

@@ -0,0 +1,3 @@
+img:=PPM(800,800);
+drawPat(0,0,(3).pow(5),img);
+img.write(File("foo.ppm","wb"));