Explanation of the...

This image created with the basin of attraction algorithm is based on the dynamical system characterized by the expression,
where x' is the first derivative of x with respect to time, t, and x'' is the second time derivative of x.

The domain of this image in the map of possible states for this system is,
(-5.04, 10)/(7.75, -9.86).

The parameter values are a=24.5, ω=1 φ=0, b=1, and μ=0.025.

There is a single attractor for this system but it is so extensive that we can fool the basins of attraction algorithm into reading separate parts of it as individual attractors. See the River of Gold and Confused images explanation for more on this. The fringing between basins of attraction here reflects a larger than optimum size of the time increment used in integration.