Attractor Pictures

Ikeda Attractor

The pictures below show the strange attractor that results from the time evolution of an optical cavity containing a nonlinear dielectric subjected to a periodic string of light pulses. The picure is a cumulative plot of the phase

and amplitude A of the pulse. For a given output pulse the complex number

is obtained (Re(Z) = horizontal axis and Im(Z) = vertical axis). Pixel colors are plotted according to how often Z falls in that pixel. The bright yellow signifies high density, often visited region and the red region signifies low density, rarely visited region of the attractor. The two pictures are set at different parameter values and the right picture is also "zoomed in".

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KAM islands

This is probably a picture of the Standard map which is a Hamiltonian (conservative) system. An obvious feature of the picture is the KAM islands.

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Tinkerbell Attractor

The Tinkerbell attractor is represented by the curve and its basin of attraction is represented by the black color. Other colors denote points which escape to infinity as one continually iterates the two-dimensional map. The colors are shaded according to how fast the points escapes to infinity.

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