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 rhombus grid, n=6 becomes allowed. The diagonals of the rhombic building block are 1 and √15/3. The scaling factor from one generation to the next is 1/√6, and the rotation angles are approximately 52.239 degrees (left), and 127.761 degrees with mirroring (right) between successive iterations. The first angle with mirroring and the second without are also allowed, but the fractals are similar in appearance.
All images copyright Robert Fathauer
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