DominoLife (CA on aperiodic domino tilings)

[Andrew]

I've written a Lua script called DominoLife that lets you explore various CA rules on aperiodic domino tilings. The tilings are created using simple substitution rules, as in these two examples:

https://tilings.math.uni-bielefeld.de/s ... on/domino/
https://tilings.math.uni-bielefeld.de/s ... o-variant/

The script runs within Glu, not Golly, so if you want to try it out you'll need to download Glu 0.8 or later:

https://sourceforge.net/projects/glu1/files/

After starting up Glu, select "Download Script..." from the File menu and click the link for DominoLife. A button called DominoLife should appear in the DOWNLOADS column. Hit that button and select View > Help (or type H) for details on how to use the script.

You can see a screenshot showing DominoLife's interface at the bottom of Glu's website:

https://glu1.sourceforge.io/

I've also put a collection of interesting patterns/rules/tilings on my website:

https://www.trevorrow.com/glu/DominoLifePatterns.zip

Have fun and let me know if you find anything interesting or have suggestions for improving the script.

[Andrew]

The pattern format used by DominoLife is text based, so sharing discoveries is easy. Select and copy the following to the clipboard, then choose "Open Clipboard" from DominoLife's File menu (or just type shift-O):

Code: Select all

DominoLife version=1
# This rule has only(?) two oscillators in the Domino tiling:
# A weird p31 and a p4.
view=9 558 297
tiling=Domino
level=8
rule=B25S2N4
7843=2 7844=1 7845=1 7848=1 7849=2 7850=2 7851=1 7852=1 6337=2 6339=1
6340=1 7833=1 7835=1 7836=1 6349=1 7841=1 7842=2 10237=1 10228=2 10240=1
8599=3 10238=2 10232=3 10227=1

You should see something like this (I've scaled the image to half size):

p31p4.png (65.23 KiB) Viewed 1041 times

[Andrew]

Because the Domino tiling is not periodic, tiles can have quite different neighborhoods:

neighbors.png (12.75 KiB) Viewed 1031 times

The yellow tile on the left has 9 neighbors (the maximum number) made up of 6 orange tiles that share an edge and 3 red tiles that only share a corner. The yellow tile on the right has only 5 neighbors (the minimum number).

DominoLife supports rules that behave much like those used by Golly's Generations algorithm, but with a different syntax. For example, B3S23N2 is a 2-state Life-like rule (but unfortunately no gliders it seems). If the rule string ends with E then only neighbors that share an edge are counted. If it ends with C then only corner neighbors are counted, so a rule like BS0N2C can be used to find tiles that don't have any corner neighbors, as in the above yellow tile on the right.

[Andrew]

I've uploaded a new version of DominoLife with the following changes:

* Increased the maximum states in a BSN rule from 4 to 9.
* Added a Detect Oscillation option to the Control menu.
* Added a Show History option to the Control menu.
* Select All now selects history tiles as well as live tiles.
* The translucent paste pattern can be reflected/rotated using keyboard commands (X, Y, period, comma).

This image illustrates oscillation detection and history tiles (light blue):

p31.png (116.17 KiB) Viewed 603 times

PS. Sci-fi fans might also want to download TheNuMoon, a short movie about Elon Musk's 13th son.