Search found 490 matches

by pcallahan
May 21st, 2016, 1:40 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Open question: how many new tiles (colored appropriately) would we need to add to represent the non-stable neighborhoods. These would include the dead cells with three live neighbors (birth) and live cells with 0, 1, 4, 5, 6, 7, 8 neighbors. By making the top surfaces interlocking (nub->nub birth, d...
by pcallahan
May 21st, 2016, 1:30 pm
Forum: General Discussion
Topic: Realizing CGOL rules in mechanical unit
Replies: 28
Views: 15755

Re: Realizing CGOL rules in mechanical unit

I'll try to read this more carefully, but I have often thought about this kind of thing before. One idea I did not see on the thread is using a system of siphons. I'm not totally sure how that would work, but I'm imagining the kind of system (like in a toilet tank) in which exceeding a certain water...
by pcallahan
May 20th, 2016, 10:16 am
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

If one treats the grey tiles and white tiles as being the same color, the second problem becomes moot, as empty space is still empty space, regardless of whether the tile divisions occur on cell boundaries or not. I never thought the extra tilings were serious problems, but I like this explanation ...
by pcallahan
May 19th, 2016, 9:39 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

That's really cool. Pictures like that at thingiverse might increase the probably of someone trying it out. (As well as removal of the old pictures from previous attempts at the tiles, which will just confuse people.) Can OpenJSCAD confirm that the pieces fit together as placed? (No intersections at...
by pcallahan
May 19th, 2016, 2:14 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Thanks! I got OpenJSCAD to work, but I would not have thought of copy-pasting the code like that. Hmm... appletviewer is an executable that should come with any Java JDK, but it might not be in your path. It's a shame that applets never caught on and are now effectively deprecated for security reaso...
by pcallahan
May 19th, 2016, 1:17 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

When I try to open it in OpenJSCAD I get this error:
"Error in line 28: Uncaught SyntaxError: Unexpected identifier"
by pcallahan
May 19th, 2016, 9:49 am
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Also looking at each edge of pretty similar tiles, and figuring out its key, is also a disaster. If I were doing the tiling, I would consider the visual cue to be the fact that you can't have 3 teeth around an empty cell or 4 teeth around a live cell. The edge constraints would just be there to sto...
by pcallahan
May 18th, 2016, 11:24 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

By the way, I noticed that in your most recent tile set, the blue and whitish teeth are the same width. There is a problem with that, which I mentioned before. You need to make sure that the blue/blue boundary is different from the blue/white boundary or else you can place tilings that aren't still ...
by pcallahan
May 18th, 2016, 7:05 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Taking this in the other direction, I thought it would be useful to see calcyman's tile set with most of the magic taken away. I think this is accurate Screen Shot 2016-05-18 at 3.47.50 PM.png Assigning letters arbitrarily based on mnemonics: L is "lonely", C is "crowded", s/S is "survives." (but S ...
by pcallahan
May 18th, 2016, 9:26 am
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

EDIT4 I think for the 4 and more teeth we can use this holder: The quarter tiles also need to fit together by themselves, e.g. for this neighborhood: Screen Shot 2016-05-18 at 6.21.07 AM.png I'm not sure what can be done with that tile set without adding a new connector tile. If the white teeth are...
by pcallahan
May 18th, 2016, 1:36 am
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

I found one problem in this partial tiling around the block. You might not have realized that the cross piece does double duty both connecting live neighborhoods and forming the corner between 4 live cells (which is where it originally came from). The trick is getting it small enough to fit inside t...
by pcallahan
May 18th, 2016, 1:03 am
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

BTW took me time to realize the octagon for the living cells is smaller... You probably noticed this by now, but the blue teeth are constrained to meet at the boundary of the octagon the tiling is based on. There is more flexibility with the white teeth, because you can shrink the inner part of the...
by pcallahan
May 17th, 2016, 9:21 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Nice images! Now I would really like to see a set of those 3D printed. I'm personally not that worried about the pattern holding together. Most tilings don't (e.g. Penrose). With solid enough material on a surface with a little friction, you wouldn't be worried about the pieces moving themselves aro...
by pcallahan
May 17th, 2016, 4:04 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Adding bump will not actually work - because some of the shapes require all 8 symmetry options, and this means you can't chose the location of the bump, so two bumps could meet. Sorry. My explanation was incorrect. This is what I was thinking of, though it is a somewhat optimized since my first tho...
by pcallahan
May 16th, 2016, 8:40 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

