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Tuesday, 24 April 2007

Fractal Zoom

I have had another flood of emails asking about fractals, both of them raising the same two questions. (Hey, what about using the comment facility, fellahs, so's others can join in and help me out?) However, I will do my humble best. Before that, though, a word of warning: both emailers seem to have scooted off to my website expecting some sort of enlightenment there. Far be it from me to dissuade anyone from visiting my website or to suggest that enlightenment is not to be found there, but I feel I ought to point out that enlightenment on fractals is conspicuous by its absence. Much else you may find in the way of spiritual insight, but not that.

The first point raised was that it is difficult, when presented with a series of individual plots, to see the relationship between them. I don't think I actually presented a series in that sense with that intention, but here's one which I hope will help. You will see that I have marked on each the area to be magnified for the next plot.

The other query is of a rather more technical nature. I realised, reading the emails, that I had not explained - or not explained clearly enough - the process by which a fractal is produced. Fractals are produced naturally or artificially - in a computer. In either case (matter in the first instance, data in the second) becomes the input for a process which wreaks a small change in it. The slightly modified data or matter (the output from the process) then becomes the new input. It is fed back into the process and modified again in the same manner, before becoming output once more. The new output is fed back in... the process being repeated, usually thousands of times without variation, to produce the fractal, which may be either of two types: self-repeating or self-similar.