From Richard Kenyon's homepage gallery:
(source: rkenyon at www.math.brown.edu)
I want to understand the mathematics of this, and similar/related transformations. ... An explanation in words (1st year uni level maths) would be ideal.
I've been learning about conformal mapping & complex functions in the last year or 2, and trying to get my head around the Cannon/Floyd/Parry papers - Squaring Rectangles, The Length-Area Method etc. Can't say I totally understand them but have made progress. :-) Although it's been a few months since reading this stuff, e.g. I've forgotten the difference between the Discrete and the Finite R.M.T, and which one this involves. I've read about the electrical circuit way of doing squaring, if that helps.
This is I suppose a transform of a square grid with $\sqrt{z}$, then the weights from the flow/cut adjustments are drawn as the side lengths etc etc. But exactly how to do that.. I don't have much idea. I'd really appreciate some pointers. Where do I read about this stuff? (Besides those guys' papers, and Kenyon's?) This is "conformal geometry" right? It's hard for me to even know what to call the subject. (excuse my deficient tagging.) Thank you!
Update: There's a comment it's "about coding not math." I totally disagree that it's not about maths! Gee. The question is about me trying to understand the maths. I think I didn't explain myself well. Uh..forget about the program bit. Should I delete that part? For me, 'understanding something mathematical' = 'being able to write a program about it'. Understanding every part of making tilings like this. Every part of which is a mathematical thing. If I can't write a program about it, I don't understand it. It doesn't mean it's "about coding". Maybe I shouldn't have mentioned C++. Just it's the only language I know well, and I've seen a lot of newer languages on here I know nothing about.
Update: This question was shut down because people thought it wasn't about maths! I find that amazing. Truly ridiculous. I was instructed to read the help page; I can't find anything objection on the help page. It says "we welcome questions about..Understanding mathematical concepts". Well, obviously you don't, gee. Something is wrong here. I can see it "might be better asked" on stack overflow, but the help doesn't say anything about why it might be off-topic here. I don't understand. Anyway, I will delete any reference to writing a program etc. But I strongly object to it being shut down like it was. I feel very unreasonably bullied. The question involves a few different ideas and areas of mathematics. I don't know if the people who voted to close the question could have answered and chose not to, or they just assumed what is involved in the answer, without knowing what a lot of different mathematical ideas are involved. Anyway, I'm new here, what do I know.