Thread: "puzzle avalanche continues"

From: Roice Nelson <roice3@gmail.com>
Date: Sat, 21 May 2011 14:55:16 -0500
Subject: puzzle avalanche continues



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I have yet to solve any, as I'm still getting distracted with finding new
puzzles and colorings :) If any of the following sound fun, grab the
latest here
.

- Two new {5,4} Petals, a non-orientable 6 color and an orientable 12
color (the relationship between the two is reminiscent of that between the
Megaminx and hemi-Megaminx). The first is like an easier version of the
{5,5} Petal, because there are no 1C pieces. Although these puzzles feel
pretty simple and only have 2C edge pieces, both are as deepcut as can be,
since the twisting circles are tangent to their identified counterparts.
Also, I'm liking the hyperbolic tilings with square vertex figures because
you get beautiful ultra-parallel lines running everywhere.
- A 5 Color {4,5} with a neat slicing, but I bet it will be pretty
difficult to solve. This one is also as deepcut as can be, but in this case
that's deeper than with the {5,4}s above.
- A Pretty {3,6} with 8 Colors. This torus puzzle should be a fun one.
- {4,4} Edge Turning, 9 Colors.
- Yet another {8,3}, with 8 Colors this time. There are so many possible
coloring combinations, and wild how some end up fitting together! I should
figure out how to calculate the genus of all these guys.

Cheers,
Roice

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I have yet to solve any, as I'm still getting distracted with find=
ing new puzzles and colorings :) =A0If any of the following sound fun, grab=
the latest=A0agicTile_v2_Preview.zip">here.

Cheers,
Roice

<=
br>


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From: Melinda Green <melinda@superliminal.com>
Date: Sat, 21 May 2011 18:36:14 -0700
Subject: Re: [MC4D] puzzle avalanche continues



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Wow, what a bounty of riches!

The ultraparallel lines are indeed beautiful. Can the edges be adjusted
so that those lines are straight rather than bumping along?

Still haven't figured out the 8-color {5,5}. I don't know how pretty or
interesting it may turn out to be but it is definitely close to my
heart, topologically at least.

I think that my favorite is the 8-colored Euclidean {6,3}. It is easy to
grok and will look very familiar to all twisty puzzle enthusiasts while
having its exotic non-orientableness front and center.

I would like to name your 9-color edge turning {4,4} to be the
"Harlequin" tiling.

Regarding calculating genus, it is not difficult though you do have to
be extremely cautious in your counting. You need to count the number of
*unique* vertices, edges and faces in a single minimal repeat unit and
plug those values into the Euler formula F-E+V = 2-2g and solve for g.
Just go super slow so that you don't skip any unique elements or count
any more than once. For instance, a simple toroidal {4,4} repeat unit is
a simple open cylinder with exactly 4 vertices, 4 horizontal and 4
vertical edges, and 4 faces. Plugging into the Euler formula you get 4 -
8 + 4 = 2 - 2g. Solving for g we get g = (0- 2)/-2 = 1 which is what we
would expect for any torus. See here
for the
complete description with diagrams.

-Melinda

On 5/21/2011 12:55 PM, Roice Nelson wrote:
>
>
> I have yet to solve any, as I'm still getting distracted with finding
> new puzzles and colorings :) If any of the following sound fun, grab
> the latest here
> .
>
> * Two new {5,4} Petals, a non-orientable 6 color and an orientable
> 12 color (the relationship between the two is reminiscent of
> that between the Megaminx and hemi-Megaminx). The first is like
> an easier version of the {5,5} Petal, because there are no 1C
> pieces. Although these puzzles feel pretty simple and only have
> 2C edge pieces, both are as deepcut as can be, since the
> twisting circles are tangent to their identified counterparts.
> Also, I'm liking the hyperbolic tilings with square vertex
> figures because you get beautiful ultra-parallel lines running
> everywhere.
> * A 5 Color {4,5} with a neat slicing, but I bet it will be pretty
> difficult to solve. This one is also as deepcut as can be, but
> in this case that's deeper than with the {5,4}s above.
> * A Pretty {3,6} with 8 Colors. This torus puzzle should be a fun
> one.
> * {4,4} Edge Turning, 9 Colors.
> * Yet another {8,3}, with 8 Colors this time. There are so many
> possible coloring combinations, and wild how some end up fitting
> together! I should figure out how to calculate the genus of all
> these guys.
>
> Cheers,
> Roice

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Wow, what a bounty of riches!



