Matrix Substitutions

We can create images from matrices with integer values by assigning the colour of the pixel at position $(i,j)$ according to the value of the the corresponding matrix entry. By implementing a rewriting rule similar in spirit to an L-system, we can make these images quite complicated. To produce the images on this page, we start with an initial matrix (say, the matrix $[1]$) and apply an iterated rewriting rule that replaces every entry with value $i$ with a certain square matrix $A_i$.

Here we have the same idea with a slightly different presentation. Instead of representing each matrix entry by a single pixel, we use a polygon for a more artistic look.