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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*x3-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: (-3.598, 14.4)/(5.633, -14.7) The parameter values are a=21.46, ω=1, φ=0, b=1 and μ=0.024. This system has a single attractor similar to the River of Gold image system. By increasing the resolution with which the algorithm discriminates among attractors we can confuse it into displaying multiple segments of the single attractor as having their own basin of attraction. See the Color Bird image for an extreme example. |