I thought a little about fractal implementation of 3^6, but it seems to be =
even less regular than 3^7. What we need is to show painted 3^6 cube. It's =
not difficult to show painted "main" faces - but now we decompose the cube =
by secondary dimensions first - so it will look like 27 painted 3^3s (and e=
very 3d "sticker" represents one cubie of 3^6 - but actual main stickers ar=
e 2d now). But then we need to show colors of parts of secondary faces. I s=
ee place for them around the main cube - somethis like cloud of small squar=
es parallel to each face. It may be one layer of squares (6*3^2*3^2) - if w=
e show secondary faces of one layer of cubies only - or 3 layers (6*3^3*3^2=
) arranged like sides of 4D puzzle 9x9x9x3. Looks difficult.
Another idea - to show two cubes with different division to main/secondary =
dimensions: one cube shows main faces and another - secondary (and they hav=
e different arrangement of cubies). I can imagine even 3^9 implemented this=
way (it will look like 2187 Ribik's cubes 3^3 arranged in 3 cubes 9x9x9). =
What is good there - we don't need spacing between stickers on the deepest =
level. And we spend only 2 triangles for each sticker (instead of 12). But =
if we try to make 7D or 8D this way then third view will be very strange: f=
or 3^7 it will look like 9^3 cube of bi-colored objects (segments with pain=
ted ends, or coins with painted sides, or just pairs or parallel squares). =
May be for 3^7 it will be better not to show 14-th face. For 3^8 third view=
will consist of 3^2 Rubik's cubes (prisms 3x3x1 with 4 painted sides).
May be it will be better than 4D-like interface. I don't know.
Andrey
Andrey,
You are right. I forgot that N^3 stickers are flat whereas stickers of
the N^4 have the nice quality of being stackable cubes. Therefore the
fractal dimensional pattern 4 + 3 + 3 + 3 ... seems to make good sense
even if symbolically it looks a little odd.
-Melinda
I've pretty much given up on this ever working on my laptop now. I have sp=
ent several hours trying to get it to work (thanks for all the help via ema=
il Andrey, but it didn't work) and I just keep getting a message on screen =
saying the program has stopped working. Guess I will just wait for a later=
version and hope it starts working then, by some miracle. So far I've bee=
n doing my best installing various things (like that .NET 2.0) which I'd ne=
ver heard of before, and even resorted to using command prompt (I've NEVER =
used that before!), as well as Andrey giving me a slightly different versio=
n to download.
As a last ditch attempt, I'm opening this up a wider audience here in case =
any tech-savvy people here have any bright ideas. I have 64-bit Win7, and =
I should have .NET 2.0, .NET 3.5, and directx9 installed now. I have all t=
he files in the same folder, and I have extracted them all. Any help will =
be much appreciated, though I've tried lots of thing already with no succes=
s.
Matt
--- In 4D_Cubing@yahoogroups.com, "Andrey"
>
> 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 twist=
s with it and see results.
> Unfortunately, I'm not sure that it will run on your computers: it co=
ntains DirectX 9, and I don't know if it will be able to find and use it in=
all situations.
>=20
> 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) bui=
lt of smaller cubes (in secondary dimensions).=20
> Sides of smaller cubes (we call them "blocks") are directed in second=
ary dimensions. Note that orientation of all blocks is the same, so sticker=
s 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 ca=
n see all stickers of cubies on main sides, but only some stickers on secon=
dary sides. It means, for example, that we don't see colors of centers of s=
econdary 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.=20
> What can you do:
> The first thing is the navigation in 3D image of the cube. Left butto=
n of mouse can be used to rotate the image, right button (or ctrl-left butt=
on) - to zoom in and out, shift-left button - to change the direction of vi=
ew (sometimes it's called "pan").
> Right-click of the sticker highlights other stickers of its cubie - b=
ut only visible stickers. Sometimes you can see more than 7 of them (up to =
16), it's because secondary stickers may be shown more than once: each of t=
hem appears at every visible main sticker of the cubie. To reject highlight=
ing just click somewhere in empty space.
> Twisting is implemented in 2-click way: first you select face and one=
of its 2C centers, and then select "target" center. It's difficult to find=
2C cubies in the image, so there are some more ways for selection.
> If you want twist main face from main direction to another main direc=
tion, click any large sticker of 2C block of the face. Then click any large=
sticker of the face in the target direction, or any large sticker of the 2=
C block of the twisting face that is directed to the target direction. If t=
arget direction is secondary, second click should go to any small sticker i=
n that direction.
> To twist main face from the secondary direction you may make first cl=
ick either in sticker of 2C cubie (it's inside the side - center of some fa=
ce of the central block), or in the center of face of any not-2C block of t=
he twisting side. Second click goes as it the first case.
> To twist the secondary face from the main direction click the small s=
ticker of any cubie that has only one small sticker (it is at the center of=
face of some block). Second click should go to any sticker of the target f=
ace - main or secondary.
> To twist the secondary face from the secondary direction find some cu=
bie that has exactly two small stickers. One of them should belong to the t=
wisting face and another be directed in the start direction.
> If you are not sure have you made first click or not, click in the em=
pty space. Next click will be considered as the first click of the twist.
> To see other sides of the cube use ctrl-click. There are 1-click and =
2-click commands: if the first click is made not in large sticker of the ce=
ntral side, then the side containing this sticker goes to the central posit=
ion. If you click sticker of the central side then you want to keep it in c=
enter but change two other sides (probably to switch between main and secon=
dary ). It works in the same way as the main side twisting and requires two=
clicks.
> Another features are usual: Undo/Redo; Open/Save log file, Scramble (=
1-5 twists or "full") Full scramble of 3^7 is a little slow operation (it t=
akes 1260 twists). Also you can select another puzzles - from 3^4 to 5^7. B=
e careful: 3D image of 5^7 has about 800K visible stickers and requires 10M=
triangles. It may be very slow.
>=20
> Good luck!
> Andrey.
>