Julia set
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Generate and draw a Julia set.
- Related tasks
AWK
<lang AWK>
- syntax: GAWK -f JULIA_SET.AWK [real imaginary]
BEGIN {
c_real = (ARGV[1] != "") ? ARGV[1] : -0.8 c_imaginary = (ARGV[2] != "") ? ARGV[2] : 0.156 printf("%s %s\n",c_real,c_imaginary) for (v=-100; v<=100; v+=10) { for (h=-280; h<=280; h+=10) { x = h / 200 y = v / 100 plot_char = "#" for (i=1; i<=50; i++) { z_real = x * x - y * y + c_real z_imaginary = x * y * 2 + c_imaginary if (z_real ^ 2 > 10000) { plot_char = " " break } x = z_real y = z_imaginary } printf("%1s",plot_char) } printf("\n") } exit(0)
} </lang>
- Output:
-0.8 0.156 # # # # #### #### ###### ######## # ## ######## ## # # ######## ## # ######### # # ##### # # ######## ### ######## # # ### # ## # # #### ##### # ##### # ##### #### # # ## # ### # # ######## ### ######## # # ##### # # ######### # ## ######## # # ## ######## ## # ######## ###### #### #### # # # #
C++
<lang cpp>
- include <windows.h>
- include <string>
- include <complex>
const int BMP_SIZE = 600, ITERATIONS = 512; const long double FCT = 2.85, hFCT = FCT / 2.0;
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; } DWORD* bits() const { return ( DWORD* )pBits; }
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 julia { public:
void draw( std::complex<long double> k ) { bmp.create( BMP_SIZE, BMP_SIZE ); DWORD* bits = bmp.bits(); int res, pos; std::complex<long double> c, factor( FCT / BMP_SIZE, FCT / BMP_SIZE ) ;
for( int y = 0; y < BMP_SIZE; y++ ) { pos = y * BMP_SIZE;
c.imag( ( factor.imag() * y ) + -hFCT );
for( int x = 0; x < BMP_SIZE; x++ ) { c.real( factor.real() * x + -hFCT ); res = inSet( c, k ); if( res ) { int n_res = res % 255; if( res < ( ITERATIONS >> 1 ) ) res = RGB( n_res << 2, n_res << 3, n_res << 4 ); else res = RGB( n_res << 4, n_res << 2, n_res << 5 ); } bits[pos++] = res; } } bmp.saveBitmap( "./js.bmp" ); }
private:
int inSet( std::complex<long double> z, std::complex<long double> c ) { long double dist;//, three = 3.0; for( int ec = 0; ec < ITERATIONS; ec++ ) { z = z * z; z = z + c; dist = ( z.imag() * z.imag() ) + ( z.real() * z.real() ); if( dist > 3 ) return( ec ); } return 0; } myBitmap bmp;
}; int main( int argc, char* argv[] ) {
std::complex<long double> c; long double factor = FCT / BMP_SIZE; c.imag( ( factor * 184 ) + -1.4 ); c.real( ( factor * 307 ) + -2.0 ); julia j; j.draw( c ); return 0;
} </lang>
COBOL
Plots—in ASCII or EBCDIC art—a Julia set for the function f(z) = z2 + c, based on a value of c input by the user (real part then imaginary part, pressing the carriage return key after each). The sample output is for the inputs -0.8 and 0.156. <lang cobol>IDENTIFICATION DIVISION. PROGRAM-ID. JULIA-SET-PROGRAM. DATA DIVISION. WORKING-STORAGE SECTION. 01 WS-COMPLEX-CONSTANT.
