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| Description: A familiar Seahorse Valley Mandelbrot with an unusual coloring: the "grad" of the smoothed iterations. Black = the smoothed iteration value increases in the positive real direction, violet = positive imaginary, white = negative real, pinkish = negative imaginary. This coloring method, when used with a cyclic gradient with strong luminance contrast, produces an embossed, three-dimensional look. A second layer with normal smoothed iterations darkens the seahorse cores and turns the edge of the minibrot yellow-brown. Mathematically, the calculations resemble those for distance estimator. The derivative dzn/dc is maintained, starting as 0 (since z0 = 0 is a constant independent of c) and being updated by new-der = 2 times old-der times zn + 1. So far, so identical to distance estimator. The difference is in what's done at the end of the iteration. For distance estimator, the modulus of the escaped z is multiplied by its own logarithm and by half, and divided by the modulus of the derivative. For this, I multiply the escaped z (not its modulus) by half and divide by the modulus of the derivative, leaving the logarithmic term of the product out entirely and yielding a complex number. That's the grad. It's the argument of this complex number that is used for the coloring: the direction of the gradient. Stats: Total Favorities: 1 View Who Favorited Filesize: 437.22kB Height: 900 Width: 1200 Discussion Topic: View Topic Keywords: Mandelbrot Seahorse Valley Posted by: Pauldelbrot  September 09, 2011, 03:05:59 AMRating:  by 2 members.Image Linking Codes
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Comments (2)  |
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Pauldelbrot
Fractal Senior  Posts: 2592 
| September 15, 2011, 04:54:40 PM Thanks.  |
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Ross Hilbert
Fractal Phenom  Posts: 469
| September 15, 2011, 04:30:27 PM Nicely done! |
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