Thread: "MHT633 v0.1 uploaded"

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Andrey,

This is quite amazing, of course. I'm starting to get used to regular=20
miracles from you. :-)

It doesn't look so large to imagine that someone wouldn't solve it=20
fairly soon after it is feature-complete and debugged. Or maybe I'm just=20
just not seeing much of it? How many unique faces does it have?

For those who are reluctant to download and run it, I've uploaded a=20
couple of screen-shots to the MC4D image gallery=20
=
.=20
The last image is very cool. I find it slightly frustrating that I can't=20
rotate the 3D view to see the faces on the other side of the {6,3}=20
tiling. Implementing sticker-shrink would definitely help.

Here are my UI suggestions:

* Make the normal left drag perform simple 3D rotation of the
projection.
* Make shift-left drag do the 4D rotation that you currently do with
normal left drag.
* Make alt-left drag do the panning that you currently do with
shift-left drag.

The first two changes would maintain compatibility with the MC4D UI.=20
MC4D has no equivalent to your panning.

Like Roice, I would like to see an autorotation option. I don't think it=20
would be terribly useful but it would definitely look cool.

Great stuff, Andrey! I strongly encourage everyone to check it out.

-Melinda

On 10/27/2010 10:56 AM, Andrey wrote:
> Thank you, Roice!
> I knew that you'll recognize it quickly (may be even without running t=
he progam, just by name :) ). After failing of search of periodic paintings=
of {5,3,4} and {4,3,5} I found the note about "11 H3 honeycombs which have=
infinite (Euclidean) cells and/or vertex figures" and took a better look i=
n them.
> It was evident that {6,3,3} and {4,4,3} can be derived from set of ori=
spheres such that each of them tangents infinitely many of others and tange=
nt points make {3,6} or {4,4} lattice in the orisphere (that is congruent t=
o Euclidean plane). So I took my favorite model (half-space), orisphere z=
=3D1 and tangent points a+b*i or a+b*j (where i^2+1=3D0, j^2-j+1=3D0 when w=
e consider (x,y) plane as C=3D{x+i*y}). For each point there was sphere wit=
h center (a+b*j,1/2) and radius 1/2. These spheres make first level of the =
tesselation.
> To build next levels I had to describe movements of H3. It was easy: t=
his group is equivalent to the group of M=F6bius transformations of C ((a*w=
+b)/(c*w+d)). To preserve the tesselation we should take a,b,c,d from CZ=3D=
Z[j]/(j^2-j+1). So we can show that orispheres may be indexed by "rational"=
numbers CQ=3DQ[j]/(j^2-j+1)=3DCZ/CZ.
> Periodic colorings of CQ may be derived from colorings of {6,3}. Each =
of them is defined by some ideal IZ=3DZ[x]/{c0,c1*x+c2,x^2-x+1}. If we take=
fractions a/b "coprime" a,b from IZ and call a1/b1 and a2/b2 equivalent on=
ly when a1=3Da2*x^k, b1=3Db2*x^k (where x is the element from definition of=
IZ), we'll get coloring of CQ :) Not very easy, and I haven't tried to wri=
te strict description of all this.
>
> Sticker shrinking is not implemented - now I took fixed coordinates of=
blocks' verticies. It's one of more things to do.
> (b) puzzles use some reduction of paintings described here. I've not t=
ested them, may be there are some wrong points in the model.
> Autorotation and autosliding - may be... Are you sure that it will hel=
p more than moving of the mouse?
>
> Good luck!
>
> Andrey
>
> --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
>> Wow Andrey, this is amazing!
>>
>> I didn't even know a {6,3,3} tessellation was attainable. I glossed
>> over such possibilities after reading on Wikipedia that there were only =
4
>> hyperbolic honeycombs. But going back now, I see that claim is "constra=
ined
>> by the existence of the regular polyhedra {p,q},{q,r}". So in this case=
,
>> the "regular polyhedron" {p,q} is an infinite hexagonal tiling! (am I
>> understanding right?) I'm looking forward to studying this more.
>>
>> I'd also be curious to hear of any new found knowledge about how you
>> determined allowable coloring sets.
>>
>> I've only had a few minutes to play with it, but here are a couple quick
>> comments:
>>
>> - the sticker size slider isn't working for me, and I wasn't having much
>> luck trying to edit this setting in the settings file either.
>> - both of the (b) puzzles crash the program for me, and I have to delete=
the
>> settings file to get the program to start again after that.
>> - I would love it if you could implement the auto-spinning as in MC4D. =
I so
>> want to set the thing in motion and watch it for a while to try to
>> understand the space better. I'm facing the frustrating feeling people =
must
>> get when they want more from something I make! Care to open source your
>> code? :D
>>
>> Truly Fantastic Andrey!
>>
>> Roice
>>
>>
>> On Wed, Oct 27, 2010 at 5:19 AM, Andrey wrote:
>>
>>> Guess what is it ;)
>>>
>>>
>>> http://groups.yahoo.com/group/4D_Cubing/photos/album/1962624577/pic/452=
190950/view?picmode=3Dlarge&mode=3Dtn&order=3Dtitle&start=3D1&dir=3Dasc
>>>
>>> Program is here:
>>>
>>> http://games.groups.yahoo.com/group/4D_Cubing/files/MC7D/mht633.zip
>>>
>>> It is not complete - Save/Load, animation and macros are not implemente=
d,
>>> and not tested at all. But there is Help window (for clicks and navigat=
ion)
>>> - on Ctrl-F1 key. For colors editing and highlighting by mask use Ctrl-=
Right
>>> click on the sticker.
>>>
>>> My first impression - solving is impossible even for small puzzles:)
>>>
>>> Good luck )))
>>>
>>> Andrey
>>>
>>>
>>>
>>> ------------------------------------
>>>
>>> Yahoo! Groups Links
>>>
>>>
>>>
>>>
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

