Sunday, November 23, 2008

Mandelbrot Fractals

I recently returned to my explorations of the Mandelbrot fractals, using my custom, multi-processor implementation of the classic algorithm. One rude surprise: Java's Bicubic interpolation, which my code had counted-on for antialiasing the images, has spontaneously ceased to work somewhere in the couple of years since I last went diving in Dr. Mandelbrot's seas. One custom down-sampler later, and I'm back in business, but still wondering what happened to the Bicubic interpolation support. (Some Google searches confirm the issue, but don't explain why it ever worked, or how to get it working again.)

Anyway, some of these images are new, while some are higher-resolution renderings of images I'd previously produced. All use 16:1 antialiasing for clarity. Unfortunately, Blogger has scaled-down the images in accordance with its internal size limits. To see these, and other Mandelbrot images, at full resolution, visit my Mandelbrot fractals page.

(0.251264159878095-0.000071302056312561i,+0.2512651036183039-0.000071898102760315i) (0.2512619694073995-0.000070631504058838i,+0.25126574436823523-0.000073015689849854i) (0.2512600819269816-0.00006943941116333i,+0.25126763184865314-0.000074207782745361i) (-1.9415377561052738+0.000004419728327122i,-1.9415377426291933+0.00000441121711836i)

The image above had to be computed to a depth of 2.5 million iterations. At lesser depths, the structure appears to be a part of the Mandelbrot set. How many other apparent parts of the set would turn-out not to be, if they were examined deeply enough?

(-1.9405475727980244+0.000000000020618141i,-1.9405475727568255-0.000000000020580682i) (-1.9405475727807724+0.000000000003366096i,-1.9405475727740777-0.000000000003328637i) (-1.9405470533408833+0.000000000011699758i,-1.9405470533399718+0.000000000010788309i) (-1.9405469455956967+0.000000000712956i,-1.9405469445200192-0.00000000072128073i) (-1.9405469451864226+0.000000000549857802i,-1.9405469449474801+0.000000000398946793i) (-1.940547686187619+0.000000000256137123i,-1.9405476861868012+0.000000000255319443i) (-1.940546945070056+0.000000000267948696i,-1.940546945067154+0.000000000265046485i) (-0.7499062220255533+0.01945350170135498i,-0.7498911221822102+0.019443964958190917i)

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