The ultraparallel lines are indeed beautiful. Can the edges be
adjusted so that those lines are straight rather than bumping along?



Still haven't figured out the 8-color {5,5}. I don't know how pretty
or interesting it may turn out to be but it is definitely close to
my heart, topologically at least.



I think that my favorite is the 8-colored Euclidean {6,3}. It is
easy to grok and will look very familiar to all twisty puzzle
enthusiasts while having its exotic non-orientableness front and
center.



I would like to name your 9-color edge turning {4,4} to be the
"Harlequin" tiling.



Regarding calculating genus, it is not difficult though you do have
to be extremely cautious in your counting. You need to count the
number of *unique* vertices, edges and faces in a single minimal
repeat unit and plug those values into the Euler formula F-E+V =
2-2g and solve for g. Just go super slow so that you don't skip any
unique elements or count any more than once. For instance, a simple
toroidal {4,4} repeat unit is a simple open cylinder with exactly 4
vertices, 4 horizontal and 4 vertical edges, and 4 faces. Plugging
into the Euler formula you get 4 - 8 + 4 = 2 - 2g. Solving for g we
get  g = (0- 2)/-2 = 1 which is what we would expect for any torus.
See href="http://superliminal.com/geometry/infinite/infinite.htm">here
for the complete description with diagrams.



-Melinda



On 5/21/2011 12:55 PM, Roice Nelson wrote:
cite="mid:BANLkTi=4tmbq4dbVZ=uL+em96me27qkqcA@mail.gmail.com"
type="cite">


I have yet to solve any, as I'm still getting distracted with
finding new puzzles and colorings :)  If any of the following
sound fun, grab the latest href="http://www.gravitation3d.com/magictile/downloads/MagicTile_v2_Preview.zip">here.



Cheers,

Roice






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From: Roice Nelson <roice3@gmail.com>
Date: Sun, 22 May 2011 00:46:17 -0500
Subject: Re: [MC4D] puzzle avalanche continues



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> The ultraparallel lines are indeed beautiful. Can the edges be adjusted so
> that those lines are straight rather than bumping along?
>

Can you send me an image of the bumping you are seeing? I uploaded a pic of
a {5,4} as it is
rendering for me, and all the ultra-parallel lines of cell boundaries appear
as nice, smooth arcs.

Still haven't figured out the 8-color {5,5}. I don't know how pretty or
> interesting it may turn out to be but it is definitely close to my heart,
> topologically at least.
>

I think I'll play with this some. I've since realized a puzzle based on
this coloring may still be possible... if the twisting circles are smaller
than the circumcircle for a face, we can keep them from intersecting.


> I would like to name your 9-color edge turning {4,4} to be the "Harlequin"
> tiling.
>

Done, and uploaded
:)
Naming is something I wish I was more creative with, so if anybody else is
struck by names they like, please let me know!

I probably should wait longer before mentioning this (until things are more
stable), but if anyone would like to try to make their own puzzles, you can
copy some of the existing puzzles in the config/puzzles directory to the
config/user directory to use as a template, then edit them. They will then
show up in the menu, and if you create any good ones, you can send them to
me to include in the standard list of puzzles. The display name is just one
of the xml nodes, so you can be free to give your creations any unique name
you'd like. Strange configurations can easily make the program puke, which
is why this suggestion is probably premature. I'll plan to do a round to
make failures in this area more robust, but will throw caution to the wind
in the mean time. Just be warned :)

Regarding calculating genus, it is not difficult though you do have to be
> extremely cautious in your counting. You need to count the number of
> *unique* vertices, edges and faces in a single minimal repeat unit and plug
> those values into the Euler formula F-E+V = 2-2g and solve for g. Just go
> super slow so that you don't skip any unique elements or count any more than
> once. For instance, a simple toroidal {4,4} repeat unit is a simple open
> cylinder with exactly 4 vertices, 4 horizontal and 4 vertical edges, and 4
> faces. Plugging into the Euler formula you get 4 - 8 + 4 = 2 - 2g. Solving
> for g we get g = (0- 2)/-2 = 1 which is what we would expect for any torus.
> See here for the
> complete description with diagrams.
>

