I most often get a flavor of this comment/question...
- I want to learn more about this!
- Can you teach me how this is generated?
- What resources can I use to learn about non-Euclidean geometry?
TilingBot creates images of kalideoscopic tilings, that is, tilings generated by repeatedly reflecting an image in mirrors. I've seen this process is called "folding". Roy Wiggins wrote some nice blog articles, with code, about how this works.
I gave a talk at ICERM with a good bit of discussion about TilingBot.
The TilingBot source code can be a resource, but it can be a bit to dig through. A much more distilled version of this same approach is the python code that Anton Sherwood used to generate many of the images on Wikipedia.
Another good resource along these lines are shaders, like this one by Mathew Arcus, because all of the code is available for inspection.
I've seen two main approaches to coding hyperbolic tilings, each with advantages and disadvantages. Many (including myself) started with the Poincare disk model and the circle inversion formula to generate tessellations. The second approach is to work in the hyperboloid model, which is analogous in many ways to coding spherical tilings on a sphere. Here is a twitter thread discussing tradeoffs.
Visual Complex Analysis, by Tristan Needham
This is a bit of a commitment but I also can't recommend the book enough. The first six chapters give a good foundation for non-Euclidean geometry. It is not coding oriented, but it would provide all the mathematics necessary to get started. It's how I first started learning about the geometry, the models, Mobius transformations, etc.
Tessellations: Mathematics, Art, and Recreation by Robert Fathauer. TilingBot makes an appearance in this one.
Tilings and Patterns, aka the tiling Bible.
There are many Mathematica demonstrations on hyperbolic geometry.
Let me know if there are other good resources you think should be listed here.