W SPACE - MULTI-STAR FRACTAL

For documentation of the algorithm, see Appendix A in:
J. A. Shuster and J. Koeplinger, "Elliptic complex numbers with dual multiplication.",
Appl. Math. Comput. 216 (2010), pp. 3497-3514
http://www.jenskoeplinger.com/P/PaperShusterKoepl_WSpace.pdf

License: Creative Commons Share-alike with attribution, v3.0.

For source code and details how to run, see the BitBucket git repo.

Click on the thumbnails below for a 800x802 bitmap, or click on the links under the thumbnails for the command line that created the bitmap, and for the full 5000x5010 pixel bitmap (large). All bitmaps have the used color pallette embedded at the top.

Last updated: 17 September 2010

(1) Multi-star in the {[-2.1, +2.1], [-2.1, +2.1]} parameter range of the {real, w} plane.
Rendered at 5000x5000 pixels, iteration depth 25, with varying colorization templates.
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(2) Multi-star zoomed into the left cusp, range {[-1.4, -0.6], [-0.1, +0.7]}
Rendered at 5000x5000 pixels, iteration depth 25, with varying colorization templates.
full size full size full size full size full size full size
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(3) Further zoom into left cusp, range {[-1.04, -0.96], [-0.01, +0.07]}
Rendered at 5000x5000 pixels, iteration depth 25, with varying colorization templates.
full size full size full size full size full size full size
command command command command command command

(4) Mandelbrot algorithm with +W/-W proliferation of multiplication results,
in the {[-2.5, +2.0], [-2.1, +2.4]} parameter range of the {real, w} plane.
Rendered at 5000x5000 pixels, iteration depth 12, with varying colorization templates.
command command command command command