Awesome, thanks! The great thing about this is that with the "show only
fundamental" setting, counting these elements is greatly simplified. In
fact, with your description, I may very well be able to automate the genus
calculation in code :)

Take Care,
Roice

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argin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
=3D"#ffffff" text=3D"#000000">The ultraparallel lines are indeed beautiful.=
Can the edges be
adjusted so that those lines are straight rather than bumping along?>

Can you send me an image of the bum=
ping you are seeing? =A0I uploaded a m/magictile/pics/%7B5,4%7D.png">pic of a {5,4} as it is rendering for m=
e, and all the ultra-parallel lines of cell boundaries appear as nice, smoo=
th arcs.


;border-left:1px #ccc solid;padding-left:1ex;">
t=3D"#000000">
Still haven't figured out the 8-color {5,5}. I don't know how p=
retty
or interesting it may turn out to be but it is definitely close to
my heart, topologically at least.

=
I think I'll play with this some. =A0I've since realized a puz=
zle based on this coloring may still be possible... if the twisting circles=
are smaller than the circumcircle for a face, we can keep them from inters=
ecting.

=A0
border-left:1px #ccc solid;padding-left:1ex;">
=3D"#000000">
I would like to name your 9-color edge turning {4,4} to be the
"Harlequin" tiling.

>Done, and cTile_v2_Preview.zip">uploaded=A0:) =A0Naming is something I wish I was=
more creative with, so if anybody else is struck by names they like, pleas=
e let me know!


I probably should wait longer before mentioning this (u=
ntil things are more stable), but if anyone would like to try to make their=
own puzzles, you can copy some of the existing puzzles in the config/puzzl=
es directory to the config/user directory to use as a template, then edit t=
hem. =A0They will then show up in the menu, and if you create any good ones=
, you can send them to me to include in the standard list of puzzles. =A0Th=
e display name is just one of the xml nodes, so you can be free to give you=
r creations any unique name you'd like. =A0Strange configurations can e=
asily make the program puke, which is why this suggestion is probably prema=
ture. =A0I'll plan to do a round to make failures in this area more rob=
ust, but will throw caution to the wind in the mean time. =A0Just be warned=
:)


;border-left:1px #ccc solid;padding-left:1ex;">
t=3D"#000000">
Regarding calculating genus, it is not difficult though you do have
to be extremely cautious in your counting. You need to count the
number of *unique* vertices, edges and faces in a single minimal
repeat unit and plug those values into the Euler formula F-E+V =3D
2-2g and solve for g. Just go super slow so that you don't skip any
unique elements or count any more than once. For instance, a simple
toroidal {4,4} repeat unit is a simple open cylinder with exactly 4
vertices, 4 horizontal and 4 vertical edges, and 4 faces. Plugging
into the Euler formula you get 4 - 8 + 4 =3D 2 - 2g. Solving for g we
get=A0 g =3D (0- 2)/-2 =3D 1 which is what we would expect for any toru=
s.
See target=3D"_blank">here
for the complete description with diagrams.
=

Awesome, thanks! =A0The great thing about this is that with =
the "show only fundamental" setting, counting these elements is g=
reatly simplified. =A0In fact, with your description, I may very well be ab=
le to automate the genus calculation in code :)


Take Care,
Roice=A0


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From: Melinda Green <melinda@superliminal.com>
Date: Sun, 22 May 2011 01:57:50 -0700
Subject: Re: [MC4D] puzzle avalanche continues



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On 5/21/2011 10:46 PM, Roice Nelson wrote:
>
> The ultraparallel lines are indeed beautiful. Can the edges be
> adjusted so that those lines are straight rather than bumping along?
>
>
> Can you send me an image of the bumping you are seeing? I uploaded a
> pic of a {5,4}
> as it is
> rendering for me, and all the ultra-parallel lines of cell boundaries
> appear as nice, smooth arcs.

Now I'm not sure which puzzle I was commenting on. Looking again, the 6
color {5,5} is the only "petals" puzzle that look bumpy. All the rest
are smooth arcs.

