First Method | |||

Begin with a square and replace each side with a broken line made of
8 segments, each of length | |||

Second Method | |||

We use the shape divided into subsquares as a blueprint and follow its pattern replacing each subsquare with a suitably reduced original shape. | |||

Coloring the reduced shape helps visualize the process. | |||

We will start by noticing there are four subsquares (red) in the center. | |||

Replace these by four reduced original shapes which are then grouped to form one object. | |||

Next we see the parts extending out from the center are identical except they are rotated from one to the other. | |||

Each extension contains three subsquares. The upper right are colored blue. The four extensions are then fit into the central shape and all five pieces are grouped to form one object. | |||

Continue the process, generating a tile with a fractal boundary. | |||

Return to fractal tilings.