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OfflineSpecialEd
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Registered: 01/30/03
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Chaos Theory
    #2056875 - 10/30/03 01:07 PM (13 years, 6 months ago)

When I was in High School, in advanced programming i recieved this assignment.

1. Plot a triangle and give each corner a variable name.
2. Pick a random point inside of the triangle.
3. Using a random number generator, pick one of the three corners of the triangle.
4. Plot a point halfway between your starting point and the selected corner.
5. Working off of this new point, reselect a corner and plot a point halfway between that point and the corner.

When you automate this random process with a never ending loop you will get some very interesting results. Your program will render sirpinski's triangle.

The point of all of this is that form and structure can come out of chaos once a feedback loop has been established. You can render fractals and geometric designs with processes like this.

It makes me wonder if the chaos theory could be applied to evolution and the formation of life. Because of sexual reproduction, a feed back loop (think natural selection) is established, so that biological advantages that are favorable to survival last and are passed on. As this process repeats itself, very complex forms and structures are established.


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InvisibletrendalM
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Re: Chaos Theory [Re: SpecialEd]
    #2056885 - 10/30/03 01:13 PM (13 years, 6 months ago)

What Chaos Theory shoes is that as entropy rises in a system, an abstracted or "higher" form of order is produced.

Life is in many ways a chaotic system. I think chaos theory shows that life is inevitable: it is a result of the nature of the universe.

Oh, and the triangle you are talking about is called the Sierpinski Triangle. It is a type of fractal. If you are interested in programming this kind of thing, the next one I suggest you play with is the Mendelbrot set. It's a recursive algorithm using imaginary numbers


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OfflineSpecialEd
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Posts: 6,220
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Re: Chaos Theory [Re: trendal]
    #2056905 - 10/30/03 01:20 PM (13 years, 6 months ago)

I will look into that.

"Life is in many ways a chaotic system. I think chaos theory shows that life is inevitable: it is a result of the nature of the universe."

Huh, I guess I will start thinking about life forms as fractals. This would explain why the golden ratio is built into us.


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InvisibleinfidelGOD
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Re: Chaos Theory [Re: SpecialEd]
    #2056928 - 10/30/03 01:30 PM (13 years, 6 months ago)

The point of all of this is that form and structure can come out of chaos once a feedback loop has been established

true

When you automate this random process with a never ending loop you will get some very interesting results. Your program will render sirpinski's triangle.

but the process isn't really random is it? it's actually quite structured. the values used are random, but in the example of Sierpinski's triangle, they are constrained within an ordered repeating algorithm, so it will result in a predictable ordered pattern. of course, the exact sequence of events is never predictable... the next iteration isn't predictable, but the overall pattern is.

so when applied to evolution and the formation of life. maybe random values are constantly being generated, but since they follow ordered processes (laws of physics, chemistry, biology etc.), they give rise to ordered, complex forms and structures.




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OfflineSpecialEd
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Re: Chaos Theory [Re: infidelGOD]
    #2056947 - 10/30/03 01:35 PM (13 years, 6 months ago)

"but the process isn't really random is it? it's actually quite structured. the values used are random, but in the example of Sierpinski's triangle, they are constrained within an ordered repeating algorithm, so it will result in a predictable ordered pattern. of course, the exact sequence of events is never predictable... the next iteration isn't predictable, but the overall pattern is.

so when applied to evolution and the formation of life. maybe random values are constantly being generated, but since they follow ordered processes (laws of physics, chemistry, biology etc.), they give rise to ordered, complex forms and structures."

yeah, I was using random process in a finger quoting sense, but you completed the analogy very well about how the universe has inherent structures in it that may encourage specific results much as the triangle does


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Offlineentiformatie
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Re: Chaos Theory [Re: infidelGOD]
    #2057565 - 10/30/03 04:53 PM (13 years, 6 months ago)

man! i try to put that into words so often it frustrates me! at least now i know it's possible, heh.

i believe that if our reality is similar to this triangle, our free will is in choosing that first random spot. and we can even use logic to try and figure out what will happen as a result, but only to a certain point.


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Invisiblemuhurgle
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Registered: 10/29/03
Posts: 299
Re: Chaos Theory [Re: entiformatie]
    #2057924 - 10/30/03 06:36 PM (13 years, 6 months ago)

> our free will is in choosing that first random spot

We haven't really observed anything in nature that exhibits this kind of randomness, except at particle level.. Even if there is something that is completely random at particle levels (ie. not dependant on any former state) then how does that give rise to free will?

Anyway, chaos is cool.. it's really beautiful that simple rules can create such complex behaviour.


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OfflineSeussA
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Re: Chaos Theory [Re: muhurgle]
    #2059876 - 10/31/03 06:56 AM (13 years, 5 months ago)

> but only to a certain point.

It depends upon where you view the system from. If you stand back and look at the system as whole, you see a pretty pattern. If you get down in with the lines and points, you can only see the randomness around you.


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