I’ve exhibited at Colony of Artists several times, a vibrant art festival at Abbeyhill Colonies in Edinburgh.

One of the things I was showing and selling was my tesselation pieces: designs inspired by MC Escher’s work, particularly matamorphosing tesselations.

Some of these pieces play with negative space and the transition from 3D to 2D:

Sometimes I do some GLSL or similar: much graphics and geometry. I usually scribble down some back-of-envelope variant of the usual geometry equations, but I’ve never consistently decided what to call things or how to write them down.

Here I’m setting down the notation I’m going to use, and capturing the definitions. Reference pseudo-implementations are given too (Swift).

The equations and source given here have been unit tested; full source to come after tidying.

After seeing my post on ChatGPT dazzle , a friend asked what the code for that exact problem would look like if I rewrote it in a better way.

I did criticise the original code, so it’s fair that I should show my own version.

I’ve long known about the power of computer visualisation to dazzle and distract, to give cover to bad or poorly supported ideas. The case study I saw at university was about a famous computer animation of the single-bullet theory in the JFK assassination.

This general idea of dazzle pops up in different contexts over the years. Most recently we can see ChatGPT and other AI tools being used in some very low-effort dazzle attempts.

Here’s a recent example in a post from Twitter:

Introducing the simplex generator for higher dimension pascal/combinatorics and looking at the bigger picture: exhaustive function composition.

This is the first of a few notes about combinatorics and probability. Simpler concepts first, and eventually might get to stuff like analytic combinatorics.

I’m interested in the point where more simple combinatorics and multinomials become blunt tools and we have to move to higher concepts like generators and species.