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@ -3,3 +3,4 @@ Produce a graphical representation of a [[wp:Sierpinski triangle|Sierpinski tria
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An example of Sierpinski's triangle (order = 8) looks like this: <br/><br/>
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[[File:Sierpinski_Triangle_Unicon.PNG]]
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@ -0,0 +1,130 @@
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use16
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org 0x7c00
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start:
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;graphics mode 11h
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mov ax, 0x0011
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int 0x10
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;reserve 8 bytes on the stack
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;word [bp+6] is the state of the xorshift16 prng
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;word [bp+2] is the current x position
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;word [bp+4] is the current y position
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sub sp, 8
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mov bp, sp
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mov cx, [numbers]
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outerloop:
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push cx
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mov word [bp], cx
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dec word [bp]
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shl word [bp], 2
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;seed the random number generator with 1
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mov word [bp+6], 1
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;initialize the current position
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mov word [bp+2], 320
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mov word [bp+4], 240
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;run the main loop 65535 times
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mov cx, 0xffff
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mainloop0:
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mov di, 3
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call rand
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mov di, ax
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add di, word [bp]
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call ave
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mov di, [bp + 2]
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mov si, [bp + 4]
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call pset
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loop mainloop0
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pop cx
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loop outerloop
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busyloop:
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jmp $
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ave:
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push ax
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push bx
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push cx
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push dx
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shl di, 2
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mov ax, [corners + di]
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mov bx, [corners + di + 2]
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mov cx, [bp + 2]
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mov dx, [bp + 4]
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add cx, ax
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add dx, bx
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shr cx, 1
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shr dx, 1
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mov [bp + 2], cx
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mov [bp + 4], dx
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pop dx
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pop cx
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pop bx
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pop ax
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ret
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rand:
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push bx
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push cx
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push dx
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mov ax, [bp+6]
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mov bx, ax
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shl bx, 7
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xor ax, bx
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mov bx, ax
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shr bx, 9
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xor ax, bx
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mov bx, ax
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shl bx, 8
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xor ax, bx
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mov [bp+6], ax
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xor dx, dx
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div di
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mov ax, dx
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pop dx
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pop cx
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pop bx
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ret
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pset:
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push ds
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mov bx, 0xa000
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mov ds, bx
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push ax
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push bx
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push cx
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push dx
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xor dx, dx
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mov cx, di
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shr di, 3
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and cx, 0x07
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mov bl, 0x80
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shr bl, cl
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mov cl, bl
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mov ax, 80
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mul si
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add ax, di
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mov bx, ax
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mov al, [bx]
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or al, cl
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mov [bx], al
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pop dx
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pop cx
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pop bx
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pop ax
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pop ds
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ret
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;this calculates the number of triangles.
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numbers:
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dw ((filler-corners) / 16)
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;--------------------------------------------------------------
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;the format for the corners is x1, y1, x2, y2, x3, y3, 4 bytes filler
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;you can theorically have up to 65536 triangles.
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;It'll draw them one at a time.
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;But, you have only 512 bytes. That not enough for 65536 triangles. :(
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corners:
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dw 320, 0, 0, 480, 640, 480, 0xffff, 0xffff
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;just put more triangles here.
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filler:
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times 510-($-$$) db 0
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magic:
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dw 0xaa55
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@ -0,0 +1,37 @@
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pragma Ada_2022;
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with Ada.Command_Line; use Ada.Command_Line;
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with Ada.Text_IO; use Ada.Text_IO;
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with Easy_Graphics; use Easy_Graphics;
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procedure Sierpinski_Triangle_Graphical is
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Max_Order : constant Integer := 8;
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subtype Valid_Order is Integer range 0 .. Max_Order;
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Length : constant Positive := 2 ** (Max_Order + 1);
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Order : Valid_Order;
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Img : Easy_Image := New_Image ((1, 1), (550, 550), BLACK);
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Turtle : Turtle_Rec := New_Turtle (Img'Unrestricted_Access);
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procedure Sier_Triangle (Order : Valid_Order; Length : Positive) is
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begin
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if Order > 0 then
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for I in 1 .. 3 loop
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Sier_Triangle (Order - 1, Length / 2);
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Turtle.Forward (Length);
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Turtle.Right (120);
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end loop;
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end if;
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end Triangle;
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begin
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if Argument_Count /= 1 then
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Put_Line ("Usage: sierpinski_triangle_graphical <order>");
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Put_Line ("Where: <order> is 0 .. 8");
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return;
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end if;
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Order := Natural'Value (Argument (1));
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Turtle.Pen_Color (MAGENTA);
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Turtle.Go_To ((25, 25));
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Turtle.Pen_Down;
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Sier_Triangle (Order, Length);
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Write_GIF (Img, "sierpinski_triangle.gif");
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end Sierpinski_Triangle_Graphical;
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@ -0,0 +1,20 @@
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require "bitmap"
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local bmp
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local function sierpinski_triangle(level, x, y, size)
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if level > 0 then
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local col = color.black
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bmp:triangle(x, y, x + size, y, x, y + size, col, 1)
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local size2 = size // 2
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sierpinski_triangle(level - 1, x, y, size2)
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sierpinski_triangle(level - 1, x + size2, y, size2)
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sierpinski_triangle(level - 1, x, y + size2, size2)
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end
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end
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local size <const> = 800
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local level = 8
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bmp = bitmap.of(size, size, color.white, "Sierpinski Triangle")
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sierpinski_triangle(level, 20, 20, size - 40)
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bmp:view()
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@ -0,0 +1,36 @@
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(import srfi/231)
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(define (bit-Kronecker-product A B)
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;; Assumes that A and B are specialized arrays with u1-storage-class
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;; i.e., that each array element is zero or one.
