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Exponent Increment IIIncrementing Exponent IVNewton Varying Power 5
Incrementing Exponent IV
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Description: Based on an idea by gamma.

The formula is the standard third-order Newton's method, but with a twist -- each pixel's loop begins with the exponent set to 3, then at each iteration of the loop, the exponent increases.

For this image, the exponent increment was i (that is, real part 0, imaginary part 1.0).

Aggressive 9x9 anti-aliasing was used because this gets severely noisy in the negative real half-plane.

The coloring (unlike the others in this series) is based on the histogram of the counts with a 2X repeat of the underlying gradient. The gradient starts at white and ends at black, so there is a discontinuity from white to black when it wraps around. I felt this thematically matched the presence of the branch cuts induced by the complex exponents.
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Posted by: HPDZ March 21, 2009, 09:39:01 PM

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