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Author Topic: Cellular Automata  (Read 4773 times)

Realmfighter

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Cellular Automata
« on: May 10, 2010, 04:24:10 pm »

In my enriched math class, we have to write a essay explaining how a modern math mathematical concept pertains to the modern world (I think. I didn't understand it very well). I decided to use Cellular Automata like Conways game of Life because it looks awesome, not realizing that i do not understand how they work very well, and i don't understand there purpose at all.

Because the Wikipedia page's make my head hurt, and the GIFs make me zone out after a class of trying to find out i still don't know. Do any of you smart people know this stuff?

Wikipedia page
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LeoLeonardoIII

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Re: Cellular Automata
« Reply #1 on: May 10, 2010, 04:46:41 pm »

I remember this from an old game I used to play that was on FLOPPY floppy disks.

Basically you have this grid, and anything in the grid is either ON or OFF. We can think of ON cells as "alive".

Now we have turns, and every turn we check every single cell according to uor rules. Maybe the rules are that if you have an ON cell, it turns OFF and it turns all neighboring cells ON. So you start with some random cells ON, and you advance turn after turn, and the ON cells do their thing. You let it go until you decide to turn it off, or a certain number of turns passes, or it turns off when there are no more ON cells.

The rules get more complex. They have to take into account things like reproduction, death due to overpopulation, etc.

I don't know what else they use them for.
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Realmfighter

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Re: Cellular Automata
« Reply #2 on: May 10, 2010, 04:49:18 pm »

I get the rules for death and birth of cells, what i don't know is what it is used for outside of games.
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sonerohi

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Re: Cellular Automata
« Reply #3 on: May 10, 2010, 04:54:16 pm »

Not much really.
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LeoLeonardoIII

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Re: Cellular Automata
« Reply #4 on: May 10, 2010, 04:55:17 pm »

I don't understand that part. Sometimes mathematicians get excited about something simply because it's a new tool that can be used in the future for something unexpected. Often you don't realize there is a problem to solve until you have a tool that makes it easy to solve. And a solution to a previously unknown problem may change how we think about something in an applied science, leading to a change in experimentation that leads to new knowledge.
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Oglokoog

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Re: Cellular Automata
« Reply #5 on: May 10, 2010, 04:56:44 pm »

Well, the fluid dynamics system in DF is a type of a cellular automaton.
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LeoLeonardoIII

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Re: Cellular Automata
« Reply #6 on: May 10, 2010, 05:14:57 pm »

Oh! True true. At least as far as I can tell, who knows how Toady coded it?
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alway

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Re: Cellular Automata
« Reply #7 on: May 10, 2010, 05:35:00 pm »

Oh! True true. At least as far as I can tell, who knows how Toady coded it?
Judging by the CPU draw, it is probably a sentient cellular automata.

Jokes aside, you probably could have found a better topic. It really doesn't have all that much application aside from demonstrating the point that simple rules can end up creating extraordinarily complex systems; something seen throughout the universe.
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eerr

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Re: Cellular Automata
« Reply #8 on: May 10, 2010, 06:15:35 pm »

Oh! True true. At least as far as I can tell, who knows how Toady coded it?
Judging by the CPU draw, it is probably a sentient cellular automata.

Jokes aside, you probably could have found a better topic. It really doesn't have all that much application aside from demonstrating the point that simple rules can end up creating extraordinarily complex systems; something seen throughout the universe.

flat bodies of Water flow only in one direction at a time over the entire map.

Which direction/for how long, is random.

I'm not sure on the exact calculation for pressure.
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LeoLeonardoIII

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Re: Cellular Automata
« Reply #9 on: May 10, 2010, 06:52:39 pm »

Well, you can get a flow to travel in another direction by channeling it away into a reservoir and thence onward, back toward the source even. And sometimes you see a river go from the west side to the north side, so it's not like it just always flows in a straight line.

I think he was talking about water in a 7/7 tile flowing into neighboring dry tiles.
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Vector

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Re: Cellular Automata
« Reply #10 on: May 10, 2010, 07:00:49 pm »

I get the rules for death and birth of cells, what i don't know is what it is used for outside of games.

That's pretty much the entire point.  It's a weird thing that has patterns, and mathematicians spend their lives dicking around with patterns.  Interestingly, it's a universal Turing machine, which basically means you can compute anything computable with it.  How's that for an application?

Also, I recommend the book Three Scientists and Their Gods (it's a popularization).  It has a rather large section on this subject.
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LeoLeonardoIII

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Re: Cellular Automata
« Reply #11 on: May 11, 2010, 06:56:49 pm »

After thinking about this over the night, cellular automata modelling can be used to graphically display more complex modelling. The rules that determine which cells turn on, or off, or toggle each turn can be thought of as biological processes, or actions of individual people, etc.

For example, let's say I believe that voting doesn't matter, because my vote counts only if it's the tie-breaker. (This assumes nobody knows the vote counts until after the voting has ended). Normally, that would have no effect on the voting of the rest of the population.

But what if I spread that idea? It may induce others to not vote, but more importantly they have a chance to spread the idea.

And so if I care about the voting process, and I want people to vote, I had better not tell anyone about my belief.



Furthermore, the rules can be more complex if each cell represents more than an on/off state. What if each cell is a hex pair, giving you 256 possible states in each cell? You can encode one piece of information with 256 possible choices, or maybe two pieces of info with 16 choices each. If you're clever or if you track this using binary instead of the hex character themselves, you can encode many on/off states in each cell.


Perhaps you could use this to model the spread of disease in a population. But to make good rules, you'd need good data on how the disease actually spreads. But you could look at the disease cases, and test out a huge range of different rule sets, until you discover a rule set that works to model the real world events.


Perhaps economic modeling, like trying to predict stock market outcomes.


Certainly it would have a use in modeling very low-level physics, but you have to count each cell as an incredibly small space, and have a massive swath of cells, otherwise it's not granular enough.


But maybe I don't know what I'm talking about. If I were you, I'd choose something with more obvious applications to write about.
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Jay

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Re: Cellular Automata
« Reply #12 on: May 11, 2010, 07:24:24 pm »

Conway's Game of Life has a very specific algorithm.
I believe it requires that all so-named "ON" cells require three(?) "ON" neighbors or it turns "OFF".
I'm sure it's more complicated then that, but that's as far as I've bothered with it, honestly.
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Re: Cellular Automata
« Reply #13 on: May 11, 2010, 07:50:04 pm »

3 for off to turn on, 2 or 3 for on to remain on, otherwise it turns off(overcrowding or starvation).

Someone made a computer that calculated prime numbers in the "wireworld" cellular automata.

It all depends on what you do with them, but I think that they are very versatile. (I think that the various falling sand games could possibly be described as cellular automata, too)

I doubt that they are limited to 1 or 2 dimensions, either.
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Vector

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Re: Cellular Automata
« Reply #14 on: May 11, 2010, 09:49:49 pm »

I doubt that they are limited to 1 or 2 dimensions, either.

No, they aren't.  I've had to write proofs for an n-dimensional Game of Life-derivative before.
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