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Technical Description of
Fractal Generation
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General:
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.
In Detail:
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.
Processing Time:
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.
Movie Making:
By changing additional variables in the formulas per images, one
can
create animated videos from fractal images.
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).
Software:
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..
Karl Scherer
Atlantis Puzzles & Games
11 Utting Street, Birkdale, Auckland, New Zealand
Email: see my home page
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