Trapezoid divided by four

The scaling factor from one generation to the next is 1/2. Three examples are shown through seven iterations. The fractal at left below can also be formed from the four-equilateral-triangle reptile, as shown on Larry Riddle's page "Triangle Fractals". It can also be seen in Bernat Espigulé's paper on "Fractal Trees".

Two spatially-developing fractal-gasket polyhedra based on the left gasket above are shown below. In the left example, the layer thickness scales the same as the lateral features from one generation to the next. In the right example, the layer thickness is nearly constant, but there are small variations depending on which of the three positions the smaller copy occupies.

All images copyright Robert Fathauer

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