6-Rhombus Fractal Reptile 2

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 angle is approximately 52.239 degrees (left), with mirroring between successive iterations on the right.




All images copyright Robert Fathauer

Fractal Diversions home

Fractal Tiling Fractal Knots Gasket Fractals Fractal Trees Hyperbolic & Folded Fractals Polyhedra Papers