Fractal Generation

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The word "fractal" (as I use it on this website) refers to computer-gerated images.

The computer needs two mathematical formulas to create one image.

Years of experimenting, mathematical background, programming skill and a luck are necessary to

find good formulas that create good images.

After about ten years of experimenting I have created a set of about onehundred formulas which create amazing images.

The computer is given a pair of mathematical formulas. Each of the two formulas has two variables, say x and y.

The coordinates of the computer screen's pixels measured from the center of the screen (say (x,y) = (50,50))

are then used as input variables for these formulas. This creates two results.

These two results we call then 'x' and 'y' and feed them back into the formula.

This is done many times (say up to 100 times).

After each such "iteration" the program checks whether the point (x,y) is moving further away from the origin (0,0) than a given limit ("it moves to infinity").

The number of rounds it takes to move beyond that (arbitrary) limit is a measure for the speed with wich this point "runs away". This number of rounds is then translated into a colour.

For example, if the point (50,50) we started from moves beyond the limit in 16 rounds, it may be given the colour red.

If the point moves beyond the limit in 17 rounds, it may be painted orange, and so on.

This way the computer is able to give a colour to any point on the screen.

The processing time necessary for each picture varies of course with the complexity of the formula and with the maximum number of rounds processed.

On a 2.4 Gigahertz processor this can take between 10 sec and 10 minutes for a 768x1024 resolution.

This can be very time consuming, even when using software which produces many images automatically after each other,

One scene of one minute length seconds for example took three days computer run time (at 24 images per seconds).

Back in 1988 I used the German software "Turbo Fractal Generator" (TFG) to create my first fractals.

Later I used the American freeware "Fractint", which also has a special tool for creating movies from fractals..

Atlantis Puzzles & Games

11 Utting Street, Birkdale, Auckland, New Zealand

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