A few days ago, our ds106 friend Stefanie posted a nice warholized image of Coco the clown. I am impressed with her work, not only for the coloring but for the regressive tiling down into the lower left corner. It has its roots in math, not quite Fibonacci, not quite what Escher would do, not quite what Penrose would do, but something that Stephanie did.
I have taken her idea a little futher. Recognizing that the pattern she created could be used to fill a plane (like wallpaper that needs to line up at the seams), I duplicated her image four times and placed the new tiles into a square twice as large along the horizontal and vertical dimensions. Though I didn’t do it, this would work with other aspect ratios, such as making the overall pattern eight or sixteen times longer than tall.
Finally, just for the fun of it, I played around with inverting the colors in some squares. I thought of the Hadamard transform (used, among other things, to create the Walsh codes used in CDMA cellular systems), where the lower right corner is always inverted from the basic pattern. This could be increased as large as you want, doubling the dimensions each transform.