Square divided by sixteen

The scaling factor from one generation to the next is 1/4. This reptile has four-fold rotational symmetry and mirror symmetry, allowing for choices in the orientation of the smaller units in cases where those units have less symmetry than a square. If the four center squares are removed, there are no additional choices for subsequent iterations (at left below). There are many other possibilities for removing one or more squares. One example is shown at right below, through four iterations.

All images copyright Robert Fathauer

Fractal Diversions home

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