# The Wonder-World of Mandelbrot

## Introduction

The Mandelbrot fractal set is defined by the following iteration on complex numbers:
z := z * z + c
Those c values belong to the set for which the above iteration does not converge to infinity. The canonic set is defined when z started from zero. Other starting values produce distorted versions of the set. The Julia sets are defined on the z value as domain with a fixed c value. It is easy to see that the iteration converges to infinity if the absolute value of z reaches 2. Therefore it is a usual technique to color the points outside the set according to the number of iterations before z reached 2. The points of the set are colored black. The table above contains the canonic Mandelbrot set (in the middle) with some interesting parts magnified. Click on the images to see a large resolution (1262x984) version of them.

## My Programs to Draw the Mandelbrot/Julia Sets

As I am a programmer and love these fractal images I wrote programs to calculate and draw the Mandelbrot set for every types of computers I worked on (e.g. Commodore 64, Enterprise, PC, SGI etc.), and I used various languages (Basic, Pascal, C, Assembly). I cannot provide you with all those programs simply because I do not have most of them around any more. However, I am happy to present some of them for your pleasure and entertainment.
• XJulia Very fast Julia set generator program with algorithm and source. The Julia set is generated by a mouse click on the Mandelbrot set and it is so fast, that you can "fly" over the Mandelbrot set and see a REALTIME movie (20 frames/sec) of the corresponding Julia sets.

• XMandel An X-Windows Mandelbrot set generator program with source. Contains a "smart" random demo, which finds nice regions to zoom in.

• ZsManJul Mandelbrot/Julia generator program for PC(VGA)
Similar features to the above programs, surprising speed from a PC.

## Links to other Fractal sites

If you are new to fractals I recommend to have a look at the Fractal Lesson page by Cynthia Lanius, which is a good introduction to fractals in general.
David E. Joyce has a good description of Julia and Mandelbrot sets.