Multiflake Fractal Generator

The multiflake (or n-flake) generalizes the Sierpinski triangle to regular polygons with any number of sides. When N=3, it produces the Sierpinski triangle. When N=4, it produces a Vicsek fractal. When N=5, it produces the pentaflake.

How It Works

Starting with a regular polygon of N sides, N smaller copies are placed at each vertex, scaled by the factor 1/(1 + 2·sin(π/N)). The process repeats recursively at each copy, creating an intricate self-similar pattern.

Hausdorff Dimension

The Hausdorff dimension varies with the number of sides: dim = log(N) / log(1 + 2·sin(π/N)). For example, the Sierpinski triangle (N=3) has dimension ≈ 1.585, while the pentaflake (N=5) has dimension ≈ 1.862.

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