Sequence Fractals Part V #7

388.jpg

z^{s_i}+c
si = 2,-2, … (two step repeating)
Center:-1.23909+0.87230i; Zoom = 4096

Combining two steps of this sequence fractal give the rational function \frac{cx^4+2c^2x^2+c^3+1}{x^4+2cx^2+c^2}. As with polynomial sequence fractals with a two-step sequence this is actually a picture of a degree 4 rational function.

These take a long time to render. Every point runs to the full iteration limit. My code is very inefficient, each step uses complex exponentiation. At higher iteration levels, most of the artifacts will disappear and the image will look like a sea of colored sand, containing a few smooth islands. (I was going to optimize the code and create such an image, but I ran out of time.)

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