Simple Fractal Tilings

Method 1

Select and group these five shapes to make a new shape.

If we continue by placing copies above, below, left, and right of the original, we obtain a pattern that does not tile the plane.

The size and position of the gap suggests that we may try a tile consisting of nine copies of the original shape.

While this collection will tile the plane, in the limit it no longer has a fractal boundary.

Return to Method 1.