>
> Still haven't figured out the 8-color {5,5}. I don't know how
> pretty or interesting it may turn out to be but it is definitely
> close to my heart, topologically at least.
>
>
> I think I'll play with this some. I've since realized a puzzle based
> on this coloring may still be possible... if the twisting circles are
> smaller than the circumcircle for a face, we can keep them from
> intersecting.
>
> I would like to name your 9-color edge turning {4,4} to be the
> "Harlequin" tiling.
>
>
> Done, and uploaded
> :)
> Naming is something I wish I was more creative with, so if anybody
> else is struck by names they like, please let me know!
>
> I probably should wait longer before mentioning this (until things are
> more stable), but if anyone would like to try to make their own
> puzzles, you can copy some of the existing puzzles in the
> config/puzzles directory to the config/user directory to use as a
> template, then edit them. They will then show up in the menu, and if
> you create any good ones, you can send them to me to include in the
> standard list of puzzles. The display name is just one of the xml
> nodes, so you can be free to give your creations any unique name you'd
> like. Strange configurations can easily make the program puke, which
> is why this suggestion is probably premature. I'll plan to do a round
> to make failures in this area more robust, but will throw caution to
> the wind in the mean time. Just be warned :)
>
> Regarding calculating genus, it is not difficult though you do
> have to be extremely cautious in your counting. You need to count
> the number of *unique* vertices, edges and faces in a single
> minimal repeat unit and plug those values into the Euler formula
> F-E+V = 2-2g and solve for g. Just go super slow so that you don't
> skip any unique elements or count any more than once. For
> instance, a simple toroidal {4,4} repeat unit is a simple open
> cylinder with exactly 4 vertices, 4 horizontal and 4 vertical
> edges, and 4 faces. Plugging into the Euler formula you get 4 - 8
> + 4 = 2 - 2g. Solving for g we get g = (0- 2)/-2 = 1 which is
> what we would expect for any torus. See here
> for the
> complete description with diagrams.
>
>
> Awesome, thanks! The great thing about this is that with the "show
> only fundamental" setting, counting these elements is greatly
> simplified. In fact, with your description, I may very well be able
> to automate the genus calculation in code :)

Yea! I'm just glad that I had something mathematical to contribute.

Having the software do the arithmetic is a great idea because it is *so*
easy to mess up when attempting it by hand. Before I got the above right
I made the classic mistake of dropping a minus sign and ended up asking
myself for about the hundredth time whether a surface with a negative
genus makes any sense. (It doesn't)

Another possible way to screw up is to choose a repeat unit that is not
minimal. Sometimes it's easier to build a tiled surface from some
multiple of minimal repeat units, but you can't use them to compute the
genus of the surface. So it's very possible for someone builds a puzzle
that way causing your code to produce the wrong genus. I guess that any
way you do it you still need to be very careful. Be warned indeed! :-)

-Melinda

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On 5/21/2011 10:46 PM, Roice Nelson wrote:

cite="mid:BANLkTin3ZPtJYmPE56QCFFxAee+y7D65Hg@mail.gmail.com"
type="cite">



The ultraparallel lines
are indeed beautiful. Can the edges be adjusted so that
those lines are straight rather than bumping along?






Can you send me an image of the bumping you are seeing?  I
uploaded a href="http://www.gravitation3d.com/magictile/pics/%7B5,4%7D.png">pic
of a {5,4}
as it is rendering for me, and all the
ultra-parallel lines of cell boundaries appear as nice, smooth
arcs.





Now I'm not sure which puzzle I was commenting on. Looking again,
the 6 color {5,5} is the only "petals" puzzle that look bumpy. All
the rest are smooth arcs.



cite="mid:BANLkTin3ZPtJYmPE56QCFFxAee+y7D65Hg@mail.gmail.com"
type="cite">





Still haven't figured
out the 8-color {5,5}. I don't know how pretty or
interesting it may turn out to be but it is definitely close
to my heart, topologically at least.






I think I'll play with this some.  I've since realized a
puzzle based on this coloring may still be possible... if the
twisting circles are smaller than the circumcircle for a face,
we can keep them from intersecting.

 


I would like to name
your 9-color edge turning {4,4} to be the "Harlequin"
tiling.






Done, and href="http://www.gravitation3d.com/magictile/downloads/MagicTile_v2_Preview.zip">uploaded :)
 Naming is something I wish I was more creative with, so if
anybody else is struck by names they like, please let me know!




