Graphics2D Julia Set Applet

This is based on Pascal code for the Julia set for quadratic polynomials. From another page on the ThinkQuest website is this information: "The main difference between the Julia set and the Mandelbrot set is the way in which the function is iterated. The Mandelbrot set iterates z = z² + c with z always starting at 0 and varying the c value. The Julia set iterates z = z² + c for a fixed c value and varying z values. In other words, the Mandelbrot set is in the parameter space, or the c-plane, while the Julia set is in the dynamical space, or the z-plane." See our introduction to fractals from the Mandelbrot set.

In the code we recycle the colours, but you could easily extend the range with code such as setColor(new Color(80, 240, 60)), where you supply as parameters the red, green and blue components of each customised colour.

za := (Double(i) / xsize) * (x2corner - xcorner) + xcorner;

The code below generates the following graphic.

A Julia set fractal from code below

It is interesting to change the values of variables. Changing ca to 0.4 resulted in this very different fractal.

Julia set fractal with ca = 0.4

By changing instead the values of cornerx, connery, cornerx2 and cornery2 to -0.5, -0.5, 0.5 and 0.5, respectively, we obtained this close-up of a portion of the first graphic.

Julia set fractal with corners set to -0.5 and +0.5

The code of JuliaDemo.pas

namespace julia;

interface

uses
  java.util,
  java.applet.*,
  java.awt.*;

type
  JuliaDemo = public class(Applet)
  private
    xcorner, y2corner, x2corner, ycorner, ca, cb, za2, za1, za, zb : Double;
    xsize, ysize, k, i, xgap, ygap, max, count : Integer;
  public
    method init; override;
    method paint(g: Graphics); override;
    method iterate;
  end;
implementation

method JuliaDemo.iterate;
begin
  count := 0;
  za2 := za;
  while true do
    begin
      za1 := za2;
      za2 := (za1 * za1 - zb * zb) + ca;
      zb := za1 * zb * 2 + cb;
      if za2 * za2 + zb * zb > 4 then
        exit;
      count := count + 1;
      if count > max  then
        exit;
    end;
end;

method JuliaDemo.init;
begin
  xsize := getSize.width;
  ysize := getSize.height;
  xcorner := -1.5;
  ycorner := -1.5;
  x2corner := 1.5;
  y2corner := 1.5;
  max := 50;
  xgap := 10;
  ygap := 10;
  ca := 0.360284; //Try ca := 0.365;
  cb := 0.100376; //Try cb := 0.095;
end;

method JuliaDemo.paint(g: Graphics);
var
  g2 : Graphics2D;
begin
  g2 := Graphics2D(g); 
  for k := ysize downTo 1 do
    for i := 1 to xsize do
      begin
        za := (Double(i) / xsize) * (x2corner - xcorner) + xcorner;
        zb := (Double(k) / ysize) * (y2corner - ycorner) + ycorner; 
        iterate;
        if count > max then 
          count := 0;
        case count mod 10  of
          0 : g2.setColor(Color.darkGray);
          1 : g2.setColor(Color.red);
          2 : g2.setColor(Color.orange);
          3 : g2.setColor(Color.yellow);
          4 : g2.setColor(Color.green);
          5 : g2.setColor(Color.cyan);
          6 : g2.setColor(Color.blue);
          7 : g2.setColor(Color.magenta);
          8 : g2.setColor(Color.black);
          9 : g2.setColor(Color.white);
        end;
        g2.drawLine(xgap + i, ygap + ysize - k, xgap + i, ygap + ysize - k);
      end; 
end;

end.