Mandelbrot Magic

MANDELBROT MAGIC


by Barry Hunt & Neil Palmer





Nothing fractal-related would be complete without a good ol'


Mandelbrot Set generator and, out of the heap of excellent ones that


came tumbling in, I deemed this one by Barry Hunt and Neil Palmer to


be the neatest, mainly because of its size (or lack of it).





So what is the Mandelbrot Set then? Er, it's highly mathematical, but


basically it involves iterating the equation x=x+i in the complex


plan, and plotting a point when x fails to tend to infinity. Simple,


eh? The end result is that a weird pattern is generated which, if


examined closely, can be seen to be infinitely complicated.





On running the program you'll be asked to enter a series of numbers.


To plot the whole set, in as much detail as possible, enter the


following numbers.





a = -2.568


b = -1.25


aside = 3.636


bside = 2.5


width = 255


height = 175


accuracy = 10





The trouble is, the whole thing takes hours to generate. Erm, 11 of


them to be precise. It's worth the wait though, and the author points


out that using Mallard Basic on the +3 reduces this to about three


hours, and a compiled version should do even better still.


Alternatively, you can either reduce the area of the screen that's


filled by the pattern by changing the Width and Height variables, or


simply reduce the accuracy.





This is only the beginning though. By choosing a new starting


co-ordinate (by changing a and b) and viewing a smaller area of the


set (by lowering aside and bside) you can examine parts of it in


detail. The interesting bits are located at co-ordinates around the


edges of the shape. Anywhere else tends to give a blank screen. If you


discover any really nice areas, write the relevant numbers on the back


of a Luncheon Voucher and send them to the usual address. Also, if


anyone feels like writing a Machine Code version, perhaps with a zoom


facility, let me know.