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> Practically it can lead to better encryption like I linked above, superior understanding and prediction of weather

This is the problem. Maybe it will, but as of yet nobody has figured out a practical application beyond "helping us appreciate nature" (replace nature with any chaotic system).

We are pretty good with weather prediction and getting better all the time. The fundamental problem is the chaotic nature. CA does practically help us in anyway there.

Fractals on the other hand has so many practical applications. Just the other day I was applying factual theory to the prediction of criminal activity.

Maybe all CA needs to do is help us appreciate nature and simple machines.

> This is the problem. Maybe it will, but as of yet nobody has figured out a practical application beyond "helping us appreciate nature" (replace nature with any chaotic system).

Why is this a problem? Doing maths purely for its own sake is as valid and useful as painting a picture, or cooking a delicious meal instead of just eating dry bread.

If that's not good enough for you, there are plenty of examples of maths that was considered useless at the time but ended up finding a use years, decades, or centuries later.

> Why is this a problem? Doing maths purely for its own sake is as valid and useful as painting a picture, or cooking a delicious meal instead of just eating dry bread.

It's a problem because Wolfram named his book A New Kind of Science, not A New Kind of Doing Maths Purely for Its Own Sake.

If Wolfram just went around saying "hey, cellular automata are fun and interesting for their own sake` he wouldn't get the hate he does.

It's a problem when someone is claiming that a technique Solves the Big Problems when it clearly doesn't.

Maybe it will one day, and no one is saying it's not an interesting avenue to explore.

But making grandiose claims is not doing science. Making novel falsifiable concrete predictions is science, and Wolfram hasn't made enough of those to justify the extreme self-regard.

I strongly agree with the spirit of what you're saying, but:

> making grandiose claims is not doing science. Making novel falsifiable concrete predictions is science

It seems to me that making grandiose claims is absolutely essential to science every now and then. A good example is when Einstein made the grandiose (and unfalsifiable) claim that the mathematical theory of relativity already worked out by Lorentz and Poincare and whoever was best seen as the denial of the existence of simultaneity etc., a claim which obviously turned out to be very fruitful since it lead to General Relativity.

However (and this is one reason I so strongly argee with the spirit of what you're saying), (a) there isn't room for very much of this stuff, (b) Einstein was much better at it than Wolfram is, and (c) Einstein was listened to because at the same time (ha ha) as he was making grandiose claims he was making unarguably gobsmacking breakthroughs in atomic theory and quantum mechanics.

I think it is fair to assert that if maybe one day it will solve big problems, that it should have solved a little problem already.

Quantum mechanics rapidly gained credibility because once its formalism became established, it was easy to show how classical mechanics came out of it in a limit.

> Why is this a problem? Doing maths purely for its own sake is as valid and useful as painting a picture, or cooking a delicious meal instead of just eating dry bread.

Nothing is wrong with this at all. I never wrote nor even implied there was anything wrong with this.

If you had read to the end of my comment you would have seen I wrote:

> Maybe all CA needs to do is help us appreciate nature and simple machines.

So looks like we are in agreement in appreciating the beauty of maths.

You are certainly right. But what I was referring to was CA being linked to physics, but without any tangible link.

From your first link:

> The digital images can be converted to binary data and encrypted with Advanced Encryption Standard (AES). However, the high correlation between adjacent pixels may still be kept after encrypting a digital image without considering the property of digital images.

What do you mean by this? It sounds like it’s suggesting that, e.g., the AES-CBC ciphertext of an image has detectable internal correlations. In other words, AES is completely broken as a cipher. Surely I’m misinterpreting the claim here.

Yeah, this paper is a good representation of the whole "chaos cryptography" theme — snake oil cryptography invented by authors who don't even attempt to study cryptography before producing their bullshit and publishing it in sketchy or generalist, unrelated to cryptography, journals.

In this particular paper:

1. The motivation for "image encryption" is completely wrong, as you pointed out.

2. There is no secret key. The "key" is produced by hashing the image with SHA-256.

3. Claim: "No any useful information can be acquired from encrypted images". Actually: since this is convergent encryption (https://en.wikipedia.org/wiki/Convergent_encryption, "key" derived from SHA-256 of data), encrypting any two equal images will produce the same ciphertext, globally.

4. Finally, the actual "key" can't be more than 64 bits, since SHA-256(image) is then split into two groups of 32-bit words, which are xored together to produce two key values. Thus, this whole "encryption" scheme is limited to 64-bit security (probably even less than that). We don't even have to analyze the whole "chaos" system they invented to conclude that it's insecure.

I guess they’re referring to AES-ECB, which is notoriously weak at encrypting images (it’s weak in general of course, just most obviously with respect to images): https://words.filippo.io/the-ecb-penguin/.

But I don’t think the same is true of the other AES cipher modes.

I work on weather prediction, both with traditional simulation methods and machine learning. I have not seen any examples of cellular automata used for useful predictions in this space.

> "Let’s bring it all together now. By studying cellular automata, we can observe patterns which correspond to a chaotic map of those patterns. By looking at that, we are able to make deeper inferences about the overall total pattern by knowing that what we observe in a small scale will also exist at n+1 scale."

Okay, this follows themes of fractal self-similarity, very interesting stuff. However, the next leap sounds completely unsupported. One reason is that physics often doesn't scale like this (see gravity and why we don't have elephant-sized ants):

> "Meaning, when we see the loner slime mold evolve the other parts, it’s reasonable to infer through scale that loner humans may also contribute evolutionary information."

The cellular automata stuff sounds valid mathematically, though I'm no expert, but the leap to other areas of science? Even the jump to slime mold evolution... I mean, where is the valuable addition? Slime mold evolution doesn't seem to require any cellular automata theory to understand. It's an interesting biological system that has aspects of both independent microbial cellular life as well as multicellular cooperation under stress conditions.

Plus the tedious self-promotion, I've know academics like that, the type who march into every room tooting their own horn and banging their drum. Working for people like that is a big mistake for many reasons. For example, if your results disagree with theirs they'll go overboard trying to sabotage you. Your only possible roles in that situation will be those of loyal sycophant, or, if you don't follow along, excommunicated heretic.

>a chaos map is a mapping of how a fractal expands or changes across space time.

My jaw actually dropped in real life when I read this line. It fits so well. Thank you so much for this explanation.

So then is it less of a proof mechanism and more of a simulation one?