Footprints of π
To celebrate the “π day of the century” in 2015, UT's Physics Mathematics Astronomy Library held a small online exhibit of π-related art. I contributed documentation of two cases in which π appeared under unusual circumstances, with unknown designs. I would like to continue this documentation project, and I encourage anyone with knowledge of similar visitations to contact me, with the assurance that your identity and your connection to the events you describe will remain confidential to whatever extent you request.
Each record has been formatted in two ways: as a web page and as a (hopefully) print-ready PDF. See the web page for companion text not shown in the PDF, and the PDF for detail not visible in the web images.
The Markov algorithm model is a simple model of computation which is equivalent in power to the Turing machine model, and gives the same time complexity classes modulo P. Typomatic is a cute, colorful, and bizarrely addictive tool for watching Markov algorithms at work. I’ve had great luck, and great fun, using Typomatic as a hands-on way of introducing middle through high school students to the idea of computability.
The long and short radii a and b of an ellipse lie on the hyperbola a2 – b2 = f2, where f is half the distance between the foci.
Weighted affine midpoint maps
At a conference, Ren Yi asked whether you can modify the midpoint map to get irregular polygons as attracting fixed points. For the affine midpoint map, this sketch shows that the answer is clearly yes, but I don’t know how to prove it. I also don't know which polygons you can get.