An
iterated
function system (
IFS) is a function or
set of functions which operate on
data repeatedly. Often, the
input and/or functions are kept
simple so as to be more easily analyzed. Some
examples of IFS include the
dragon fractal,
Sierpinski triangle,
Koch curve,
L-systems and the
Mandelbrot set. By way of example, below is the Sierpinski
triangle followed by another similar
fractal shown step by
step (for three steps each):
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________
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--------
________________
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________ ________
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-------- --------
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--------------------------------
____
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----
________
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--------
____ ____
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---- ----
________________
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----------------
____ ____
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---- ----
________ ________
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-------- --------
____ ____ ____ ____
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---- ---- ---- ----
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________________
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----------------
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--------------------------------
________________
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----------------
________
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--------
________ ________
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-------- --------
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--------------------------------
________________
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----------------
____ ____
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---- ----
____
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----
________
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--------
________ ________
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-------- --------
____ ____
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---- ----
____ ________ ____
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---- -------- ----
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With the three-way IFS above, many of the fractals that are produced are simple
reflections or restatements of each other. Out of 512 possible fractals, only 200 or less are
unique for this particular IFS form.
I worked in the extra spaces above to make sure that the overall idea is clear.