A087089 Periods of logistic map intervals in order of size.

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

1,2

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<a<3.84150.

References

For references see A087046.

Links

Table of n, a(n) for n=1..60.

Crossrefs

Sequence in context: A101942 A344534 A050170 * A367750 A197382 A332521

Adjacent sequences: A087086 A087087 A087088 * A087090 A087091 A087092

Keyword

nonn

Author

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

Status

approved