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chaos-theory

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Quotes filed under chaos-theory

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It__ not an academic question any more to ask what__ going to happen to a cloud. People very much want to know__nd that means there__ money available for it. That problem is very much within the realm of physics and it__ a problem very much of the same caliber. You__e looking at something complicated, and the present way of solving it is to try to look at as many points as you can, enough stuff to say where the cloud is, where the warm air is, what its velocity is, and so forth. Then you stick it into the biggest machine you can afford and you try to get an estimate of what it__ going to do next. But this is not very realistic.

JG
James Gleick

Chaos: Making a New Science

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If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase r to get another period doubling gets smaller and smaller for each new bifurcation. This cascade of period doublings is reminiscent of the race between Achilles and the tortoise, in that an infinite number of bifurcations (or time steps in the race) can be confined to a local region of finite size. At a very special critical value, the dynamical system will fall into what is essentially an infinite-period limit cycle. This is chaos.

GF
Gary William Flake

The Computational Beauty of Nature - Computer Explorations of Fractals, Chaos, Complex Systems & Adaption (Paper)

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In short, the idea dawns that the one universal principle which possibly ... between force and structure, the embodiment of the Principle of Least Action and the (unknown) force, which in mathematics is known as the attractor which pulls ... in the direction of the most optimal and relatively stable self-organized criticality, could very well be the Golden Ratio dynamic. the universal principle which as the balance between finiteness and infinity, stability and flexibility underlies self-similar fractal forms emerging at the 'edge of chaos' indeed seems to be the Golden Ratio Spiral.

MV
Marja de Vries

The Whole Elephant Revealed: Insights into the existence and operation of Universal Laws and the Golden Ratio