Based on entropy filtering and sampling, I was able to find CA rules which remind me of and resemble the Girih tiles, known in the Islamic part of the world. A sample list of rules which exhibit that behavior:
I have chosen Rule #238385. Below you will find a picture of the first hundred steps in the evolution of the selected CA.
Project: Developing 2D continuous wavelet transform framework and benchmark suite in Mathematica
As the wavelet transform becomes more and more popular due to its excellent characteristics, we cannot but try to apply it to various problems in different fields of interest. Measuring the multi/fractal dimension is one such problem and it has been extensively studied. However, the traditional methods rely on some tedious predicates, whereas we can benefit from the fast numerical implementations of the continuous wavelet transform combining them with fractal analysis. Applying them on medical images, stock market time series, or DNA walks, we will be able to interpret and/or predict changes in them.
Favorite Outer Totalistic r=1, k=2 2D Cellular Automaton