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It draws a randomly selected Julia fractal set each time.



Fern Fractal drawn using its Fractint IFS definition.



This is a simple decision maker. It chooses the best option between N items. Each item can have M constraint values (non-zero). It is assumed each constraint has equal importance (weight).



This fractal created by converting logic statements into equations using fuzzy logic operators:

X: X is as true as Y is true

Y: Y is as true as X is false

See: Scientific American Magazine, February 1993, "A...



Feigenbaum constant calculation.

For more info:

http://en.wikipedia.org/wiki/Feigenbaum_constant



2 chaotic Lorenz dynamical systems get synchronized with time.
(Notice 2 y and 2 z values start differently but approach each other later.)

I used the x variable as the synchronization signal but y or z can also be used.



Lambert W function.



Halley's method for solving equations of type f(x)=0.



Shannon entropy of a string indicates minimum average number of bits per symbol required for encoding (compressing) the string.



Numerical Integration using Monte Carlo method.