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Part 1 of these postings is here: viewtopic.php?f=11&t=1123

If you want to skip all the text below, here's what you want to download:
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Open this link:
https://drive.google.com/folderview?id= ... sp=sharing
Select "For Golly 2.4" or "For Golly 2.5", and then download ""Tiling Project Parts 1 & 2"
(These are the same files which were listed in Part 1.)
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In this post I'll cover the 22 tilings listed here:
http://en.wikipedia.org/wiki/List_of_co ... rm_tilings
(I suggest opening this link in another window for reference)

Hexagonal tiling and regular triangular tiling are covered elsewhere on this forum.

Hexagonal Tiling: See viewtopic.php?f=7&t=263 , viewtopic.php?f=11&t=632&p=4342 , viewtopic.php?f=11&t=1027 , viewtopic.php?f=11&t=935, and others as well.

Triangular Tiling: See Andrew's Trilife script, and viewtopic.php?f=11&t=960&p=7016 , viewtopic.php?f=11&t=965 , and viewtopic.php?f=11&t=1023&p=7417

Excluding square, hex, and regular-triangular tilings, that leaves 16 tilings.

Of the 16 tilings, using only lifelike rules, I found spaceships in 14 of them -- I couldn't find spaceships in Pentagonal Floret tiling or the related Deltoidal Trihexagonal tiling. This was a surprise to me, as tiles in the two tilings have 8 and 9 neighbors respectively, as opposed to some of the more exotic tilings.

Of the 16 tilings, I could figure out how to emulate all but two of them in a reasonable number of states -- I couldn't find a Golly-compatible emulation for Triakis Triangular tiling or Kisrhombille tiling, although I was able to emulate them on my own CA program, and could find spaceships and other patterns that way.

Here's a rundown of the 16 tilings:

Truncated Square Tiling: Octagons with 8 neighbors and squares with four neighbors alternate on a checkerboard. This tiling's emulation is nice in that Golly cells don't have to be split into tiles -- instead, the Moore and von Neumann neighborhoods can stand in for octagons and squares. To show which cells touch, octagons can be represented with square icons, and squares can be represented with diamond icons.

In other threads on this forum, people have discussed alternating between the Moore and Von Neumann neighborhoods by generation, or by birth and survival (8 neighbors for birth, 4 for survival), so this tilling can be seen as another way to alternate - in space -between the two neighborhoods.

Many of the B2 rules are non-exploding rules with spaceships, puffers, rakes, etc. I didn't explore this tiling very much, as it seemed less exotic to me than many of the others, but there are almost sure to be lots of B2 rules which allow for interesting engineering (guns, etc). TruncatedSquare-B2/S346 has ships, puffers, and rakes. There is a a very common naturally occurring backrake, and its mechanism relies on briefly creating and then destroying a forward traveling spaceship.

Tetrakis Square Tiling: I thought this tiling would be a bit boring - just another triangular tiling - but it is fun.
TetrakisSquare-B1/S is the most lifelike B1/S I've ever seen! Spaceships, puffers, breeders, etc. Various B3 and B4 rules have spaceships.

Snub Square Tiling: Squares with 12 neighbors and triangles with 9 neighbors alternate. This link shows how the tiling can be implemented on a checkerboard: http://en.wikipedia.org/wiki/Snub_squar ... ed_tilings
B3 rules readily form spaceships, although many of them slowly explode as spaceships collide and form new spaceships. B3/S23 has sparky spaceships, and has analogs to small life patterns - the blinker, the tub, the barge, etc. I thought it was funny to see a blinker made of triangles and squares.

Cairo Pentagonal Tiling: This tiling was covered in part 1. To be continued.

Trihexagonal Tiling, also known as the "Kagome Lattice": For an example of Kagome basketweaving, see http://en.wikipedia.org/wiki/Trihexagonal_tiling . To emulate this tiling on the square grid, a square cell is split into a hexagon and two triangles. Each hexagon has 12 neighbors, each triangle has six neighbors. For each tiling I always try B3/S23 first, and Kagome didn't disappoint -- Kagome-B3/S23 is the most interesting Kagome rule I've found. It explodes but it never degrades into static -- instead, patterns readily become a never-ending cascade of spaceships and puffers. As with Life, there are many variants of this rule (B36/S23, B36,12/S23, etc), some explosive and some more quiet.

Truncated Hexagonal Tiling: Dodecagons and Triangles. Despite using exotic-looking Dodecagons, this tiling is topologically just like Kagome, except that the triangles have only 3 neighbors while the Dodecagons (which can be represented by hexagons) still have 12 neighbors. This appears to be the best tiling of the 16 for creating interesting rules with lifelike dynamics. And best of all, it is a non-alternating rule.

