Hyper Mandelbrot & Julia Set Fractal Generator/Plotter.

December, 2007

Martin Carradus

Copyright © 2007 Leaf Mindcraft.

Downloading, Unpacking and Using !HypaJulia

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This is an Acorn RISC OS software application that generates/plots Mandelbrot Fractals and Julia Sets for (Hyper) powers from two to five, and is available for free download.

After having downloaded and unzipped the !HypaJulia Application, drag the application to a suitable directory on your hard disc. Double click on the !HypaJulia icon run the application.

1. The Mandelbrot Fractal.

This program generates Fractal plots caused by observing the behaviour of computation with complex numbers.

A Complex Number has both a 'real' and an 'imaginary' part, and can be represented as a co-ordinate number pair in a plane (Argand Diagram).

The method used is to perform a calculation (function) on a complex number, then keep on taking out the complex number so formed and putting it back into the function again (iterating the function).

The function concerned is to raise the complex number to a certain power, (usually two), add a fixed complex number, then keep on repeating the process.

The starting value for this is zero, but the successive complex numbers formed can either remain bounded (converge), or start becoming larger and larger (diverge).

As we vary the complex number that is added on to the power, the behaviour alters.

So the plot you see on the screen is the complex plane near zero, with the degree of instability of the iteration for each added complex number in this plane marked by a colour.

The black coloured region is where the iteration remains stable.

The plot takes more time in the black region, as the iteration is performed the maximum number of times.

It also tends to take more time with higher powers due to the increased amount of computation.

After or during Plotting, you may halt the process and choose a sub area to zoom in on and investigate.

You may also choose a point to base a Julia Set on.

2. Julia Sets.

You may only generate a Julia Set once you have generated a full screen Mandelbrot Fractal.

The calculation that is performed is similar to the Mandelbrot, only it is the starting point for the iteration that is varied, instead of it always being zero.

The added complex number is not varied, but is held constant throughout, so there is a Julia Set corresponding to each point in the Mandelbrot.

Having opted to generate a Julia Set, a pointer appears that can be moved to the chosen fixed complex number.

Choose an unused Plot Number to generate the initial Mandelbrot with a new Power.

Sprite File, written to, is called '!SysSprite' in the directory 'Sprites' within application.

Please read the text file !Help present within this application (Hold down 'Shift' and double-click), for conditions of use.

Click on icon to DownLoad Zipped !HypaJulia.

This document was generated on 14th December 2007 for Acorn Applications written and distributed by Martin Carradus.