HatLife

Post by **Andrew** » May 11th, 2023, 1:34 am

There wasn't much interest in DominoLife, but I didn't let that discourage me! I've written another Lua script called HatLife that lets you explore CA rules on an aperiodic tiling using the recently discovered monotile known as the hat. Details here:

https://arxiv.org/pdf/2303.10798.pdf
https://www.quantamagazine.org/hobbyist ... -20230404/

HatLife runs within Glu, 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 HatLife. A button called HatLife should appear in the DOWNLOADS column. Hit that button and select View > Help (or type H) for details on how to use the script.

Here's a couple of screenshots:

https://glu1.sourceforge.io/screenshots/hatlife.png
https://a.fsdn.com/con/app/proj/glu1/sc ... /max/max/1

Bug reports and suggestions for improving HatLife are all welcome.

EDIT: It seems some people are unable to download files from SourceForge, so here are alternative links to Glu and HatLife:

https://www.trevorrow.com/glu/glu-1.1-mac.dmg (Glu 1.1 for macOS)
https://www.trevorrow.com/glu/glu-1.1-win-64bit.zip (Glu 1.1 for Windows)
https://www.trevorrow.com/glu/glu-1.1-gtk-64bit.tar.gz (Glu 1.1 for Linux)
https://www.trevorrow.com/glu/glu-1.1-src.tar.gz (source code for Glu 1.1)
https://www.trevorrow.com/glu/HatLife.zip (HatLife version 2)

Post by **Andrew** » May 11th, 2023, 2:00 am

When HatLife starts up it reads a file called tiling.txt to create the hat tiling. This file was created by a separate script that extracted a large rectangular region of hats from 5 iterations of the H7/H8 substitution method described in the arxiv paper. It should be quite easy to replace tiling.txt with another hat tiling. See HatLife's help for details.

The tiling has a total of 21,781 hats: 19,008 normal hats and 2,773 reflected hats. Note that HatLife has the option of displaying dead reflected hats using a slightly darker gray. Untick View > Show Reflected Hats to turn off that option (or hit alt-R to toggle it).

Post by **Andrew** » May 11th, 2023, 2:16 am

HatLife supports rules with a variety of formats:

Bbbb...Ssss...Nn[E]

These rules behave like those used in Golly's Generations algorithm. The b values (1 to 7) specify the state 1 neighbor counts necessary for an empty hat to be born (as state 1) in the next generation. The s values (0 to 7) specify the state 1 neighbor counts necessary for a state 1 hat to survive to the next generation. The number n specifies the maximum number of states (2 to 9). If n is greater than 2 then hats don't die immediately but "decay" to the next higher state, or 0 if at the maximum state (n-1). A hat's neighbors normally includes all other hats that share an edge or a vertex, but if the rule ends with E then only neighboring hats that share an edge are counted.

RrBbmin-bmaxSsmin-smaxNn

This format is based on the Larger than Life rules. The r value (1 to 5) specifies the number of rings of neighboring hats surrounding the central hat. Note that the total number of hats in this neighborhood varies from hat to hat (a reasonably accurate upper limit is 4r(r+1)). To see the neighborhood, enter a rule like R5B1-1S1-1N2, set a hat to state 1 and advance one generation. The bmin and bmax values specify the range of state 1 neighbor counts necessary for an empty hat to be born (as state 1) in the next generation. The smin and smax values specify the range of state 1 neighbor counts necessary for a state 1 hat to survive. The minimum value in both ranges must be less than or equal to the maximum value, and bmin must be greater than 0. The number n specifes the maximum number of states and hats decay just like in the above BSN rules.

WireWorld

A simple implementation of Brian Silverman's Wireworld CA. I think this rule is also Turing-complete on the hat tiling (see below).

Worms

This rule was designed to support spaceships ("worms") that travel within the wide gaps between two parallel lines of reflected hats (the worms don't survive for very long within the thin gaps). Worms are extensible with a minimum length of 4 hats. The Worms rule also supports still lifes, oscillators, wickstretchers and possibly other objects (a worm gun anyone?) that might be useful for determining if this rule is Turing-complete.

A new rule can be entered via Control > Change Rule, or created randomly via items in the File menu.

GUYTU6J · Post by **GUYTU6J** » May 11th, 2023, 3:40 am

B35S234N2 has long-lived soups from which oscillators emerge.
p7