Lyapunov 34

An other Lyapunov.

Produced using the development versions of Saturn and Titan, the target date for the new version (2.0) is the 31st March 2012.

Titan Version 2.0 development

Parameters

Formula: "Lyapunov"

x = r*x*(1 - x)

Programs: saturn and titan

Initial value of x is 0.5.
A location in the image is represented by (a,b), the value of
r is dependent of the sequence, when the sequence value is A
r is set to a and when it is B r is set to b. The sequence is
is executed for a number of cycles of the sequence to allow for
behaviour to settle. When settling cycles have been completed the
lyapunov coefficient is calculated. For each calculation iteration
the following expression is evaluated:

log(abs(r - 2*r*x))/log(2)

the values are accumulated and the total is divided by the number of
iterations. The number of iterations is number of calculation cycles
multiplied by the length of the sequence. The Lyapunov co-efficient
will be either negative (stability) or positive (chaos)

Sequence: AAABABBAABBBBBB
Image centre: a = 3.14616004630222222, b = 3.80888318179164815
Image width: 0.0030294033445925926
Rotation about image centre: 0 degrees
Negative coefficient colouring: multi-colour
Positive coefficient colouring: multi-colour

Settling cycles: 120
Calculating cycles: 600