n-flake

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n-flake

Summary

An n-flake (or polyflake) is a fascinating family of self-similar fractals created by repeatedly replacing a regular polygon—such as a triangle, square, pentagon, or hexagon—with smaller copies of itself arranged around its vertices (and sometimes at the center). Each repetition reveals increasingly intricate geometric patterns while following the same simple construction rule, making n-flakes a beautiful example of how complexity can emerge from recursion.

 Famous members of this family include the Sierpiński triangle, pentaflake, and hexaflake, each with unique symmetry and fractal dimension. Although these shapes can have infinitely detailed boundaries and infinite perimeter, they enclose zero area in the limit, and their construction can even be extended into three dimensions using regular polyhedra. 

ARTICLE (WIKIPEDIA)