River of 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=21.46, ω=1, φ=0, b=1 and μ=0.023. This system has a single attractor but it is a complicated affair, like an elongated oval with a twist in each end. It is so far around the whole twisted oval that the basin of attraction algorithm can't believe it is all of one piece, so it considers each twisted end to be a separate attractor with its own basin of attraction. I could fix the algorithm but then the image would be one solid color and not very interesting. |