Anyone here familiar with the #hyperbolicgeometry of neural networks? Or networks in general?

I’m trying to understand whether hyperbolic embeddings actually preserve meaningful social distance, or just compress graphs nicely.

Mathy people often look down on crochet due to misogyny or minimizing of the arts (math is a male dominated field BTW) , but crochet should not be gendered let alone demeaned because it's associated with female crafts.
Crochet is not just able to be applied to math, but is inherently mathematical. To make anything in crochet at minimum you need to be counting and planning what you are doing. You can use math to plan out specific shapes and to understand what process you need to follow to make that shape. Making something in crochet is making something with one string (usually) so it is a very complicated mesh. You can make complex images using a pixel grid sort of style. You can also leave the flat "2D" creations and move in 3 dimensions. Using math, you can make things ripple or have waves or be flat, or stretch, or whatever.
For example, you can crochet hyperbolic shapes:
https://m.youtube.com/watch?v=xtlDND7NVp8

#math #crochet #engineering #geometry #hyperbolicgeometry

Ported Seuphorica (Scrabble solitaire deckbuilder) to RogueViz for a more intuitive and powerful interface!

(1) Infinite square grid, with standard Seuphorica special powers. Letters E and R (inverse colors close to the gigantic EE top left) are "reversing", hence "RE" is accepted and "EE" is accepted multiple times. Note the word GEESE which uses a portal to get a multiplier for gigantic 'E' two times in a single word. "PETER" uses a mirror.

But since this is RogueViz, let us make the board geometry abstract, to have even more fun with geometry and topology!

(2) Usually, words can only go "right" and "down". In hyperbolic geometry, we have holonomy, so "right" and "down" are not globally defined. So we have to accept both directions. (Or, optionally, only accept words if they are valid both ways.)

(3) In this one, "right" and "down" are not globally defined either, but "horizontal" and "vertical" are (in a somewhat twisted way), so Seuphorica "horizontal" and "vertical" multiplier powers can work.

Although the hexagons somehow turn a horizontal word into a vertical one...

#RogueViz #NonEuclideanGeometry #mathart #noneuclidean #HyperbolicGeometry #Seuphorica #scrabble

(to be continued...)

Developer's intention: A beautiful visualization feature!

What the users share: A chaotic art generator! BREAK THE LIMITS! 🎨🔥

#HyperRogue #RogueViz #HyperbolicGeometry #NonEuclideanGeometry #NonEuclidean

Every tile in a hyperbolic tiling is randomly colored red or blue. How far should we move to find a specific pattern (a shape constructed out of tiles, with specific colors)?

The distance is usually proportional to \(n\), the number of tiles in the pattern -- this is because at a given location the pattern appears with probability \( 1/2^n \), and there are \(\Theta(c^d)\) possible locations in distance d.

So, for example, HyperRogue normally displays 582 tiles, and for every specific coloring of these 582 tiles, it should be somewhere in about 742 steps (and all of them in about 753 steps). If we used symbols (26 letters + space) instead of colors and were looking for a specific message of 1000 characters, it should appear in radius 6000.

Problem: however, it is not clear how to find such a pattern (and whether it would be still true for a given pseudorandom generator). What it the most elegant coloring algorithm with similar properties but where requested patterns can be found by following some procedure? (If you do not know how hyperbolic geometry works, might be easier to think about binary trees)

#NonEuclideanGeometry #NonEuclidean #HyperbolicGeometry #HyperRogue #roguelike #procgen