05 C-REAL PIC S9V999. 05 C-IMAGINARY PIC S9V999.
01 WS-ARGAND-PLANE.
05 X PIC S9(9)V999. 05 Y PIC S9(9)V999.
01 WS-COMPLEX-VARIABLE.
05 Z-REAL PIC S9(9)V999. 05 Z-IMAGINARY PIC S9(9)V999.
01 WS-TEMPORARY-RESULTS.
05 X-SQUARED PIC S9(9)V999. 05 Y-SQUARED PIC S9(9)V999. 05 X-TIMES-Y PIC S9(9)V999. 05 Z-REAL-SQUARED PIC S9(9)V999.
01 WS-LOOP-COUNTERS.
05 HORIZONTAL PIC 999. 05 VERTICAL PIC 999. 05 ITERATIONS PIC 99.
77 WS-PLOT-CHARACTER PIC X. PROCEDURE DIVISION. INPUT-COMPLEX-CONSTANT-PARAGRAPH.
ACCEPT C-REAL FROM CONSOLE. ACCEPT C-IMAGINARY FROM CONSOLE.
CONTROL-PARAGRAPH.
PERFORM OUTER-LOOP-PARAGRAPH VARYING VERTICAL FROM 1 BY 10 UNTIL VERTICAL IS GREATER THAN 320. STOP RUN.
OUTER-LOOP-PARAGRAPH.
PERFORM COMPUTATION-PARAGRAPH VARYING HORIZONTAL FROM 1 BY 10 UNTIL HORIZONTAL IS GREATER THAN 560. DISPLAY UPON CONSOLE.
COMPUTATION-PARAGRAPH.
SUBTRACT 280 FROM HORIZONTAL GIVING X. SUBTRACT 160 FROM VERTICAL GIVING Y. DIVIDE X BY 200 GIVING X. DIVIDE Y BY 100 GIVING Y. MOVE '#' TO WS-PLOT-CHARACTER. PERFORM COMPLEX-MULTIPLICATION-PARAGRAPH VARYING ITERATIONS FROM 1 BY 1 UNTIL ITERATIONS IS GREATER THAN 50 OR WS-PLOT-CHARACTER IS EQUAL TO SPACE. DISPLAY WS-PLOT-CHARACTER UPON CONSOLE WITH NO ADVANCING.
COMPLEX-MULTIPLICATION-PARAGRAPH.
MULTIPLY X BY X GIVING X-SQUARED. MULTIPLY Y BY Y GIVING Y-SQUARED. SUBTRACT Y-SQUARED FROM X-SQUARED GIVING Z-REAL. ADD C-REAL TO Z-REAL. MULTIPLY X BY Y GIVING X-TIMES-Y. MULTIPLY X-TIMES-Y BY 2 GIVING Z-IMAGINARY. ADD C-IMAGINARY TO Z-IMAGINARY. MULTIPLY Z-REAL BY Z-REAL GIVING Z-REAL-SQUARED. IF Z-REAL-SQUARED IS GREATER THAN 10000 THEN MOVE SPACE TO WS-PLOT-CHARACTER. MOVE Z-REAL TO X. MOVE Z-IMAGINARY TO Y.</lang>
- Output:
### ## ## # ### #### # ################ ### # # # ############### # ####### ## ##### ######## # # ##### ## ######## ### ######## # ### ### # ## # ## # #### # # # #### # #### ### # # # ### # # ######### # ## ###### # ######### # ######### ###### # ### ### ## ## ############ # # # ######### ## ## # ##### #### # # ### #
Elixir
<lang elixir>defmodule Julia do
def set(c_real, c_imag) do IO.puts "#{c_real}, #{c_imag}" vlist = Enum.take_every(-100..100, 4) hlist = Enum.take_every(-280..280, 4) Enum.each(vlist, fn v -> Enum.map(hlist, fn h -> loop(c_real, c_imag, h/200, v/100, "#", 0) end) |> IO.puts end) end defp loop(_, _, _, _, char, i) when i>=50, do: char defp loop(_, _, _, _, " ", _), do: " " defp loop(c_real, c_imag, x, y, char, i) do z_real = (x * x - y * y) + c_real z_imag = x * y * 2 + c_imag char = if z_real * z_real > 10000, do: " ", else: char loop(c_real, c_imag, z_real, z_imag, char, i+1) end
end
c_real = if r=Enum.at(System.argv, 0), do: Float.parse(r) |> elem(0), else: -0.8 c_imag = if c=Enum.at(System.argv, 1), do: Float.parse(c) |> elem(0), else: 0.156 Julia.set(c_real, c_imag)</lang>
- Output:
-0.8, 0.156 # # ## ####### ## #### ## # #### ## # # # ### ### # ## # # ###### ########## # # # # ###### ########## # # ### ### # ############ ###### # ################ ################### # # ### # ################ #################### ## # ### ## ## ############################## ### #### # ####### ### # ## ## # ##################### # #### ## #### ### ########### ###### # # ##### ##################### # # ## ###################### ### ####### #### # ####################### # ### ############ ### ## ## ## ## ## ################# ######################## ### ########### ## ### ### ################# ## ###### # # ################### # ##### ## ######## # ### # ###### ############ ## ## # ### ############## # ## ### ## # #### # # ## ### ## ########### ## #### ############# ## # ## ### ## ## ####### ## ##### ######### ############# ### # # ####### # # ### ############# ######### ##### ## ####### ## ## ### ## # ## ############# #### ## ########### ## ### ## # # #### # ## ### ## # ############## ### # ## ## ############ ###### # ### # ######## ## ##### # ################### # # ###### ## ################# ### ### ## ########### ### ######################## ################# ## ## ## ## ## ### ############ ### # ####################### # #### ####### ### ###################### ## # # ##################### ##### # # ###### ########### ### #### ## #### # ##################### # ## ## # ### ####### # #### ### ############################## ## ## ### # ## #################### ################ # ### # # ################### ################ # ###### ############ # ### ### # # ########## ###### # # # # ########## ###### # # ## # ### ### # # # ## #### # ## #### ## ####### ## # #
J
<lang j>load '~addons/graphics/fvj4/complex_dynamics.ijs' pal2=: 255,~0,<.(254$1 0.8 0.6)*Hue 5r6*(i.%<:)254 g=: [: %: 0.3746j0.102863 0.132565j0.389103 _0.373935j_0.353777 1&p. view_image pal2;b=:g escapetc (10 255) 500 zl_clur _1.5 1.5j1.5</lang>
See also: Fractals Visualization and J, 4th edition, Part 1 (by Clifford A. Reiter), Chapter 6
See http://webbox.lafayette.edu/~reiterc/mvp/ec_julia/index.html for some other examples. (That said, note that this is a link into a small college site and it might drift over time. In the past, for example, you would have had to use 'www' where it currently says 'webbox')
Java
<lang java>import java.awt.*; import java.awt.image.BufferedImage; import javax.swing.*;
public class JuliaSet extends JPanel {
private final int maxIter = 300; private final double zoom = 1; private double cY, cX;
public JuliaSet() { setPreferredSize(new Dimension(800, 600)); setBackground(Color.white); }
void drawJuliaSet(Graphics2D g) { int w = getWidth(); int h = getHeight(); BufferedImage image = new BufferedImage(w, h, BufferedImage.TYPE_INT_RGB);
cX = -0.7; cY = 0.27015; double moveX = 0, moveY = 0; double zx, zy;
for (int x = 0; x < w; x++) { for (int y = 0; y < h; y++) { zx = 1.5 * (x - w / 2) / (0.5 * zoom * w) + moveX; zy = (y - h / 2) / (0.5 * zoom * h) + moveY; float i = maxIter; while (zx * zx + zy * zy < 4 && i > 0) { double tmp = zx * zx - zy * zy + cX; zy = 2.0 * zx * zy + cY; zx = tmp; i--; } int c = Color.HSBtoRGB((maxIter / i) % 1, 1, i > 0 ? 1 : 0); image.setRGB(x, y, c); } } g.drawImage(image, 0, 0, null); }
@Override public void paintComponent(Graphics gg) { super.paintComponent(gg); Graphics2D g = (Graphics2D) gg; g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON); drawJuliaSet(g); }
public static void main(String[] args) { SwingUtilities.invokeLater(() -> { JFrame f = new JFrame(); f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); f.setTitle("Julia Set"); f.setResizable(false); f.add(new JuliaSet(), BorderLayout.CENTER); f.pack(); f.setLocationRelativeTo(null); f.setVisible(true); }); }
}</lang>
Julia
The following code creates the fractal as a ppm file named julia.ppm. There is no need of an external library to create this image since the ppm format is straightforward to generate.
