Take a square, divide it into four smaller squares, and discard the smaller square on the top right. Do the same to each of the subsquares, dividing it into four sub-subsquares, then discarding the one on the top right. And repeat with the sub-subsquares. And the sub-sub-squares. And the sub-sub-sub-squares. And so on. The result is a fractal like this:

Stage 1

Stage 2

Stage 3

Stage 4

Animated fractal

Final fractal (static)

It looks as though this procedure isn’t very fertile. But you can enrich it by rotating each of the subsquares in a different way, so that the discarded sub-subsquare is different. Here’s an example:

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6

Stage 7

Animated fractal

Final fractal (static)

Here are more examples of how rotating the subsquares in different ways produces different fractals:

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Animated fractal

Static fractal

Previously pre-posted:

• Square Routes — first look at this kind of fractal