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Andrey,



This is quite amazing, of course. I'm starting to get used to
regular miracles from you.  :-)



It doesn't look so large to imagine that someone wouldn't solve it
fairly soon after it is feature-complete and debugged. Or maybe I'm
just just not seeing much of it? How many unique faces does it have?



For those who are reluctant to download and run it, I've uploaded a
couple of screen-shots to the MC4D href="http://wiki.superliminal.com/wiki/Image_gallery#MagicCube4D_Image_Gallery">image
gallery. The last image is very cool. I find it slightly
frustrating that I can't rotate the 3D view to see the faces on the
other side of the {6,3} tiling. Implementing sticker-shrink would
definitely help.



Here are my UI suggestions:

• Make the normal left drag perform simple 3D rotation of the
  projection.


• Make shift-left drag do the 4D rotation that you currently do
  with normal left drag.


• Make alt-left drag do the panning that you currently do with
  shift-left drag.

Thank you, Roice!
  I knew that you'll recognize it quickly (may be even without running the progam, just by name :) ). After failing of search of periodic paintings of {5,3,4} and {4,3,5} I found the note about "11 H3 honeycombs which have infinite (Euclidean) cells and/or vertex figures" and took a better look in them. 
  It was evident that {6,3,3} and {4,4,3} can be derived from set of orispheres such that each of them tangents infinitely many of others and tangent points make {3,6} or {4,4} lattice in the orisphere (that is congruent to Euclidean plane). So I took my favorite model (half-space), orisphere z=1 and tangent points a+b*i or a+b*j (where i^2+1=0, j^2-j+1=0 when we consider (x,y) plane as C={x+i*y}). For each point there was sphere with center (a+b*j,1/2) and radius 1/2. These spheres make first level of the tesselation.
  To build next levels I had to describe movements of H3. It was easy: this group is equivalent to the group of Möbius transformations of C ((a*w+b)/(c*w+d)). To preserve the tesselation we should take a,b,c,d from CZ=Z[j]/(j^2-j+1). So we can show that orispheres may be indexed by "rational" numbers CQ=Q[j]/(j^2-j+1)=CZ/CZ.
  Periodic colorings of CQ may be derived from colorings of {6,3}. Each of them is defined by some ideal IZ=Z[x]/{c0,c1*x+c2,x^2-x+1}. If we take fractions a/b "coprime" a,b from IZ and call a1/b1 and a2/b2 equivalent only when a1=a2*x^k, b1=b2*x^k (where x is the element from definition of IZ), we'll get coloring of CQ :) Not very easy, and I haven't tried to write strict description of all this.

  Sticker shrinking is not implemented - now I took fixed coordinates of blocks' verticies. It's one of more things to do.
  (b) puzzles use some reduction of paintings described here. I've not tested them, may be there are some wrong points in the model.
  Autorotation and autosliding - may be... Are you sure that it will help more than moving of the mouse?

  Good luck!

  Andrey

--- In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@...> wrote:

Wow Andrey, this is amazing!

