Orbit Diagram of the Logistic Map

magnification

3

Plot the points

(λ,

x

n

)

, where

x

0

=0

and the

x

n

are the iterates of the quadratic map

x↦

2

x

+λ

. Each

λ

leads to a distinct orbit; for example, for

λ=1.5

, the orbit is 0, -1.5, 0.75, -0.9375, …. For constant λ, the set of

x

n

is infinite, but in this picture only a finite sample is shown. The whole plot is called the orbit diagram for the map. The set of points on the right that looks like a curve consists of stable points. In the middle the points orbit between two values. Both of these cases are examples of attractors.

External Links

Attractor (Wolfram MathWorld)

Logistic Map (Wolfram MathWorld)

Permanent Citation

Ed Pegg Jr

"Orbit Diagram of the Logistic Map"
http://demonstrations.wolfram.com/OrbitDiagramOfTheLogisticMap/
Wolfram Demonstrations Project
Published: September 28, 2007