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A087089 Periods of logistic map intervals in order of size.

Original entry on oeis.org

1, 2, 4, 8, 3, 6, 16, 6, 5, 12, 10, 12, 32, 12, 10, 4, 5, 7, 24, 24, 20, 20, 8, 8, 7, 24, 10, 14, 9, 64, 24, 10, 16, 14, 20, 8, 18, 14, 9, 48, 48, 14, 20, 40, 6, 48, 16, 9, 40, 40, 7, 18, 48, 16, 20, 16, 28, 18, 9, 28
Offset: 1

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Author

Enrico T. Federighi (rico125162(AT)aol.com), Aug 11 2003

Keywords

Comments

The region of stability for period 8 after the point where period 4 splits in two is from 3.5440903596 to 3.5644072661 or a width of .0203169065. The period 3 cycle starts at 3.8284271247 = 1+sqrt(8) and ends at 3.8414990075, a width of .0130718828. This is less than that of period 8 so it follows it in sequence. The logistic map is just the real part of the Mandelbrot set.
The equation f(x)=a*x(1-x), f2(x)=f(f(x)) has a period 3 oscillation whenever 3.82843

References

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