Jonathan. Frech’s WebBlog

Haferman Carpet (#106)

Jonathan Frech

The Haferman Carpet is a fractal which kind of looks like a woven carpet. To gen­er­ate it, you start with a single black pixel and apply in each cycle a set of rules.
In each generation, every pixel in the carpet will be replaced by nine pixels according to the rules. A black pixel is represented by a 0, a white one by a 1.

The Rules

$$0\rightarrow\left(\begin{array}{ccc}1&0&1\\0&1&0\\1&0&1\end{array}\right)\text{and }1\rightarrow\left(\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right)$$$$0\rightarrow\left(\begin{array}{ccc}1&0&1\\0&1&0\\1&0&1\end{array}\right)\text{and }1\rightarrow\left(\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right)$$

Source code: haferman-carpet.py