Exploration of Rules with Varying Isotropic Neighborhoods

[Saka]

The rules we have mostly explored so far use the Moore neighborhood, some use vonNeumann and Hexagonal. However, those three neighborhoods, along with their LTL extended versions are all we have pretty much explored so far (LTL circular and Triangular neighborhood rules have been explored, but just a little bit.).

However, I would like to start exploring rules with different neighborhoods, a few shown below, with white being the center cell and red being the neighbors.

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x = 21, y = 5, rule = LifeHistory
D3.D5.D5.D3.D$2.D7.D6.3D$.DCD4.2DC2D4.DCD$2.D7.D6.3D$D3.D5.D5.D3.D!

I have created a (buggy) program that can run these rules called CoordCA, which can be found Here. All details can be found in that post and the README in the GitHub repository which is linked in that post.

What Has Been Found so Far?
Not much.
I have been searching for rules and apgsearching them for a while now (That is why "isotropic" is in the title.), and here's a collection things I consider interesting, across various rules:
1891891-2_3_2-3: 2c/12o, c/14d, p52, p19, p24 (Other periods can be found as well but these oscillators are more "interesting" to me.)

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x = 29, y = 23, rule=1891891-2_3_2-3
2bobo4b3o$3obo4bob2o$3b3o3b2obo$2bo7b2o$2bo7b2o9$2b3o9b2o9bo2bo$4o21b4o$o5bo5b2o2b2o$3b4o18b4o$2b3o9b2o10b2o$25b4o$14b2o9bo2bo$14b2o$14b2o$14b2o!

This (above) seems like the most interesting rule so far, so please search it (Use the "Generate APGTable" function in the "Simulation" menu. Also, please name the file "b3-s23-farcorners" to keep the searching in one place. The "farcorners" name is because this was before I made the CoordCA rule format.).

123BDC4-2_4-7-9_3-4-6: p8, c/2o, p6

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x = 11, y = 15, rule=123BDC4-2_4-7-9_3-4-6
8b2o$9b2o2$9b2o$2b2o4b2o$b3o$4bo$2b2o5$b2ob2o$6o$b2ob2o!

18B99D1-2_4-7-9_3-4-6: c/2o, p12, p21

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x = 28, y = 15, rule=18B99D1-2_4-7-9_3-4-6
3b2o$4b2o$3b2o$4b2o$3b2o6$b5o8bobo7bobo$2obob2o6b2ob2o5b2ob2o$2b3o$2bobo8b2ob2o5b2ob2o$2b3o9bobo7bobo!

As you can see, not much has been found, especially for moving objects.

Things I Would Like
Here are some things I would like to see come out of the exploration of these rules:

• Infinite growth.
• A "B3/S23" / Good birth and survival cell count for 12-cell neighborhoods, current best is B4-7-9/S3-4-6.
• Possible technology advancements.
• More spaceships.
• Possible new search programs.

Small Note
With these custom neighborhoods, you can have "rotated neighborhoods", which is one neighborhood rotated 45°:

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x = 18, y = 14, rule = LifeHistory
9.E5.D$2.3D4.2E3.D.D$2.DCD.6E.D.C.D$2.3D4.2E3.D.D$9.E5.D5$2.D6.E3.D.D
.D$.3D5.2E3.D.D$2DC2D.6E.D.C.D$.3D5.2E3.D.D$2.D6.E3.D.D.D!

These neighborhoods allow for 2 universes to exist simultaneously without interacting with one another:

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x = 16, y = 21, rule = 122A544-2_3_2-3
13bo$12bobo$bo9bo3bo$obo7bo$3bo11bo$o9bo2$12bo4$b2o$4o9bo$3b2o7b3o$2o
9b2ob2o$10b2o3bo$10bo4bo$10bo4bo$10bo$12bo$12bo!

While these are cool, they don't really do anything, so try to avoid rotated neighborhoods. You can tell a neighborhood is rotated by copying the pattern and pasting the copy it one cell to the right/left/up/down and running it; if it works like the original pattern, then it's a rotated neighborhood.

--
Please let me know if there's anything wrong with this post, thanks!

[fluffykitty]

You can also tell that a neighborhood is rotated by checking if all cells in the neighborhood have the same color.

[CARuler]

you can now use islptng's script for this

[confocaloid]

[...] 1891891-2_3_2-3: 2c/12o, c/14d, p52, p19, p24 (Other periods can be found as well but these oscillators are more "interesting" to me.)

Code: Select all

x = 29, y = 23, rule=1891891-2_3_2-3
2bobo4b3o$3obo4bob2o$3b3o3b2obo$2bo7b2o$2bo7b2o9$2b3o9b2o9bo2bo$4o21b4o$o5bo5b2o2b2o$3b4o18b4o$2b3o9b2o10b2o$25b4o$14b2o9bo2bo$14b2o$14b2o$14b2o!

This (above) seems like the most interesting rule so far, so please search it (Use the "Generate APGTable" function in the "Simulation" menu. Also, please name the file "b3-s23-farcorners" to keep the searching in one place. The "farcorners" name is because this was before I made the CoordCA rule format.).

The p14 spaceship appears to move two cells per cycle (p14 diagonal c/7), here is the same collection reposted in a supported format (custom neighbourhoods):

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x = 29, y = 23, rule = R2,C0,S2-3,B3,N@891891
2bobo4b3o$3obo4bob2o$3b3o3b2obo$2bo7b2o$2bo7b2o9$2b3o9b2o9bo2bo$4o21b
4o$o5bo5b2o2b2o$3b4o18b4o$2b3o9b2o10b2o$25b4o$14b2o9bo2bo$14b2o$14b2o$
14b2o!

[...] 123BDC4-2_4-7-9_3-4-6: p8, c/2o, p6

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x = 11, y = 15, rule=123BDC4-2_4-7-9_3-4-6
8b2o$9b2o2$9b2o$2b2o4b2o$b3o$4bo$2b2o5$b2ob2o$6o$b2ob2o!

[...]

The same collection reposted in a supported format:

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x = 11, y = 15, rule = R2,C0,S3-4,6,B4,7,9,N@23BDC4
8b2o$9b2o2$9b2o$2b2o4b2o$b3o$4bo$2b2o5$b2ob2o$6o$b2ob2o!

[...] 18B99D1-2_4-7-9_3-4-6: c/2o, p12, p21

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x = 28, y = 15, rule=18B99D1-2_4-7-9_3-4-6
3b2o$4b2o$3b2o$4b2o$3b2o6$b5o8bobo7bobo$2obob2o6b2ob2o5b2ob2o$2b3o$2bobo8b2ob2o5b2ob2o$2b3o9bobo7bobo!

[...]

The same collection reposted in a supported format:

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x = 28, y = 15, rule = R2,C0,S3-4,6,B4,7,9,N@8B99D1
3b2o$4b2o$3b2o$4b2o$3b2o6$b5o8bobo7bobo$2obob2o6b2ob2o5b2ob2o$2b3o$2bo
bo8b2ob2o5b2ob2o$2b3o9bobo7bobo!