<lang julia> function iter(z,c)
n = 0 while (abs2(z)<4) z = z^2+c ; n+=1 end return n
end
coord(i,j,w,h,a,b) = 2*a*(i-1)/(w-1) - a + im * (2*b*(j-1)/(h-1) - b)
palette(n) = string(min(3n,255)," ", min(n,255)," ", 0);
julia(c) = (w,h,a,b,i,j) -> palette(iter(coord(i,j,w,h,a,b), c))
writeppm(f; width=600,height=300,a=2,b=1,file="julia.ppm") =
open(file, "w") do out write(out, string("P3\n", width, " ", height, "\n255\n")) writedlm(out, [f(width,height,a,b,i,j) for j = 1:height, i = 1:width], '\n') end
</lang>
We can then produce a 600x300 ppm image of the Julia set associated to the parameter -0.786+0.147i as follows.
writeppm(julia(-0.786+0.147im))
The following code makes use of the library Images to build a png image.
<lang julia>using Images
w, h = 800, 600 img = Array(UInt8, h, w, 3)
maxIter = 50 c = -0.8+0.156im
function hsv2rgb(h, s, v)
c = v * s x = c * (1 - abs(((h/60) % 2) - 1)) m = v - c
r,g,b = if h < 60 (c, x, 0) elseif h < 120 (x, c, 0) elseif h < 180 (0, c, x) elseif h < 240 (0, x, c) elseif h < 300 (x, 0, c) else (c, 0, x) end
r = round(UInt8, (r + m) * 255) g = round(UInt8, (g + m) * 255) b = round(UInt8, (b + m) * 255)
b,g,r
end
for x in 1:w
for y in 1:h i = maxIter z = Complex((x - w/2) / w * 3, (y - h/2) / h * 2) while abs(z) < 2 && (i -= 1) > 0 z = z*z + c end r,g,b = hsv2rgb(i / maxIter * 360, 1, i > 1 ? 1 : 0) img[y,x,1] = r img[y,x,2] = g img[y,x,3] = b end
end
save("JuliaSet.png", colorim(img, "RGB"))</lang>
Perl
<lang perl>use Imager;
my($w, $h, $zoom) = (800, 600, 1); my $img = Imager->new(xsize => $w, ysize => $h, channels => 3);
my $maxIter = 255; my ($cX, $cY) = (-0.7, 0.27015); my ($moveX, $moveY) = (0, 0);
my $color = Imager::Color->new('#000000');
foreach my $x (0 .. $w - 1) {
foreach my $y (0 .. $h - 1) { my $zx = (1.5 * ($x - $w / 2) / (0.5 * $zoom * $w) + $moveX); my $zy = (($y - $h / 2) / (0.5 * $zoom * $h) + $moveY); my $i = $maxIter; while ($zx**2 + $zy**2 < 4 and --$i >= 0) { ($zy, $zx) = (2 * $zx * $zy + $cY, $zx**2 - $zy**2 + $cX); } $color->set(hsv => [$i / $maxIter * 360, 1, $i > 0 ? 1 : 0]); $img->setpixel(x => $x, y => $y, color => $color); }
}
$img->write(file => 'julia_set.png');</lang>
Perl 6
with the pallette swapped, just because.
