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1. Other maps also reproduce this ratio, in this sense the Feigenbaum constant in bifurcation theory is analogous to π in geometry and e in calculus.
2. Unlike π, which nearly everyone is aware of, the Feigenbaum constant is far less known.
3. And the ratio between the values where the period doubles ends up approaching the Feigenbaum constant, approximately 4.669.
4. Pictures taken from the video I learnt about the Feigenbaum constant from.
5. It’s called the Feigenbaum constant, and it’s about 4.6692016.
6. For more than 30 years, Mitchell’s official position (obtained essentially on the basis of his Feigenbaum constant result) was as a professor at the Rockefeller University in New York City.
7. The Feigenbaum constant characterizes the geometric approach of the bifurcation parameter to its limiting value.
8. Amazingly, the Feigenbaum constant is ``universal (i.e., the same) for all 1-D Maps if has a single locally quadratic Maximum.
9. The Circle Map is not universal, and has a Feigenbaum constant of .
10. It is not known if the Feigenbaum constant is algebraic, or if it can be expressed in terms of other mathematical constants (Borwein and Bailey 2003, p. 53).
11. Amazingly, the Feigenbaum constant and associated reduction parameter are "universal" for all one-dimensional maps if has a single locally quadratic maximum.
12. The value of the Feigenbaum constant can be computed explicitly using functional group renormalization theory.
13. For a function of the form (1), the Feigenbaum constant for various is given in the following table (Briggs 1991, Briggs et al.
14. We can interpret from this constant that as we approach chaos each periodic region is smaller than the previous region by a factor of 4.669 (the Feigenbaum constant).
15. The plot above shows the source of the Feigenbaum constant, the red lines indicate where the logistic map bifurcates to a period 2, 4 and 8 orbit respectively.
16. As it was the first to be noticed and investigated, it was inevitably named before the second Feigenbaum constant was identified.
17. Following step-by-step its route to chaos through period doubling, Feigenbaum constant δ is calculated and its value is verified with noticeable accuracy.
18. This theory also states that the ratio of distance between two consecutive bifurcations is a constant, known as the Feigenbaum constant, found in a multitude of chaotic sys- tems.
19. The bifurcation logistic map is also plot- ted and the width of its tines is measured to calculate the second Feigenbaum constant.
20. Feigenbaum constants For definitions, see Eric Weisstein's MathWorld article: Feigenbaum Constant.
21. In my thesis (1996), I computed several of the Feigenbaum constants to 10s or even 100s of decimal places.
22. Does anyone know if there is a proof that the Feigenbaum constant is an irrational number.
23. This Feigenbaum constant is now regarded as being just as fundamental in nonlinear dynamics theory as the number Pi is to geometry (Peitgen et al., 1992).
24. Note that the ratio a n − 1 − a n − 2 a n − a n − 1 converges to the first Feigenbaum constant.
25. A mathematical constant that is one of the keystones of chaos theory has been named for him: the Feigenbaum constant.
26. In mathematics, specifically bifurcation theory, the Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map.
27. Other maps also reproduce this ratio, in this sense the Feigenbaum constant in bifurcation theory is analogous to pi (π) in geometry and Euler's number e in calculus.
28. See Details in the Wikipedia article: Feigenbaum constant.

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• [{'LOWER': 'feigenbaum'}, {'LEMMA': 'constant'}]