ConwayLife.com

Here's a link to Printables for these clips: https://www.printables.com/model/1843383-clips-and-panels-for-building-wieringa-roofs

I did some redesign and added printable panels as well as a guide for cutting business cards.

The pins are 72º, 108º, and 144º, which is the complete set of dihedral ...

Using printed clips angled 72, 108, 144 degrees and old business cards. You can see it roughly casts the expected shadow.

Latest Penrose variation: 3D-printed Wieringa roofs. https://www.printables.com/model/1830985-modular-pieces-for-a-wieringa-roof-penrose-tiling

These came out well. I'm surprised I have not gotten more downloads on Printables. There are four pieces consisting of assemblies of golden rhombuses with ...

Re: documenting one's own discoveries, I'd say that the next major place to store discoveries after a local hard drive is not the LifeWiki. It's a dedicated thread on the forums.


If someone has a large body of work of any kind that they want to make available, not just Life or CAs, the first ...

You've got a point. IMO I wouldn't consider this place an "academic forum". A place where formality is expected, sure. But most of us aren't actual researchers putting out studies on this stuff, because at the end of the day cellular automata isn't a very complex subject. It can just be made ...

Here is my printables page in case anyone wants to print one of these.

PLA: PLA showing tiling: In jesmonite, painted for contrast:

I am not sure if there's an official rule about whether continuous iterative systems count as cellular automata, but this may be of interest.

I Claude-coded most of this (both Python and Javascript) and would not have had time to write it myself. Sorry if it's a little bloated. It has more features ...

I was planning to kill the 12x12 periodic search when after a week or so it came back unsatisfiable. Take that with a grain of salt. It never even looked at 12x13, and because it's periodic, it does not rule out smaller sizes either.

This isn't very meaningful without the instance. I can post that ...

I was considering starting a real discussion about this under other CA, but for now I will just post it here:

https://html-preview.github.io/?url=https://github.com/PaulBC/misc_scripts/blob/main/gray_scott_explorer.html

It's a Claude-coded "explorer" for finding Gray-Scott parameters. It came out ...

Here are two 13x13 periodic still life patterns with this property. I have one running for 12x12 but it has been going for days. It seems to make some progress so I might keep it running until my laptop restarts.

I haven't looked for a 12x12 finite pattern because I thought the periodic one would ...

I don't know if this has been constructed before. It's not an intrinsically interesting pattern, but it satisfied my curiosity and was a good SAT solver application. It's a 14x14 still life that uses all 51 3x3 still life neighborhoods up to D4 symmetry. It's not proven minimal so maybe someone can ...

This won't be catching any sun but it's a different aesthetic. It is cast in AC730, a stone-like material, and I painted the grooves for contrast. Maybe I should make some cellular automata patterns like this. Either single generations of CGOL or rows of Rule 110.

Continuing in this vein, we can go back to 3x3 still life windows, which have already been explored pretty thoroughly. There are 259 that have a center cell assigned consistently with its neighborhood, and no internal crowding. These can all be stabilized as I recall, and I am hoping to construct a ...

This might be known and I might have even checked before but I don't remember.

I was looking at 4x4 windows in CGOL that potentially can be part of a still life according to local constraints. Specifically, the cells in the center 2x2 window must have 2 or 3 live neighbors of live cells and not ...

I'm curious if anyone has worked on this. It seems like a natural "puzzle" question about still life patterns though not of deep mathematical interest.

First what is known: take 3x3 neighborhoods. Some can be ruled out as part of a still life, e.g. if the center cell is a violation or if the center ...

I finally got around to making a mold for the other phase of the glider up to symmetry. You can make a mold for the symmetric phases just by printing a mirror image, or you can flip the pieces themselves upside down.
20260706_071608.jpg You need to add a few extra drops of silicone in the mold ...

Another idea: decorative motifs based on dense symmetric still life patterns. I printed this one very small as a test, but it could be printed 10cm in diameter as a coaster or cast in clear resin. There is nothing unique about this pattern, but the conditions of symmetry, density, and the still life ...

Resin cast of symmetric periodic hexagon. PLA original embedded as a coaster.

Back to my writing.

Finally, here is the looping animation, which you can generate with python3 bz_phase_render.py -n 200 -p 1.0 -r 3 -i 700 --skip 450 --seed 42 \
--phase-blur-sigma 1.5 --gif --gif-frames 60 --gif-fps 20 --gif-size 400 -o bz_phase
bz_phase_loop.gif

The discontinuity at the ...

I'm posting here, rather than sandbox, because Belousov-Zhabotinsky (BZ) simulations are similar to cellular automata, though continuous, and there are discrete CAs like hodgepodge with analogous characteristics. You can see some of my other BZ postings on sandbox. Those are more oriented towards ...

Seamless Belousov-Zhabotinsky rhombus tiles. They tile both rotated and flipped and the boundary conditions were tricky to get right. Still a work in progress but moving along. The continuity on boundaries could be better and there might be way. I've also learned a little about how these ...

I'm still working on this, but I can now set boundary conditions for 60-120 rhombus that tile both rotated and flipped. The continuity is sometimes a little off but on the whole the effect is believable. I will make some 3d-printed snap tiles when I get a chance.

Printable for anyone interested: https://www.printables.com/model/175446 ... ative-disk

I have plans to make this more general using tiles and other runs of the pattern.

I wanted to see how this came out with a glossy lens-like surface. First, here's the silicone mold after coating with more silicone. You can see how the leveling and the meniscus turns all the cells into concave mirrors reflecting the overhead light. 20260613_073732.jpg

Cast in clear resin, they ...

This is not a suncatcher yet. Here is a 6cm 3D-print of a symmetric Belousov-Zhabotinsky pattern. It captures the intensity as a height map but does not vary in color. 20260613_165508.jpg

I could print one or maybe something larger, mold it and cast it in resin (maybe smoothed out or maybe with ...