I didn't even know a {6,3,3} tessellation was attainable.  I glossed
over such possibilities after reading on Wikipedia that there were only 4
hyperbolic honeycombs.  But going back now, I see that claim is "constrained
by the existence of the regular polyhedra {p,q},{q,r}".  So in this case,
the "regular polyhedron" {p,q} is an infinite hexagonal tiling!  (am I
understanding right?)  I'm looking forward to studying this more.

I'd also be curious to hear of any new found knowledge about how you
determined allowable coloring sets.

I've only had a few minutes to play with it, but here are a couple quick
comments:

- the sticker size slider isn't working for me, and I wasn't having much
luck trying to edit this setting in the settings file either.
- both of the (b) puzzles crash the program for me, and I have to delete the
settings file to get the program to start again after that.
- I would love it if you could implement the auto-spinning as in MC4D.  I so
want to set the thing in motion and watch it for a while to try to
understand the space better.  I'm facing the frustrating feeling people must
get when they want more from something I make!  Care to open source your
code? :D

Truly Fantastic Andrey!

Roice


On Wed, Oct 27, 2010 at 5:19 AM, Andrey <andreyastrelin@...> wrote:

Guess what is it ;)


http://groups.yahoo.com/group/4D_Cubing/photos/album/1962624577/pic/452190950/view?picmode=large&mode=tn&order=title&start=1&dir=asc

Program is here:

http://games.groups.yahoo.com/group/4D_Cubing/files/MC7D/mht633.zip

It is not complete - Save/Load, animation and macros are not implemented,
and not tested at all. But there is Help window (for clicks and navigation)
- on Ctrl-F1 key. For colors editing and highlighting by mask use Ctrl-Right
click on the sticker.

My first impression - solving is impossible even for small puzzles:)

Good luck )))

Andrey



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I really wish I wasn't just a second year maths student and knew more geome=
try, unfortunately a lot of that went over my head (I'll understand it one =
day). I can still mess around with it and get a feel of how it works thoug=
h, even if I don't know much of the theory behind it. One question I do ha=
ve, how many hexagons per cell? I'm curious but I find it pretty hard to c=
ount them manually.
Another first step towards a masterpiece Andrey, and probably the craziest =
puzzle we have yet seen, so well done as usual :).

