Using square- or triangle-based grids, there is no overlapping transformation of the grid for n = 6, meaning n = 6 fractal self-replicating tiles are not allowed. By distorting a grid, for example stretching a square grid by √2, n=6 becomes allowed. The scaling factor from one generation to the next is 1/√6, and the rotation angles are approximately 35.264 (left) and -144.736 (right) degrees.
All images copyright Robert Fathauer
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