Simple Fractal Tilings

Method 1

Instead we return to our original shape with four copies.

Again, select and group these five to make a shape.

Fit four copies of these around the central shape.

Select and group these five, reduce the size of this new shape to keep the aggregate of manageable size, and place four copies around the central shape.

Some care must be taken when placing these copies since they will fit into the central shape in many different ways, but not all will produce a tessellation.

Note that in going from one stage to the next, we are replacing the area by 5 times the area and the perimeter (measured at this scale) by 12/4 = 3 times the perimeter.

The area-perimenter relation becomes 5 = 32/d, so in the limit we obtain fractal tiles with dimension d = log(9)/log(5), approximately 1.36521.

Return to Method 1.