Matt

--- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
>
> Thank you, Roice!
> I knew that you'll recognize it quickly (may be even without running th=
e progam, just by name :) ). After failing of search of periodic paintings =
of {5,3,4} and {4,3,5} I found the note about "11 H3 honeycombs which have =
infinite (Euclidean) cells and/or vertex figures" and took a better look in=
them.=20
> It was evident that {6,3,3} and {4,4,3} can be derived from set of oris=
pheres such that each of them tangents infinitely many of others and tangen=
t points make {3,6} or {4,4} lattice in the orisphere (that is congruent to=
Euclidean plane). So I took my favorite model (half-space), orisphere z=3D=
1 and tangent points a+b*i or a+b*j (where i^2+1=3D0, j^2-j+1=3D0 when we c=
onsider (x,y) plane as C=3D{x+i*y}). For each point there was sphere with c=
enter (a+b*j,1/2) and radius 1/2. These spheres make first level of the tes=
selation.
> To build next levels I had to describe movements of H3. It was easy: th=
is group is equivalent to the group of M=F6bius transformations of C ((a*w+=
b)/(c*w+d)). To preserve the tesselation we should take a,b,c,d from CZ=3DZ=
[j]/(j^2-j+1). So we can show that orispheres may be indexed by "rational" =
numbers CQ=3DQ[j]/(j^2-j+1)=3DCZ/CZ.
> Periodic colorings of CQ may be derived from colorings of {6,3}. Each o=
f them is defined by some ideal IZ=3DZ[x]/{c0,c1*x+c2,x^2-x+1}. If we take =
fractions a/b "coprime" a,b from IZ and call a1/b1 and a2/b2 equivalent onl=
y when a1=3Da2*x^k, b1=3Db2*x^k (where x is the element from definition of =
IZ), we'll get coloring of CQ :) Not very easy, and I haven't tried to writ=
e strict description of all this.
>=20
> Sticker shrinking is not implemented - now I took fixed coordinates of =
blocks' verticies. It's one of more things to do.
> (b) puzzles use some reduction of paintings described here. I've not te=
sted them, may be there are some wrong points in the model.
> Autorotation and autosliding - may be... Are you sure that it will help=
more than moving of the mouse?
>=20
> Good luck!
>=20
> Andrey
>=20
> --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
> >
> > Wow Andrey, this is amazing!
> >=20
> > I didn't even know a {6,3,3} tessellation was attainable. I glossed
> > over such possibilities after reading on Wikipedia that there were only=
4
> > hyperbolic honeycombs. But going back now, I see that claim is "constr=
ained
> > by the existence of the regular polyhedra {p,q},{q,r}". So in this cas=
e,
> > the "regular polyhedron" {p,q} is an infinite hexagonal tiling! (am I
> > understanding right?) I'm looking forward to studying this more.
> >=20
> > I'd also be curious to hear of any new found knowledge about how you
> > determined allowable coloring sets.
> >=20
> > I've only had a few minutes to play with it, but here are a couple quic=
k
> > comments:
> >=20
> > - the sticker size slider isn't working for me, and I wasn't having muc=
h
> > luck trying to edit this setting in the settings file either.
> > - both of the (b) puzzles crash the program for me, and I have to delet=
e the
> > settings file to get the program to start again after that.
> > - I would love it if you could implement the auto-spinning as in MC4D. =
I so
> > want to set the thing in motion and watch it for a while to try to
> > understand the space better. I'm facing the frustrating feeling people=
must
> > get when they want more from something I make! Care to open source you=
r
> > code? :D
> >=20
> > Truly Fantastic Andrey!
> >=20
> > Roice
> >=20
> >=20
> > On Wed, Oct 27, 2010 at 5:19 AM, Andrey wrote:
> >=20
> > > Guess what is it ;)
> > >
> > >
> > > http://groups.yahoo.com/group/4D_Cubing/photos/album/1962624577/pic/4=
52190950/view?picmode=3Dlarge&mode=3Dtn&order=3Dtitle&start=3D1&dir=3Dasc
> > >
> > > Program is here:
> > >
> > > http://games.groups.yahoo.com/group/4D_Cubing/files/MC7D/mht633.zip
> > >
> > > It is not complete - Save/Load, animation and macros are not implemen=
ted,
> > > and not tested at all. But there is Help window (for clicks and navig=
ation)
> > > - on Ctrl-F1 key. For colors editing and highlighting by mask use Ctr=
l-Right
> > > click on the sticker.
> > >
> > > My first impression - solving is impossible even for small puzzles:)
> > >
> > > Good luck )))
> > >
> > > Andrey
> > >
> > >
> > >
> > > ------------------------------------
> > >
> > > Yahoo! Groups Links
> > >
> > >
> > >
> > >
> >
>

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I can field a few of the questions :)

@Melinda

> It doesn't look so large to imagine that someone wouldn't solve it fairly
> soon after it is feature-complete and debugged. Or maybe I'm just just not
> seeing much of it? How many unique faces does it have?


It's very much like MagicTile, in that the {6,3,3} tessellation has an
infinite number of cells. So Andrey used the same approach of identifying
certain cells with each other. Hence, the number of unique faces is simply
the number of colors selected from the puzzle menu. The 8 color version
does seem like it should be quite tractable from a number-of-pieces
perspective, though perhaps still terribly difficult.

I'll be interested in ensuing discussion about Melinda's thoughts on
movement controls. I have some thoughts floating around as well, but they
aren't well formed yet.

@Matt

> One question I do have, how many hexagons per cell? I'm curious but I find
> it pretty hard to count them manually.


Not only are there an infinite number of cells in this tessellation, but
every one of these cells has an infinite number of hexagons! (The
identification of cells mentioned above also serves to turn this aspect of
the puzzle into a manageable finite situation.) The cells are a {6,3}
tiling, the same as you'd see on a bathroom floor, only going on forever.
This tiling is curved when living in hyperbolic space though, and the
result is that the view from within hyperbolic space is such that only a
small number of the hexagonal facets can be seen - the rest curve out of
view. With sticker shrink, I suppose it would be possible to display a much
larger number of the facets, since that allows one to see somewhat through
the cell.

Hope that's helpful and not too much rambling...

aside: Andrey, I think some user control over the amount of culling could
be another nice feature of this puzzle. Also, I think there may be a
problem in that the culling doesn't always recalculate after drags
(seemingly never after left-click ones), nor when a new puzzle is opened.
It seems to recalculate after the first tiny left-drag on a newly opened
puzzle, and I'm happy to send detailed repro steps offline if needed. I'm
questioning if the second image Melinda posted on the wiki is a culling
state you want to allow the user to get into - seems like the user should
always see a view more like the first image she posted.

Take Care,
Roice

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