Joshua Bowman writes The Math Less Traveled, a blog of recreational math, visualizations, and number theory with Haskell code and diagrams.
HN commenters link its factorization diagrams as a visualization they find brilliant and want to build on, and as a clear explanation of the algorithm.
That was awesome thanks for sharing. For the first minute I wasn't expecting much, but the reflections part was so cool! Plus, this connects directly to the cyclic curves in the complex plane, e.g., https://mathlesstraveled.com/2015/06/04/random-cyclic-curves-5/ The curves formed by the envelope of intersecting lines in the circular multiplication table are a slice of cyclic curve space. I animated this after reading the above blog post: https://youtu.be/myGXoLCnx-A You can see some of the curves in the lower left corner are the same ones from Mathologer.
My favorite way, though, is just to make a grid of pairs of integers (numerator, denominator), and then count them by spiraling outward on the grid. This yields duplicates, but that's ok.
Calkin and Wilf cleverly avoid duplications by arranging reals not on a lattice but on a (Stern-Borcot) tree.
http://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree
http://www.mathlesstraveled.com/?p=94
cryogenics section, for potential resuscitation of
mathematical campaigns using future technology
automated provers like coq and isabelle, I think (I also think I'm not a crackpot but ...
http://arxiv.org/abs/1211.7012
http://mathlesstraveled.com/2012/11/11/a-computer-checked-proof-of-the-odd-order-theorem/
Probably the haskell/agda camp'll want to defend their honor also
This is brilliant!
Now i want (to build) a drag and drop toy where i can multiply or summarize numbers that are represented in this way. To see how factors move (like boids).
Is this visualization algorithm called something? The explanation link from a previous HN post seems to be broken: http://mathlesstraveled.com/2012/10/05/factorization-diagrams/
It tells about the factorizations if anything, as that's the input dimensions they are using. If you haven't seen factorization diagrams, it's worth checking them out first: https://mathlesstraveled.com/factorization/
But visualisations can always deceive you into seeing something that's not there, e.g. correlation vs causation.
For those of us who are confused what "monochromatic rectangles" actually means, this article shows it perfectly:
http://mathlesstraveled.com/2012/02/09/17x17-4-coloring-with-no-monochromatic-rectangles/