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. Gary William Flake
Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.
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Deepak Chopra
In real life, I assure you, there is no such thing as algebra.
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Fran Lebowitz
I had a polynomial once. My doctor removed it.
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Michael Grant
I couldn't claim that I was smarter than sixty-five other guys--but the average of sixty-five other guys, certainly!
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Richard Feynman
What comes, is called.
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Ki Longfellow
More Quotes By Gary William Flake
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...