TruncatedHex-B2/S2 is mildly explosive but generates lots of spaceships and is pleasant to watch on a torus - it does not degrade into static. TruncatedHex-B26/S3569 has sparky spaceships and a giant useful oscillator. The oscillator can be used in pairs to make guns, it can also be used as an eater or as a 90 degree or 180 degree reflector. The sparky ships can be paired up to make rakes and puffers. TruncatedHex-B26_S3569b and TruncatedHex-B26/S3569bc (adding 11 and 12 to the survival rule) allows for all of the above plus a sparky p466 blob-shaped oblique ship. TruncatedHex-B26_S3569ab (adding 10 and 11 to the survival rule) converts the giant oscillator into a pretty bizarre natural gun. It travels back and forth, expands and shrinks, and fires spaceships in many directions.

I'm sure there are many more interesting rules to find. My only regret is that I adapted the hexagon and triangle icons from Kagome, where the triangles have their tops cut off to show fewer neighbors. It would be nice to have icons which really looked like Dodecagons and triangles!

Rhombic Tiling: A hexagonal cell is split into three rhombuses, and each rhombus has 10 neighbors. This was the first tiling I tried. I thought it might fill a gap between normal life and the Penrose tiling CAs which were in the news recently. I did find Rhombus rules with spaceships, but overall Rhombic tiling is a bit disappointing. You can see some spaceships in the patterns folder. ( I suppose I was expecting something marvelous and didn't find it, and that's what prompted me to try the other 15 tiles - one of them had to be better!)

I also tried the von Neumann neighborhood (no spaceships, of course), and I also tried a 8 neighbor version which excluded the middle corner cells, and a 6 neighbor version which included only the middle corner cells. I didn't find any good rules for any of these VN variants. Finally, I tried a Radius 2 version of the VN neighborhood, in which each rhombus has 12 neighbors (kind of like HexStar). There were a number of rules with spaceships, but again, these rules were a bit disappointing.

Triakis Triangular Tiling: This was one of the tilings I couldn't figure out to implement in Golly with a reasonably low number of states. Each triangle has 21 neighbors, and the straightforward way to emulate it was to take the Rhombus code and split each tile in half, yielding 64 states. I implemented it that way using my own program, and didn't find many spaceships. The tiling was interesting, however, in that there was an unusual progression from exploding rules to non-exploding rules to exploding rules again. Ordinarily, if B2 rules explode and B3 rule don't, then you can expect that B4, B5, B6, and all higher Bn rules also won't explode. That's not the case for Triakis Triangular tiling: B2 rules explode, B3 rules don't, but B4 rules explode, and B5 rules don't, and B6 rules do again. As for spaceships, I spotted a puffer in B3567/S02358, and there are ships in exploding rules like B4/S4 and B68/s5.

Kisrhombile Tiling: This tiling has lots of interesting rules. B3/S23 has spaceships and puffers, and many other rules are even more interesting. Kisrhomb-B1/S1 has spinners and spaceships. Kistrhomb-B3/S26 has interesting blobs and common spaceships, and some of the blobs turn out to be slow moving spaceships as well. Kistrhomb-B3/S4 has common sparky ships, oscillators, and stillifes. Kistrhomb-B3/s49 isn't very interesting, except that it has a cute spaceship. Kistrhomb-B3/s48 is a nice rule, with common blobby puffer, and has a normal-looking but less common spaceship as well. Kistrhomb-B3/s23,14 has a natural breeder of dot puffers which create a lattice. And so on!

Unfortunately, this was the other tiling I couldn't figure out how to implement for Golly in a reasonably small number of states. For my own system, where state is a just a number, I implemented this tiling by dividing a hexagon into 12 parts, yielding 4,096 states. For Golly, we could implement it in 29 states, much lower than 2^12, but 29 is still too high to tackle using Golly's make-ruletree code. (Where does 29 come from? We'd use four types of Golly cells, each split into three parts, yielding 7 states per split cell * 4 types of split cell + 1 more state for the background = 29 states.)

Floret Pentagonal Tiling: I covered this tiling in Part 1.

Deltoidal Trihexagonal Tiling: This tiling is very similar to Floret Pentagonal tiling: it can be emulated straightforwardly by dividing a hexagon into six parts (yielding a 64 states CA) and a bit less obviously by dividing three kinds of hexagons (yielding a 10 state CA). A number of B34 rules have long-lived chaos, but I haven't seen any rules with spaceships. B1 rules surprised me a bit when a single cell created a linear replicator instead of showing ordinary B1 behavior. I thought maybe the replicators could be paired up to create a spaceship, but no luck so far.

