**Equilateral triangle divided by nine**

The scaling factor from one generation to the next is 1/3. This reptile has lots of symmetry, and the gasket at far left can be thought of as a nine-triangle analog of the Sierpinski Gasket. Four other possibilities are shown below, with all of them taken through four iterations. The fractal arrangement of hexagons, second from left, has been done before, and the fractal to its right is closely related to it. The fourth fractal from the left can be seen as half a Sierpinski Carpet, tilted at an angle.

All images copyright Robert Fathauer

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