<lang perl6>use Image::PNG::Portable;
my ($w, $h) = 800, 600; my $out = Image::PNG::Portable.new: :width($w), :height($h);
my $maxIter = 255; my $c = -0.7 + 0.27015i;
julia($out);
$out.write: 'Julia-set-perl6.png';
sub julia ( $png ) {
for ^$w -> $x { for ^$h -> $y { my $z = Complex.new(($x - $w / 2) / $w * 3, ($y - $h / 2) / $h * 2); my $i = $maxIter; while (abs($z) < 2 and --$i) { $z = $z*$z + $c; } $png.set: $x, $y, |hsv2rgb($i / $maxIter * 360, 1, ?$i).reverse; } }
}
sub hsv2rgb ( $h, $s, $v ){
my $c = $v * $s; my $x = $c * (1 - abs( (($h/60) % 2) - 1 ) ); my $m = $v - $c; my ($r, $g, $b) = do given $h { when 0..^60 { $c, $x, 0 } when 60..^120 { $x, $c, 0 } when 120..^180 { 0, $c, $x } when 180..^240 { 0, $x, $c } when 240..^300 { $x, 0, $c } when 300..^360 { $c, 0, $x } } ( $r, $g, $b ) = map { (($_+$m) * 255).Int }, $r, $g, $b;
}</lang>
Processing
<lang java>void setup() {
size(640, 480);
}
float cX = -0.7; float cY = 0.27015; float zx, zy; float maxIter = 300;
void draw() {
for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { zx = 1.5 * (x - width / 2) / (0.5 * width); zy = (y - height / 2) / (0.5 * height); float i = maxIter; while (zx * zx + zy * zy < 4 && i > 0) { float tmp = zx * zx - zy * zy + cX; zy = 2.0 * zx * zy + cY; zx = tmp; i -= 1; } color c = hsv2rgb(i / maxIter * 360, 1, i > 1 ? 1 : 0); set(x, y, c); } } noLoop();
}
color hsv2rgb(float h, float s, float v) {
float c = v * s; float x = c * (1 - abs(((h/60) % 2) - 1)); float m = v - c;
float r, g, b; if (h < 60) { r = c; g = x; b = 0; } else if (h < 120) { r = x; g = c; b = 0; } else if (h < 180) { r = 0; g = c; b = x; } else if (h < 240) { r = 0; g = x; b = c; } else if (h < 300) { r = x; g = 0; b = c; } else { r = c; g = 0; b = x; }
int ri = round((r + m) * 255); int gi = round((g + m) * 255); int bi = round((b + m) * 255);
return color(ri, gi, bi);
}</lang>
Ruby
<lang ruby>def julia(c_real, c_imag)
puts Complex(c_real, c_imag) -1.0.step(1.0, 0.04) do |v| puts -1.4.step(1.4, 0.02).map{|h| judge(c_real, c_imag, h, v)}.join end
end
def judge(c_real, c_imag, x, y)
50.times do z_real = (x * x - y * y) + c_real z_imag = x * y * 2 + c_imag return " " if z_real**2 > 10000 x, y = z_real, z_imag end "#"
end
julia(-0.8, 0.156)</lang>
- Output:
-0.8+0.156i # # ## ####### ## #### ## # #### ## # # # ### ### # ## # # ###### ########## # # # # ###### ########## # # ### ### # ############ ###### # ################ ################### # # ### # ################ #################### ## # ### ## ## ############################## ### #### # ####### ### # ## ## # ##################### # #### ## #### ### ########### ###### # # ##### ##################### # # ## ###################### ### ####### #### # ####################### # ### ############ ### ## ## ## ## ## ################# ######################## ### ########### ## ### ### ################# ## ###### # # ################### # ##### ## ######## # ### # ###### ############ ## ## # ### ############## # ## ### ## # #### # # ## ### ## ########### ## #### ############# ## # ## ### ## ## ####### ## ##### ######### ############# ### # # ####### # # ### ############# ######### ##### ## ####### ## ## ### ## # ## ############# #### ## ########### ## ### ## # # #### # ## ### ## # ############## ### # ## ## ############ ###### # ### # ######## ## ##### # ################### # # ###### ## ################# ### ### ## ########### ### ######################## ################# ## ## ## ## ## ### ############ ### # ####################### # #### ####### ### ###################### ## # # ##################### ##### # # ###### ########### ### #### ## #### # ##################### # ## ## # ### ####### # #### ### ############################## ## ## ### # ## #################### ################ # ### # # ################### ################ # ###### ############ # ### ### # # ########## ###### # # # # ########## ###### # # ## # ### ### # # # ## #### # ## #### ## ####### ## # #
