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