The next three tilings are a bit of a stretch and the icons don't really show which cells are neighbors by themselves; they are just used to keep track of which cells are of the same kind.

Rhombitrihexagonal Tiling: This tiling can be seen as having two kinds of rules, a row in which a hexagon and a square alternate, and a row which consists of "spears", consisting of squares and triangles. The upward pointed spears alternate with the downward pointed spears. Complicating things, the next two rows are offset from the first two rows before the pattern repeats. Looking at the diagram in the neighborhoods folder will help!

Spaceships were hard to find in this tiling, but there is a common spaceship in Rhombitrihexagonal-B3468/s239 which is mildly explosive, and there is a rare spaceship in Rhombitrihexagonal-B346/s239 which is a non-exploding rule.

Truncated Trihexagonal Tiling: This tiling is topologically just like Rhombitrihexagonal tiling, except that the "spears" are now replaced with hexagon & square pairs, and, on the next row, the central hexagons are replaced with dodecagons. The relationship is much like the one between Kagome and Truncated Hexagonal tiling: once again, a hexagon icon can stand in for a dodecagon, and the code for the script can be reused with the neighbors changed just a bit.

B2/S2 has a spaceship and a puffer. There were many replicators among the B2 rules -- B2/S23, B2/S24, and B2/S26 all had distinctly different linear replicators.

Snub Hexagona (or "Snub Trihexagonal") Tiling: Finally, this tiling is also topologically just like Rhombitrihexagonal, except that all the squares are split into triangles. Emulating this tiling took 19 states, which meant my computer had to run all day and night just to create one Golly rule. It is too bad it takes so long, because there are a number of interesting rules: many rules had orbiters -- oscillators which appear to be a spaceship traveling in a circle and many rules had spaceships, some had both. In SnubHexagonal-B3/S247, all random patterns ended up resolving themselves as orbiters. Sparky spaceships are very common in SnubHexagonal-B389,10/S247,10 - it looked like a good candidate for constructing a rake. SnubHexagonal-B389,10/S247,10,13,15,18 had many interesting dynamics, where spaceships bounced off oscillators. SnubHexagonal-B37/S247,10 had a very diffuse sparky blobby ship.

Prismatic Pentagonal Tiling: I covered this tiling in Part 1.

Elongated Triangular Tiling: Squares with 12 neighbors and triangles with 9 neighbors alternate. This tiling is a rearranged version of Snub Square tiling, where Snub Square's checkerboard is replaced by neat rows. Like Snub Square Tiling, B3/S23 resembles Life -- there is a common spaceship (although it only travels horizontally), and there are blocks, blinkers, honeycombs, ponds, loaves, etc, but of course, they look funny as triangles alternate with squares. The spaceship from B3/S23 works in many other B3 rules as well. Other spaceships are also common in B3 rules; ElongTri-B36/S23 stood out in that it has a spaceship that looks like an LWSS in one phase.

I thought this tiling might be like its dual, Prismatic Pentagonal tiling, in that all spaceships in lifelike rules travel along one axis, but then I found ElongTri-B3/S2489, which has a very commonly occurring rake which travels in an oblique direction!

One More tiling...

Tri-Nonagonal ("Martini Lattice") Tiling: I found some of the above 16 tilings to be a bit of a stretch for Golly, so I thought I'd try to find "the perfect Golly tiling": it would have to have an unusual shaped tile, it would have to be non-alternating, and it would have a very low number of states. Looking through a list of tilings, this one fit the bill, with nonagons(!) with nine neighbors and triangles with three neighbors, in a CA with just four states. I started calling this tiling "Tri-Nonagonal" before I found that it already had a name - the "Martini Lattice" (See http://en.wikipedia.org/wiki/Percolatio ... i_lattices).

Spaceships are abundant in B2 rules. The most interesting thing I saw in Tri-Nonagonal rules was a natural forward rake/puffer in B26_S359 and B269-S359. The rake fires spacecraft directly ahead of itself. Have a look!

A coding idea for the future: The hard part of the project was to come up with the topologically equivalent tilings in the Neighborhoods folder. Creating the rule-generating scripts for the neighborhoods was fairly mechanical - all the scripts follow the same template, or at least, they could all fit into one template. It might be a fun project to actually mechanize the process. I'm envisioning a script rather like the icons-import.py script now provided with Golly version 2.5. Neighborhood icons would be entered by the user into sets of 9x9 grids like those in the Neighborhoods folder. As in the Neighborhoods folder, for each set, a central tile would be designated by the user, and the central tile's neighbors would also be designated by the user. When the user was finished, a script like icons-export.py would scan the user input and export code for a rule-generating script.