Rare Gold

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=21.45, ω=1, φ=0, b=1 and μ=0.025. This system has a single attractor similar to the River of Gold image system. By decreasing the resolution with which the algorithm discriminates among attractors we can reduce the basin of attraction of one of the single attractor's segments to the vanishing point. This is one of the clues that we are dealing here with a single attractor, not two truly separate ones. |