This applet draws Azulejo graphs, as described by Travis Clohessy and Kenneth Gibson in A Class of Pleasing Periodic Designs. Click to load, and then you can animate the picture by moving the mouse. As Clohessy and Gibson describe, geometric patterns are generated as follows. Given a matrix, or a couple of matrices, compose with each of four unimodular matrices

[1 0]

[0 1]

[0 1]

[-1 0]

[0 1]

[1 0]

[1 0]

[0 -1]

Apply each to the integer lattice and overlay the results. In this applet we are using a pair of matrices:

[13 n]

[0 1]

[13 m]

[0 1]

where n and m are controlled, respectively, by the x and y position of the mouse in the window.

Source code: Azulejo

Built with Processing