**Equilateral triangle divided by sixteen**

The scaling factor from one generation to the next is 1/4. This reptile has lots of symmetry. Four possibilities are shown below, with all of them taken through three iterations.

At far right is a path I found that essentially traces out the fractal at left. This path can be iterated such that it will trace out the fractal at any stage in non-crossing fashion and remain unicursal (a single strand). You may need to widen your browser window in order to see all five columns side by side.

All images copyright Robert Fathauer

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