Message #2361

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Re: Hyperbolic Honeycomb {7,3,3}
Date: Thu, 26 Jul 2012 10:36:34 -0500

Cool, thanks for the suggestions! I’ll try to incorporate them into a
better second video this weekend. In the meantime, here is the original
video so you don’t have to use youtube as the viewer.

www.gravitation3d.com/roice/math/ultrainf/338/338_1.wmv

It is about 35MB and was made with Microsoft Movie Maker, so in a Microsoft
format. Hopefully you’re player can work with it though.

seeya,
Roice

On Thu, Jul 26, 2012 at 1:41 AM, Don Hatch <hatch@plunk.org> wrote:

> Yeah!!
>
> I like that one seemingly-arbitrary {3,8}
> stays in one place.
>
> This particular animation path is a bit overwhelming to me though…
> how about starting with a more mundane one,
> in which the contents of the "stationary" {3,n}
> simply pans steadily horizontally or vertically?
>
> (Also… not your fault, but the youtube viewer
> seriously sucks for viewing this!
> I want to manually scrub the time back and forth slowly, and just can’t,
> and it’s really frustrating.
> Is there a way to download movies from youtube, or a less sucky way
> to view them?)
>
> As for coloring…
> yeah it won’t be periodic,
> but I think it would be really helpful
> to get a coloring of the outer {3,n}
> in which the n tris around any vertex are n different colors.
> That would accomplish the goal of getting sufficient separation
> between any two cells of the same color in the {3,3,n},
> so that it’s easier to tell which tris are from a common cell.
> (a 2-coloring of the {3,8} wouldn’t accomplish this)
>
> I think the following coloring algorithm works:
> color each tri in order of increasing distance (of tri center,
> in hyperbolic space) from some fixed
> starting point, breaking ties arbitrarily.
> When choosing a color for a tri,
> at most n-1 of its 3*(n-2) "neighbor" tris have already been colored
> (I haven’t proved this, but it seems to hold,
> from looking at a {3,7} and {3,8}).
> So color the new tri with any color other than
> the at-most-(n-1) colors used by its already-colored neighbors.
>
> Don
>
>