Hyperbolic Hopf Fibrations The Hopf Fibration of S^3 is amazing and beautiful. Rather than describe it here, I'll point you to a lovely online reference with pictures and videos by Niles Johnson. nilesjohnson.net/hopf.html To understand it better (and fibrations in general), I recommend this talk by Niles too. www.youtube.com/watch?v=QXDQsmL-8Us It turns out there is an analogue of the Hopf fibration for H^3. In fact, there is not just one "fiberwise homogenous" fibration in the hyperbolic case. There is a 2-parameter family of them, plus one additional fibration that does not fit the family. As with S^3, fibers in the H^3 cases are geodesics. They are ultraparallel in fibrations from the family, and parallel in the exceptional fibration. I found the following dissertation by Haggai Nuchi a good intro and resource to help think about all this. www.math.upenn.edu/grad/dissertations/NuchiThesis.pdf I'm posting three early pictures of H^3 fibrations below, labeled
is it possible for your software to be converted to js so they run in browser or any phone?
ReplyDeletei think that'd be great!
Xah Lee, not really, at least not easily. I predict it would require a complete rewrite, though the existing code would hopefully make such an effort easier. The code is here: https://github.com/roice3/MagicTile
ReplyDeleteisn't there many framework that convert/compile .net to js?
ReplyDeletei mean, i saw many of your software that's interesting, but they can't run on browser or mac or linux. I really want to blog them etc, or use them, but the .net source basically limit them for handful of programer only. eg those interested in math, and is programing experts on windows platform.
if it's in js, so it'd run on any linux, windows, mac, and android, iphone. I think that'd increase audience some 100 fold. i think considering this is worthwhile.
Anyway, just saying.
Great! Going to try this as soon as I get home!
ReplyDeleteScott Vorthmann, cool! Feel free to open GitHub issues for anything you find. I've done little more than make sure it starts up and some puzzles load correctly.
ReplyDeleteI noticed the OpenGL canvas is offset a little for instance, which doesn't surprise me (I've heard UI doesn't always transfer perfectly in Mono). But maybe there is something I can do to avoid that... I'll go open an issue now :)
Xah Lee, I hadn’t known about them, but a quick search reveals there is, e.g. https://bridge.net/
ReplyDeleteI’d be quite surprised if it worked and shocked if it was performant, but would simultaneously be happy!
Works nicely, Roice!
ReplyDelete