I was thinking, if we want to make some sort of physical puzzle game out of these tiles - we need to make sure they can be attached properly. You raise some good points and I have been wondering about similar issues. There are some unavoidable constraints as I see it. Matching edges need to be flip...
by pcallahan
May 16th, 2016, 12:43 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Are these relation guarantee a still life? And can any still life be represented this way? I am nearly certain about the second point (any still life can be represented), but the first requires proof. There is one trivial tiling of the plane by square pieces, but ignoring that one, I do not see any...
by pcallahan
May 16th, 2016, 1:57 am
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Here is an eater constructed with calcyman's tiles. I resisted the urge to reverse engineer the coordinates and just turned them into transparent pngs and pieced it together by hand in Google drive draw.
Screen Shot 2016-05-15 at 10.55.02 PM.png
Screen Shot 2016-05-15 at 10.55.02 PM.png (236.45 KiB) Viewed 15350 times
by pcallahan
May 15th, 2016, 8:53 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

If I'm not mistaken, the only reason to use the cross-shaped piece and not the square to connect blue neighborhoods is to preserve the color. I guess my preference is to keep the tiles simple and not worry as much about color. Actually, I like your 19-tile set (which I think is really 18 if you spli...
by pcallahan
May 15th, 2016, 1:38 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Thanks! I like the fact that no whole neighborhoods are needed.
by pcallahan
May 15th, 2016, 11:53 am
Forum: Patterns
Topic: The Hunting of the New Herschel Conduits
Replies: 968
Views: 715600

Re: The Hunting of the New Herschel Conduits

Thanks. I don't mean to sound defensive. I'm just happy it had a long life after I was done with it--and maybe my year in Switzerland was not The World's Most Pointless Postdoc Ever (TM) after all. I will probably need to retire before I have a chance to get back to any serious searching for conduit...
by pcallahan
May 15th, 2016, 10:57 am
Forum: Patterns
Topic: The Hunting of the New Herschel Conduits
Replies: 968
Views: 715600

Re: The Hunting of the New Herschel Conduits

and turned out ptbsearch set some random value hard-coded without any logic ptbsearch was not originally written for public release (I am no longer even sure of the circumstances under which it was released at all) so it contains a hodgepodge of assumptions that made sense during my search for glid...
by pcallahan
May 14th, 2016, 11:27 am
Forum: Patterns
Topic: The Hunting of the New Herschel Conduits
Replies: 968
Views: 715600

Re: The Hunting of the New Herschel Conduits

At first I was surprised that the H->MWSS wasn't found 20 years ago, but I can at least see how I missed it. I probably collided herschels with boats at some point, but not with a block catalyst present, and I would never have found it looking for faster perturbations. Very impressive find!
by pcallahan
May 14th, 2016, 9:58 am
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

calcyman wrote:I have a 16-tile set without this problem, coming soon...
I am eagerly awaiting it.
by pcallahan
May 13th, 2016, 4:57 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

calcyman: there is one problem I see with the axis-parallel splits you used. You can get infinite linear boundaries like this and slide entire sections of the tiling. Screen Shot 2016-05-13 at 1.52.57 PM.png I'm divided on whether this is a bug or a feature, because I think you will still get a vali...
by pcallahan
May 13th, 2016, 4:31 pm
Forum: General Discussion
Topic: Realizing still life constraints as a planar tiling
Replies: 110
Views: 48989

Re: Realizing still life constraints as a planar tiling

Kazyan, as biggiemac explained, the problem is two-sided. It must (1) be possible to represent any still life as a planar tiling with your tile set (which your solution would do), and (2)any possible tiling should correspond to a still life. There may be multiple tilings that represent the same stil...