Regularly Expressional Fractalations

There’s something about fractals that humans find fascinating. They manage to contain a beautiful impression of infinity despite being not very difficult to create. These fractals have been produced by a very simple recipe:

1. Split a big square of pixels into 4 quadrants and label them 1 to 4
2. Repeat this process for each of the smaller squares and add the quadrant number to the label
3. Keep cutting the squares into 4 until you’ve gone as small as you want
4. Now we can use regular expressions to find and mark boxes with certain labels

I wrote a little bit of javascript that creates such fractals from regular expressions involving the digits 1, 2, 3 or 4. Have a play here and check out some examples below.

1

[13][24][13]

12|21|34|43

13|24

13|31|24|42

[34]+2