Fractal Curves

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The fractal curves are generated from an initial curve (often a regular polygon) and one or more replacement curves. Repeatedly, each line is replaced by a properly scaled copy of one of the replacement curves. The buttons show the initial curve and first iteration of the replacement curve used.

Contributed by: Roman E. Maeder (March 2008)
Open content licensed under CC BY-NC-SA



The code for describing the curves and computing the graphic output is from Roman E. Maeder, The Mathematica Programmer, New York: Academic Press, 1994.

Snapshot 1: the classic snowflake curve

Snapshot 2: W. Gosper's flowsnake, a space-filling curve

Snapshot 3: based on work by B. Mandelbrot

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