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File: 1484999519618.png (84.66 KB, 300x300, 1445669399933-0.gif)

I have a few questions about chaos theory. Please keep your answers simple as I'm not a physicist.

Chaos appears when you are studying a system of at least three non linear and interdependent variables. Is that true ?

Does this program reflect chaotic behavior ? http://sprunge.us/KCVF?scheme

Chaos appears when you are studying a system of at least three non linear and interdependent variables. Is that true ?

Does this program reflect chaotic behavior ? http://sprunge.us/KCVF?scheme

>Does this program reflect chaotic behavior ? http://sprunge.us/KCVF?scheme

No. It is not topologically mixing, so it cannot be chaotic (as required https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics)

What this basically means, is that it should be possible to take any two subsets A and B of possible states the function can be in (in this case values of z), and then iterate A so that its possible values overlaps with those of B. If you choose A as containing "big values" and B containing "small values", then this cannot happen (as z never gets smaller).

The function is also basically a variant of the non-mixing example described in this section: https://en.wikipedia.org/wiki/Chaos_theory#Topological_mixing

I'm not a physicist so this is based on my understanding of chaos from the point of view as someone studying cs/math.

No. It is not topologically mixing, so it cannot be chaotic (as required https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics)

What this basically means, is that it should be possible to take any two subsets A and B of possible states the function can be in (in this case values of z), and then iterate A so that its possible values overlaps with those of B. If you choose A as containing "big values" and B containing "small values", then this cannot happen (as z never gets smaller).

The function is also basically a variant of the non-mixing example described in this section: https://en.wikipedia.org/wiki/Chaos_theory#Topological_mixing

I'm not a physicist so this is based on my understanding of chaos from the point of view as someone studying cs/math.

Hello, I'm the lainon who's writing the chaos piece for the LZ4.

>Chaos appears when you are studying a system of at least three non linear and interdependent variables. Is that true ?

Well no, chaos can emerge in systems that have a lower number of degrees of freedom. For example, there are loads of chaotic maps from the square in itself. It has more to do with the measure-theoretic and topological properties of maps, as >>725

said.

>Chaos appears when you are studying a system of at least three non linear and interdependent variables. Is that true ?

Well no, chaos can emerge in systems that have a lower number of degrees of freedom. For example, there are loads of chaotic maps from the square in itself. It has more to do with the measure-theoretic and topological properties of maps, as >>725

said.