ractals are sets which possess self-similarity and detail on all levels of magnification. Julia sets, named for the French mathematician Gaston Julia (1893-1978), are the premier examples of fractals. Julia's work, published in 1918 when he was 25 years old, was essentially forgotten until the 1980's when computers made possible the visualization of his creation.
All pictures in the gallery below are Julia sets for functions of the form f (z) = z2 + c. Changing the value of c changes the nature of the Julia set dramatically. Changing the color palette used to paint the area surrounding the Julia set also leads to significant differences in the final appearance.
The Julia sets shown in the thumbnails below are some of my personal favorites. If you find one that you like, click on the thumbnail to enlarge it.
f (z) = z2 - .74173 + .15518i (195K)
f (z) = z2 - .74543 + .11301i (484K)
f (z) = z2 + .29812 + .52923i (35K)
f (z) = z2 - .55947 + .64196i (105K)
f (z) = z2 + .23300 + .53780i (104K)
f (z) = z2 - .62772 + .42193i (47K)
f (z) = z2 - .62772 + .44072i (79K)
f (z) = z2 + .41453 + .34364i (144K)
f (z) = z2 - .74434 - .10772i (121K)
f (z) = z2 - .67319 + .34442i (62K)
f (z) = z2 + .03515 - .07467i (254K)
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