Are cellular automata useless?
more or less
>>8203433
They are too simple to be useful models, they are nice as examples that simple structures can be very hard to analyze and have surprising properties because you can visualize them (in contrast to e.g. lambda calculus)
>>8203433
I tried reading A New Kind of Science by Wolfram, he goes on and on about how his analysis of automata will have a profound impact in every field of study, but it comes across as 100% bunk.
>>8203487
>>it comes across as self-congratulatory advertisement
>>8203433
Yes
Or perhaps the application just hasn't been found yet
>>8203433
It's a type of Flatland, so no.
>>8203433
If you happen to want to simulate a Cone snail shell, then they're your man.
Other than that, well, would ant colony optimization count as a generalization of a cellular automaton? That seems useful.
>>8203435
>>8203436
>>8203585
>>8203487
really, how fucking retarded are you all?
you know all of wolfram alpha and mathematica is operating on and with CA.
It will soon be sophisticated enough to automate common math and statistics jobs done by humans atm.
and while you still deny the truth, I'll laugh at you pety idiots, still deriving shit manually.
>>8205135
>all of wolfram alpha and mathematica is operating on and with CA
Is this true?
Got any links to info on this? I'm genuinely very interested.
>>8205144
He does not because he is a pop-sci idiot.
>>8203433
lots of differential equations can be though off as automata, if you look at them in a finite difference way.
For example a diffusion process, discretised in space and time stemming from the PDE
[math]u_t + \Delta u = 0 [/math]
can be thought of cells checking out their neibours and filling up according to their neighbours values in the next timestep. This is
If you look at it from the numerical analysis side, you get a formulation like
[math] \frac{u_{i}^{n+1}-u_{i}^n}{\tau} + \frac{u_{i-1}^n-u_i^n+u_{i+1}^n}{h^2}=0 [/math]
by replacing differential operators with finite differences, which lets you solve for your solution vector at the n+1th timestep , when you know what it was a the nth.
>>8203645
I don't quite know about cone snail shells in particular, but a lot of pattern formation can be explained by looking for turing instability in reaction diffusion PDEs
>>8205243
>lots of differential equations can be though off as automata, if you look at them in a finite difference way.
So, as difference equations?
>>8205254
haven't heard that term yet, but from what I just read about it just now, yes.
are nonlinear implicit formulations like
[math] u_{n+1} = f(u_{n+1},u_{n}) [/math]
still in the realm of difference equations?
>>8203433
Yes, but it's a little fun you would've say.
>>8203487
I thought this was an interesting read. It was written by someone who got threatened with legal action by Wolfram after he cited the true discoverer of a result which was owned by Wolfram
http://bactra.org/reviews/wolfram/
not when you make them three dimensional and give it feelings
>>8205135
Go home Wolfram, you short unstable Jewish cock. You had five years of decent research and now you are just a miser that masturbates to his fading mind.
>>8205144
CA is used to solve and transform Diifferential Equations in Wolfram Language
just watch his TED talk he explains everything about it
CA literally is applied mathematics
I tried googling coautomata but I only found two references to archaic maths books written in the foreign language of academic mathematics
>>8206887
Reasonably, since the category of deterministic automata over a language [math] L [/math] is the category of coalgebras for the functor [math] 2\times (-)^{L}:Set\to Set [/math], we might define a deterministic coautomaton to be an object in its opposite category.
>>8206919
I was wondering since evaluating automata is comonadic/coeffectful (i.e. requiring context), if coautomata might be monadic or effectful
>>8206930
*
the context would be neighbouring cells, in cellular automata
>>8206930
I haven't studied this stuff in any real depth, so I can't offer much. But, I don't think the category of algebras for a monad is in general dual to the category of coalgebras for the comonad (assuming the adjoints are all endofunctors), so my definition would fail to satisfy what you are looking for I think.
>>8206858\
>CA is used to solve and transform Diifferential Equations in Wolfram Language
No it's not. CA can be used to approximate some PDEs that have a spatial analogy. I doubt WolframAlpha even uses CAs to solve those.
But first you said "all of wolfram alpha and mathematica is operating on and with CA" now you are saying it's just differential equations (which is also a lie). So you obviously have no idea what you're talking about.
>>8206971
I never said "just" differential equations.
http://reference.wolfram.com/language/tutorial/SomeNotesOnInternalImplementation.html
>Any transformation rule—whether given as x−>y or in a definition—is automatically compiled into a form that allows for rapid pattern matching. Many different types of patterns are distinguished and are handled by special code.
>A form of hashing that takes account of blanks and other features of patterns is used in pattern matching.
>The internal code associated with pattern matching is approximately 250 pages long.
How is this not CA? prove me wrong or be stupid somewhere else.
>>8207064
What the fuck? That has nothing to do with cellular automata you delusional retard. It just describes a compiler.
>>8207079
and how does this compiler work you retard?
seriously READ THE NOTES BEFORE YOU WRITE!!!!
>>8207079
Some automata are turing-complete.
>>8203609
Type of Flatland? You know there's such thing as three-dimensional cellular automata, right?
>>8207080
>and how does this compiler work
Not through cellular automata.
>>8207080
>ctrl+f "cellular"
>2 results - one algorithm for pseudorandom numbers and one that calculates the evolution of cellular automata
and like you would expect, the differential equation solvers are just genereric multistep methods for ODEs and method of line approach (they don't make it clear, how they discretize spatially though) for PDEs, that have nothing much to do with CA
>>8207100
Strawberries and stop signs are both red.
>>8207289
I'm saying compiler =\> not turing complete
>>8207303
not automata*
