Message #914

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] MC7D v0.01
Date: Thu, 17 Jun 2010 13:10:27 -0700

Andrey wrote:
> So… MC7D v0.01. You can download it from here: http://shade.msu.ru/~astr/MC7D/MC7D.zip . It’s not very convenient - it has no graphic settings, no color selection, no macros and no cubie search. But you can make twists with it and see results.
> Unfortunately, I’m not sure that it will run on your computers: it contains DirectX 9, and I don’t know if it will be able to find and use it in all situations.
>

Runs fine for me out-of-the-box on Win7. I just extracted the zip file
into a folder, double-clicked the .exe and there it was! The initial
views of each puzzle seems too small to be useful but scaling up is
quick and easy. 3D rotation speed is very fast!

> Suppose that you are lucky. What do you see:
> 7D space is divided to 4 main and 3 secondary dimensions. Seven large cubes are the sides of the cube directed to main dimensions, and they are arranged as faces of 4D cube. Each face is 6D cube and it’s represented as a Cartesian product of two 3D cubes - that is cube (in main dimensions) built of smaller cubes (in secondary dimensions).
>

This is a very clever solution to the problem of higher dimensional
visualization. When you run out of physical dimensions, just unfurl new
dimensions into another 3 at a new fractal level! We lose some
regularity and the ability to smoothly animate twists but we gain the
ability to "flatten" any local region into something that a human can
manage.

In hindsight I’m a little surprised that you didn’t begin with a 6D
puzzle since the fractal pattern 3 + 3 + 3 +… is more regular and all
the pieces will be square.

> Sides of smaller cubes (we call them "blocks") are directed in secondary dimensions. Note that orientation of all blocks is the same, so stickers of 7C cubie are not collected around the corner of the face: some of them are on other corners of the corner block. Small stickers that attached to sides of blocks actually belong to "secondary" sides of the cube. So we can see all stickers of cubies on main sides, but only some stickers on secondary sides. It means, for example, that we don’t see colors of centers of secondary sides of 3^7. But it’s not the problem - centers of main sides are deep inside the cloud of cubes, so we almost can’t see their color too.
>

This is the other refinement that makes the fractal unfolding practical:
Pruning away parts of the puzzle that get too far from the local region
in fractal scale. Putting these two main ideas together was brilliant!

It occurs to me that something similar might be useful to apply to MC5D
by simply not showing all the parts that are furthest from the 5D eye
point and project to microscopic bits towards the center of the display,
or at least just fading them out the further they get.

[…]

I’ve cut out the instructions because I don’t really want to comment on
the details at this point but if someone wants to help polish his
English I think that would be very helpful. I’ll be happy to host the
puzzle, instructions, or just links on the MC4D site if you like. Please
feel free to also use the MC4D Wiki to host instructions, screen shots,
and records.

> Full scramble of 3^7 is a little slow operation (it takes 1260 twists). Also you can select another puzzles - from 3^4 to 5^7. Be careful: 3D image of 5^7 has about 800K visible stickers and requires 10M triangles. It may be very slow.
>

Not on my old laptop. It only takes 1.5 seconds to create even the
largest 5^7 and I still get about 10 frames per second when rotating.
Scrambling is a bit slower, taking about 4 seconds to fully scramble the
3^7, and a full minute for the 5^7. Something tells me that if it takes
the computer a full minute just to scramble the puzzle, that we probably
don’t want to think about a human trying to unscramble it. Even though
this interface makes that possible to imagine, a puzzle with more
stickers than pixels just seems wrong :-)

Chris Locke wrote:
> […] I wonder if the group name "4D_Cubing" is really appropriate
> anymore… ? ^^

Perhaps not, but "ND_Polytoping" just doesn’t have the same ring to it. ;-)

I don’t know how all of you introduce our puzzles to your friends but
I’ve found that I need to do it *very* gently or they are easily scared
away. If I mention that we have puzzles other than the cube, or
dimensions above 4, they always become too terrified to even look at it.
I therefore think there is value in starting people off with the simple
3^4 and not mentioning anything more until they’ve touched one and
gotten a little comfortable with the idea. If anyone has advice about
how best to introduce people, I would love to hear it.

This is great stuff, Andrey. I bet that this version required you to
write more than 200 lines of code. :-) Thank you for all the great new fun!
-Melinda