Wrapped Tree  
Previous Image  Next Image  
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 iterationlayers 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 Stats: Views: 84 Total Favorities: 0 View Who Favorited Filesize: 1.95MB Height: 2400 Width: 3600 Discussion Topic: View Topic Posted by: AlexH October 07, 2018, 05:22:14 AM Rating: by 2 members. Total Likes: 1 Image Linking Codes


0 Members and 1 Guest are viewing this picture. 