Strange Attractor SearchJava

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If your browser supports Java, you will see above an endless succession of fractal images produced by the iterated map xnew = a + bx + cx2 + dxy + ey + fy2, ynew = x, znew = y, with a through f chosen randomly over the range -3 to 3. Only those cases that are bounded and exhibit sensitive dependence on initial conditions (chaos) are exhibited. The other 99.7% are discarded. Each iterate is plotted at (x, y) in a hue proportional to z. Like snowflakes, these strange attractors come in infinite variety with no two the same. Each one you see is new and almost certainly has never been seen before.

The technique is described in detail in the book Strange Attractors: Creating Patterns in Chaos by J. C. Sprott. The Java source code is available. A DOS executable version of the program is available, along with BASIC source code.

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