I probably should wait longer before mentioning this (until
things are more stable), but if anyone would like to try to
make their own puzzles, you can copy some of the existing
puzzles in the config/puzzles directory to the config/user
directory to use as a template, then edit them.  They will
then show up in the menu, and if you create any good ones, you
can send them to me to include in the standard list of
puzzles.  The display name is just one of the xml nodes, so
you can be free to give your creations any unique name you'd
like.  Strange configurations can easily make the program
puke, which is why this suggestion is probably premature.
 I'll plan to do a round to make failures in this area more
robust, but will throw caution to the wind in the mean time.
 Just be warned :)





Regarding calculating
genus, it is not difficult though you do have to be
extremely cautious in your counting. You need to count the
number of *unique* vertices, edges and faces in a single
minimal repeat unit and plug those values into the Euler
formula F-E+V = 2-2g and solve for g. Just go super slow so
that you don't skip any unique elements or count any more
than once. For instance, a simple toroidal {4,4} repeat unit
is a simple open cylinder with exactly 4 vertices, 4
horizontal and 4 vertical edges, and 4 faces. Plugging into
the Euler formula you get 4 - 8 + 4 = 2 - 2g. Solving for g
we get  g = (0- 2)/-2 = 1 which is what we would expect for
any torus. See href="http://superliminal.com/geometry/infinite/infinite.htm"
target="_blank">here
for the complete description with
diagrams.






Awesome, thanks!  The great thing about this is that with
the "show only fundamental" setting, counting these elements
is greatly simplified.  In fact, with your description, I may
very well be able to automate the genus calculation in code :)





Yea! I'm just glad that I had something mathematical to contribute.




Having the software do the arithmetic is a great idea because it is
*so* easy to mess up when attempting it by hand. Before I got the
above right I made the classic mistake of dropping a minus sign and
ended up asking myself for about the hundredth time whether a
surface with a negative genus makes any sense. (It doesn't)



Another possible way to screw up is to choose a repeat unit that is
not minimal. Sometimes it's easier to build a tiled surface from
some multiple of minimal repeat units, but you can't use them to
compute the genus of the surface. So it's very possible for someone
builds a puzzle that way causing your code to produce the wrong
genus. I guess that any way you do it you still need to be very
careful. Be warned indeed!  :-)



-Melinda




--------------060805050000010201010900--




From: Melinda Green <melinda@superliminal.com>
Date: Sun, 22 May 2011 03:46:03 -0700
Subject: Re: [MC4D] puzzle avalanche continues



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On 5/21/2011 10:46 PM, Roice Nelson wrote:
> [...]
>
> I would like to name your 9-color edge turning {4,4} to be the
> "Harlequin" tiling.
>
>
> Done, and uploaded
> :)
>

And now it is solved
! It is
simple enough to solve by intuition yet hard enough to require actual
thinking. I was hoping there was going to be something tricksy about
this one but it turns out to be very well behaved. The interesting
thing is that the only pieces that can travel are the petal-shaped ones.
They come in 2 orientations such that the vertical petals can only move
horizontally and the horizontal petals only vertically. In that regard
it reminds me a little of the 15 puzzle and seems to have roughly the
same difficulty.

Thanks Roice!

-Melinda

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http-equiv="Content-Type">


On 5/21/2011 10:46 PM, Roice Nelson wrote:
cite="mid:BANLkTin3ZPtJYmPE56QCFFxAee+y7D65Hg@mail.gmail.com"
type="cite">



 [...]


I would like to name
your 9-color edge turning {4,4} to be the "Harlequin"
tiling.






Done, and href="http://www.gravitation3d.com/magictile/downloads/MagicTile_v2_Preview.zip">uploaded :) 







And now it is href="http://wiki.superliminal.com/wiki/User:Cutelyaware#4-4-E9">solved!
It is simple enough to solve by intuition yet hard enough to require
actual thinking. I was hoping there was going to be something
tricksy about this one but it turns out to be very well behaved. 
The interesting thing is that the only pieces that can travel are
the petal-shaped ones. They come in 2 orientations such that the
vertical petals can only move horizontally and the horizontal petals
only vertically. In that regard it reminds me a little of the 15
puzzle and seems to have roughly the same difficulty.



Thanks Roice!



-Melinda




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