Wrapped Tree
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Description:
This render method differs slightly from my previous gallery post. Instead of stopping iterating when escape occurs, continue iterating until the maximum number of iterations is reached. Record each iteration that escapes.

(Side Question: My mathematical vocabulary isn't great, but is the term "escape" appropriate here? In the Mandelbrot Set, "escape" refers to the fact that a point will continue to grow forever and never return, but that's not the case here. In this case the point leaves and then eventually comes back. So the program is really just checking whether or not a particular test is passed on any given iteration.)

Each sphere is the same fractal at 100 iterations, but each one after the first has layers removed to show detail underneath. In order from largest sphere to smallest, the iteration-layers shown are:
1 to 100
10 to 100
30 to 100
50 to 100
70 to 100
90 to 100

Equation:
$Q_{n}=\frac{C - {Z_{n}}^{2}+C^{1024}}{C + Z_{n} * C}+C$

If $$real(Q_{n}) < imag(Q_{n})$$:
$Z_{n+1} = i * conj(Q_{n})$

Otherwise:
$Z_{n+1} = Q_{n}$

Escape occurs when:
$real(Z_{n}) < 0 AND imag(Z_{n}) < 0$

Iterations: 100
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Filesize: 1.95MB
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Discussion Topic: View Topic
Posted by: AlexH October 07, 2018, 05:22:14 AM

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