103 views 15th May 2012

The 30th Lyapunov fractal saved, this is the first one from Saturn.

Parameters

Formula: “Lyapunov”

x = r*x*(1 – x)

Initial value of x is 0.5.

Programs: saturn and titan

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: BAB
Image centre: a = 3.88544, b = 3.45053
Image long side: 0.119467
Rotation about image centre: 90 degrees
Negative coefficient colouring: multi-colour
Positive coefficient colouring: multi-colour

Featured on 22nd October 2011 by Fractal Paradise