It's things like this that help validate my hypothesis: If you define something in mathematical theory, eventually we'll find some way to use it for modelling something.

I've been fascinated by Cellular Automata since I read Wolfram "A New Kind of Science", but I was not overly sold that you could model the universe in the way he described.

While I still think he was incredibly over-optimistic about the uses of cellular automata, I do wonder if after a number of years we'll find some more validation in nature.

Wolfram's "A New Kind of Science" is extremely overstated.

On the other hand, I think Turing first suggested that animal coloration might turn out to be related to cellular automata. Sadly that's the kind of over-broad suggestion that turns out to be largely untrue, with possibly only a few exceptions. Mosty it's probably X-inactivation.

Well, now that it's morning I can't say that it's "mostly" X inactivation; male zebras and tigers are striped so that's not going to be X inactivation.

If you're interested in cellular automata, a must read is Greg Egan's short story _Wang's Carpets_, which later became a chapter in his novel _Diaspora_ (which is superb). It's not formally published on the interwebs but there are copies floating around everywhere.

Cellular automatons occur everywhere in nature. We don't really have the technology to explore them; I do find myself wondering if there are automata sophisticated enough to support complex structures, hiding in the higher-order interactions, which are completely invisible to us...

Yea, Diaspora was an excellent book.

Biology tends not to be much like the mathematical cellular automata; it's generally much messier. On the other hand, we're made up of lots of cells and all of those cells are just tiny machines following programs, so I guess it's true by definition. Still, it's nothing like the minimal automata everyone likes to play with.

His "permutation city" is directly about cellular automata.

Hah.. beat me to it :) I was about to recommend Permutation City while seeing your comment. That was an intense book, to say the least.

That's not really a hypothesis because it can't be disproven. More like a feeling. Evidence will accumulate to support it but nothing can weaken it. So it's already known to be as-good-as-true and not useful scientifically.

I'm actually working on a CA that'll hopefully reproduce primitive life.

Not Wolfram's way though.

https://scrollto.com/life-a-universe-simulation/

Have you read Permutation City by Greg Egan? It features a similar toy universe built as cellular automata idea.

No I haven't, I'll have to check it out, thanks for the reference.

Another cellular automata seen in animals:

https://en.wikipedia.org/wiki/Rule_30

Conus Textile is very cool - good examples look just like computer simulations!

This is what I got when I clicked on the link https://postimg.org/image/6n8pnqidj/

I thought it was some kind of joke or spam post until I scroll down to see this. https://postimg.org/image/onyt7vbdj/

Not the end when I tried to upload these screenshots to Imgur i received this https://postimg.org/image/z9g43te8n/

This is getting insane now postimg.org is down, don't believe check yourself https://ibb.co/mR1CO5

Since I can't update my comment now, here are updated links for the image

https://ibb.co/n79owQ https://ibb.co/d6F6i5 https://ibb.co/fo6CO5

Turing's paper [1] is pretty impressive. Well before the mechanics of molecular biology were understood, Turing was able to reason out how you could use a 'few lines of (reusable) (biological) code' to produce patterns as sophisticated (and seemingly unrelated) as zebra stripes, leopard spots, and even the shapes of tissues, the number of digits on a hand, and the morphology of even a whole organism. And he was mostly correct once we came to be able to actually describe the physical systems biology uses for patterning.

One example of a generalizable code for patterning by 'reaction diffusion':

- Set up a 'node' that has an inverted feedback loop for producing a 'morphogen' (produce less when lots, lots when less).

- Let the morphogen diffuse through a field.

- Digitize the morphogen concentration by some thresholded sensor.

- Use an orthogonal 'clock' mechanism to freeze the field in different states digitized above.

Generally though the simulation of biology runs into just way way way too many variables to be 'nicely' modeled. Part of the cool part is that when you have a routine that generates a spatial pattern established, tweaking parameters here and there create massive variation while still maintaining a coherent 'pattern'. A bit of chaos gives each run a fingerprint - literally.

One of the other biological patterning mechanisms I like is the Notch pathway, relying on similar principles. [2]

There are fewer variables in a chemical system, but similar reaction-diffusion related principles can be found in chemistry - which can often be 'pretty'. See the Belousov-Zhabotinsky reaction [3].

As an aside, I like that they reference the paper that describes now chameleons change color; "chameleons shift colour through active tuning of a lattice of guanine nanocrystals within a superficial thick layer of dermal iridophores." [4]

[0] (actual research referenced) http://www.nature.com/nature/journal/v544/n7649/full/nature2...

[1] (PDF! Turing's 1952, The Chemical Basis of Morphogenesis) http://dna.caltech.edu/courses/cs191/paperscs191/turing.pdf

[2] (Notch Patterning) http://www.cell.com/trends/cell-biology/fulltext/S0962-8924(...

[3] (B-Z Reaction) https://www.youtube.com/watch?v=3JAqrRnKFHo

[4] (chameleon's color via guanine nanocrystals) https://www.nature.com/articles/ncomms7368

Most cellular automata simulators are on a square grid, but that lizard's scales are on a hexagonal one. I wonder if that arrangement makes it easier to produce recurrent local patterns.

Does anyone know if there is a cellular automata simulator on a hexagonal grid?

You can simulate a hexagonal lattice on a square grid: https://geometricolor.wordpress.com/2013/01/11/hexagonal-cel...

Example in Golly, the most popular CA simulator: https://github.com/gollygang/ruletablerepository/wiki/TheRul...

what can we feed it to play the game of life

anything

I like the HN title more than the NYT title. Something behaving like a simulation is a funny way to describe it.

Err well Cellular Automata were originally designed to simulate such cellular biological systems

Not really. https://en.wikipedia.org/wiki/Cellular_automaton#History

It seems odd to say "Mr. Turing" (referring to a period in the 1950s), given that he got his Phd in 1938. The article uses "Dr." for other people.

A couple of days/weeks ago I saw on HN (I think) contributers saying (and agreeing) that people with PhDs in the UK don't usually use/demand the title of 'Dr.' unless they are medical doctors. It might not be a mistake by the times.

I've submitted a correction :-)

Wolfram should be all over this.

I expect a self-aggrandizing blog post on it any day now.

Someone should publish a scientific paper, “The Insufferability of Stephen Wolfram as a Self-Proving Hypothesis” and win the Turing Award with it. Maybe then we could all just stop wasting digital ink about it. And remember that there's no such thing as bad publicity.

Complete with comments from people who won't stop talking about how overbearing Wolfram is.

True. But consider this - there's been enough precedent on this particular issue, that we could just be talking to a bot/AI, already, albeit one running on wet-ware ..

Consider that bringing it up even when Wolfram isn't even mentioned is really, really boring.

Oh, boy, little lizard, hope you're ready for a cease and desist from the owner of "this kind of science". :)

(said in good fun)