The Hex Fractor

A regular hexagon can be divided into six equilateral triangles. An equilateral triangle can be divided into three more equilateral triangles and a regular hexagon. If you discard the three triangles and repeat, you create a fractal, like this:

Adjusting the sides of the internal hexagon creates new fractals:
Discarding a hexagon after each subdivision creates new shapes:

And you can start with another regular polygon, divide it into triangles, then proceed with the hexagons:

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