Dr. Andrew Thomas, PhD. Electrical Engineering, performed the first successful experiment on March 12, 2009 of a repeating Triangular Cellular Automata in his flat at Swansea in Wales, based on the square-based Game of Life by John Conway. The first (and still simplest, for squares) repeating GoL automata was invented by Bill Gosper based on a challenge by Conway and is now known as Gosper's Gliding Gun. Thomas' accomplishment is similar, based on a challenge by yours truly, who invented the idea of triangular GoL.

This is the first known and currently only known experiment of its kind ever performed, that is to say on a triangular version of Conway's Game of Life.

Here is Thomas' notebook page document:

The purpose of this post to to alert others to its existence, in the hope that it will aid further research into Causal Dynamical Triangulations, which in turn it is hoped will provide better knowledge, at least on the theoretical side, of what is actually happening in Reality on the smallest Planck scale of length.

Also, it looks to be quite fun just to play around in one's spare time.

Sincerely,

Steven Colyer

Amateur Applied Mathematician (MathoMcPhysicist)

BSME, Rutgers, 1979, Pi Tau Sigma

MBA, Rutgers, 1989

July 20, 2010

## 2 comments:

Hi Steven, thanks for that, but I wouldn't get too excited as I am sure John Conway considered hundreds of possible designs for the Game of Life before settling on his final version. I'm sure he considered the idea I sent you.

I think one of the most interesting things about the field of cellular automata is that nothing very useful has come from it (despite what Steven Wolfram claims). It's an area which just hit a dead end.

Hello, old friend, but you assume much, to whit:

What if Conway

didn'tconsider it? What if he found squares more interesting than triangles, and therefore he thought it more of a challenge? He did quite well with that challenge, wouldn't you say? I think so.We speak of "reality" though, Andrew. In "reality", I see no squares. I see plenty of ellipses and near circles and squashed spheres and circular-ish spirals and big ovoidal elliptics, yet very few squares and cubes.

Every three points form a triangle, but not every four points form a square. In fact, they usually don't.

Indeed, "The Great Square of Pegasus" among the constellations, is close, but not exactly.

I think this is why you may think cellular automata don't matter that much, and it's not just you.

We do after all live in "the Digital Age", which worships the x-y plane and x-y-z 3D and other squarish categories. There ARE other categories, and all I am asking is ...

... that the others be fully explored, before rejecting them.

And frankly, man? If you were to plot in Quadrant I, that is to say in the NE of the x-y plane, "Number of Occurrences" on the y-axis, and the integers on the x-axis? If you were to do so? If you were to do so, I bet you'd guess the shape would be a hyperbola. But in my explorations, I would disagree. I think you would see a "bump" at number: 3. And what the hell is the function that describes

that, if so?Lee Smolin has a nice piece in one of his books that Descartes set us on our current road that the whole x-y-t thing (in 2S+1T space) in terms of axes has "stultified" our thinking.

And our current road, Andrew, has provided more roadblocks than answers over time, especially in the last 30 years.

I'm open to Lee's thinking, at least until it is proven wrong. I see no reason to quit before we start, or just as we've started, so to speak.

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