Fractal Curves

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 first iteration of the replacement curve used. To see the initial curve, set the number of steps to 0.

Contributed by: Roman E. Maeder

Show Initialization Code

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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

"Fractal Curves" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/FractalCurves/

Contributed by: Roman E. Maeder

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