Copyright © 2007 Leaf Mindcraft.
This is an Acorn RISC OS software application that generates/plots Mandelbrot Fractals for (Hyper) powers from two to five, and is available for free download.
After having downloaded and unzipped the !HyperMand Application, drag the application to a suitable directory on your hard disc. Double click on the !HyperMand icon run the application.
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.
Choose an unused Plot Number to generate the initial Mandelbrot with a new Power.
The 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.
This document was generated on 14th December 2007 for Acorn Applications written and distributed by Martin Carradus.