Lace by Nine

A nine-fold-symmetric chaotic attractor. Taken from the from front cover of Contemporary Abstract Algebra, 3rd ed., Joseph A. Gallian, D.C.Heath, 1994.

The mapping function is

$$f(z) = (-2.5 + 8.0\vert z\vert^2 - 0.7 \mbox{Re}(z^9) - 0.9\vert z\vert)z + \bar{z}\,^8$$

This is iterated on the complex plane $30\times 10^6$ times, counting the number of times each pixel is visited during the iteration process, and then assigning a corresponding grey-level. Then histogram equalization is performed.

This image would look a lot better if it were coloured, preferably with a subtle touch.

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Copyright © 1997, 1998, 1999, Ross Moore, Mathematics Department, Macquarie University, Sydney.

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The translation was initiated by Karim Naqvi on 2003-08-06