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(array-block! (array-map (lambda (a) (array-map (lambda (b) (* a b)) B)) A)
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u1-storage-class))
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(define (bit-Kronecker-power A n)
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;; Assumes n >= 1
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(do ((i 1 (+ i 1))
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(result A (bit-Kronecker-product A result)))
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((= i n) result)))
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(define (write-pbm array file)
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(with-output-to-file file
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(lambda ()
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(let* ((domain (array-domain array))
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(rows (interval-width domain 0))
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(columns (interval-width domain 1)))
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(display "P1") (newline)
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(display columns) (display " ") (display rows) (newline)
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(array-for-each (let ((next-pixel-in-line 1))
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(lambda (p)
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(write p)
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(if (zero? (modulo next-pixel-in-line 64)) (newline))
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(set! next-pixel-in-line (+ 1 next-pixel-in-line))))
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array)))))
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(write-pbm
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(bit-Kronecker-power (list*->array 2 '((1 0 0)
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(1 1 0)
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(1 1 1))
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u1-storage-class)
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5)
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"sierpinski-triangle-5.pbm")
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@ -0,0 +1,120 @@
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option explicit
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'outputs turtle graphics to svg file and opens it
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const pi180= 0.01745329251994329576923690768489 ' pi/180
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const pi=3.1415926535897932384626433832795 'pi
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class turtle
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dim fso
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dim fn
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dim svg
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dim iang 'radians
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dim ori 'radians
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dim incr
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dim pdown
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dim clr
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dim x
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dim y
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public property let orient(n):ori = n*pi180 :end property
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public property let iangle(n):iang= n*pi180 :end property
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public sub pd() : pdown=true: end sub
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public sub pu() :pdown=FALSE :end sub
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public sub rt(i)
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ori=ori - i*iang:
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'if ori<0 then ori = ori+pi*2
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end sub
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public sub lt(i):
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ori=(ori + i*iang)
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'if ori>(pi*2) then ori=ori-pi*2
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end sub
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public sub bw(l)
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x= x+ cos(ori+pi)*l*incr
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y= y+ sin(ori+pi)*l*incr
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' ori=ori+pi '?????
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end sub
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public sub fw(l)
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dim x1,y1
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x1=x + cos(ori)*l*incr
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y1=y + sin(ori)*l*incr
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if pdown then line x,y,x1,y1
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x=x1:y=y1
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end sub
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Private Sub Class_Initialize()
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setlocale "us"
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initsvg
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x=400:y=400:incr=100
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ori=90*pi180
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iang=90*pi180
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clr=0
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pdown=true
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end sub
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Private Sub Class_Terminate()
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disply
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end sub
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private sub line (x,y,x1,y1)
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svg.WriteLine "<line x1=""" & x & """ y1= """& y & """ x2=""" & x1& """ y2=""" & y1 & """/>"
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end sub
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private sub disply()
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dim shell
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svg.WriteLine "</svg></body></html>"
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svg.close
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Set shell = CreateObject("Shell.Application")
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shell.ShellExecute fn,1,False
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end sub
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private sub initsvg()
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dim scriptpath
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Set fso = CreateObject ("Scripting.Filesystemobject")
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ScriptPath= Left(WScript.ScriptFullName, InStrRev(WScript.ScriptFullName, "\"))
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fn=Scriptpath & "SIERP.HTML"
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Set svg = fso.CreateTextFile(fn,True)
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if SVG IS nothing then wscript.echo "Can't create svg file" :vscript.quit
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svg.WriteLine "<!DOCTYPE html>" &vbcrlf & "<html>" &vbcrlf & "<head>"
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svg.writeline "<style>" & vbcrlf & "line {stroke:rgb(255,0,0);stroke-width:.5}" &vbcrlf &"</style>"
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svg.writeline "</head>"&vbcrlf & "<body>"
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svg.WriteLine "<svg xmlns=""http://www.w3.org/2000/svg"" width=""800"" height=""800"" viewBox=""0 0 800 800"">"
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end sub
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end class
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sub sier(lev,lgth)
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dim i
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'wscript.echo lev,lgth
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if lev=1 then
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for i=1 to 3
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x.fw lgth
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x.lt 2
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next
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else
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sier lev-1,lgth\2
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x.fw lgth\2
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sier lev-1,lgth\2
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x.bw lgth\2
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x.lt 1
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x.fw lgth\2
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x.rt 1
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sier lev-1,lgth\2
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x.lt 1
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x.bw lgth\2
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x.rt 1
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end if
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end sub
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dim x
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set x=new turtle
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x.iangle=60
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x.orient=0
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x.incr=10
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x.x=100:x.y=100
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'star5
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sier 7,64
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set x=nothing 'outputs html file to browser
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