Sequence Fractals Part V #16

397.jpg

z^{s_i}+c
si = 2.5, 0.5, -1.5 … (three step repeating)
Center:1.359+0.409i; Zoom = 6.4

The same formula as the previous two pictures. But with experimental coloring.

Orbit-escape detection is turned off. The negative exponent creates some similarities to Rational Fractions. See the discussion in Sequence Fractals Part V #5 and Sequence Fractals Part V #6. For the same reasons, iteration count coloring does not work here.

The coloring algorithm counts how many times the orbit gets close to zero. “Count” is inaccurate, it actually generates a weighted average of all the values that get close. The average value is a complex number. Each of the real and imaginary components are used to generate a color, and then the two colors are blended together.

For the record, here “close to 0” is defined as “|z|<0.9". That parameter is subject to much trial and error tweaking. Finding two palettes that blend nicely also takes some effort. The bottom line, today's picture is more about my aesthetic choices than mathematics.

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