Sidef
<lang ruby>require('Imager')
var (w, h) = (640, 480) var img = %s'Imager'.new(xsize => w, ysize => h, channels => 3)
var maxIter = 50 var c = Complex(-0.388, 0.613)
var color = %s'Imager::Color'.new('#000000')
for x,y in (^w ~X ^h) {
var i = maxIter var z = Complex((x - w/2) / w * 3, (y - h/2) / h * 2) while (z.abs < 2 && --i) { z = (z*z + c) } color.set(hsv => [i / maxIter * 360, 1, i]) img.setpixel(x => x, y => y, color => color)
}
img.write(file => "JuliaSet_sidef.png")</lang>
This version generates an ASCII representation: <lang ruby>var (w, h) = (141, 50)
var maxIter = 40 var c = Complex(-0.8, 0.156)
for y in ^h {
for x in ^w { var i = maxIter var z = Complex(3 * (x - w/2) / w, 2 * (y - h/2) / h) while (z.abs < 2 && --i) { z = (z*z + c) } print (i > 0 ? ' ' : '#') } print "\n"
}</lang>
- Output:
## ## ####### ######## # ## # ### ## # # ##### #### ## ## # ###### ########## # ######## ########## # ## ###### ######################## ### ################ ################### ## ## # ### # # ##################################### # ### ## # # ############################# ########### # ###### ### # # ## ########################### # ######## ################# # # # #### ##################### ### #### ##################### ### ############ ###################### # # ### ################ ### # # # ### # ################# ###################### ## ########### # ## ###### ########################### #################### ###### ## ########## ### # ### # ## ################ ## ###### ################# ######## ## # ###### ## ## #### ## # # ########### # #### ############# #### ### ####### ########### ## ###### ########## ############ ## # ########## # ## ############ ########## ###### ## ########### ####### ### #### ############# #### # ########### # # ### #### ## ## ###### # ## ######## ################# ###### ## ################ ## # ### # ### ########## ## ###### #################### ########################### ###### ## # ########### ## ###################### ################# # ### # # # ### ################ ### # # ###################### ############ ### ##################### #### ### ##################### #### # # # ################# ######## # ########################### ## # # ### ###### # ########### ############################# # # ## ### # ##################################### # # ### # ## ## ################### ################ ### ######################## ###### ## # ########## ######## # ########## ###### # ## ## #### ##### # # ## ### # ## # ######## ####### ## ##
zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
<lang zkl>fcn juliaSet{
w,h,zoom:=800,600, 1; bitmap:=PPM(w,h,0xFF|FF|FF); // White background
cX,cY:=-0.7, 0.27015; moveX,moveY:=0.0, 0.0; maxIter:=255;
foreach x,y in (w,h){ zx:=1.5*(x - w/2)/(0.5*zoom*w) + moveX; zy:=1.0*(y - h/2)/(0.5*zoom*h) + moveY; i:=maxIter; while(zx*zx + zy*zy < 4 and i > 1){
tmp:=zx*zx - zy*zy + cX; zy,zx=2.0*zx*zy + cY, tmp; i-=1;
} // convert byte to RGB (3 bytes), kinda magic to get nice colors bitmap[x,y]=i.shiftLeft(21) + i.shiftLeft(10) + i*8; }
bitmap.writeJPGFile("juliaSet.jpg",True);
}();</lang>