Lamella 13

Explanation of the Image...

This image created with the
basin of attraction algorithm
is based on the dynamical system characterized by the expression,
x''=a*cos(ω*t+φ)-b*x^{3}-μ*x',
where x' is the first derivative of x with respect to time, t, and x'' is the second derivative of x with respect to time.
The
domain
of the map of possible
states
for this system covered by this image is: The parameter values are a=0.2, ω=1, φ=0, b=1 and μ=0.08. This system has five attractors. The one whose basin of attraction, in black, wraps all around the outside of this image is the most powerful on the basis of the amount of the map of all possible states that it owns , but not very interesting. This image highlights the next two most powerful attractors, one in gold and one in blue, each featured separately in the Lamella 1 and Lamella 2 images. Since they are nearly equally powerful attractors, their basins of attraction are quite thououghly intermingled. |