I was able to view the video, and it's definitely cool, but it doesn't give the morphing Kagome picture I'm looking for. The part of the video that shows a single cube being sliced is a good warmup, for my purposes as it was for George's. But whereas George is gearing up for what happens to a COMPACT fractal assembly of UNEQUAL cubes, I'm gearing up for what happens to an UNBOUNDED assembly of EQUAL cubes. In both scenarios, hexagons and triangles are starring players, but the arrangement of them is quite different. Jim On Wed, Jul 31, 2019 at 11:29 AM George Hart <george@georgehart.com> wrote:
Hi James,
There is an example of that about two minutes into this video, as a warmup to what happens when you slice the Menger Sponge:
https://www.simonsfoundation.org/2012/12/10/mathematical-impressions-the-sur...
George http://georgehart.com
On 7/31/2019 8:10 AM, James Propp wrote:
I just realized that, to illustrate Warren Smith's way of proving the Wall of Fire theorem at my August 7 talk, it'd be cool to have a video or GIF showing how the intersection between the 2-skeleton of a moving cubical network and a fixed plane evolves in time. For instance, say the plane is {(x,y,z): x+y+z=0} and the cubical network is the standard one in Z^3 moving at constant speed in the (1,1,1) direction, which one can write as {(x,y,z); x≡t (mod 1) or y≡t (mod 1) or z≡t (mod 1)}. We see a dynamic dissection of the plane in which equilateral triangles grow and turn into hexagons and then turn into shrinking triangles pointing the other way.
Can anyone dash off such a video? If I use it in my talk I will of course give credit.
Thanks,
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