Title: False Mandelbrot Byways No. 2 Post by: element90 on May 31, 2013, 05:34:40 PM (https://copy.com/pMDzYilUtH1A)
https://copy.com/pMDzYilUtH1A (https://copy.com/pMDzYilUtH1A) An exiled Mandelbrot island in a fractal other than the standard Mandelbrot set. Coloured using iteration of minimum magnitude. Title: Re: False Mandelbrot Byways No. 2 Post by: cKleinhuis on May 31, 2013, 06:19:36 PM Great find
Title: Re: False Mandelbrot Byways No. 2 Post by: matsoljare on May 31, 2013, 08:26:05 PM And what is the entire fractal like, then?
Title: Re: False Mandelbrot Byways No. 2 Post by: element90 on May 31, 2013, 09:43:43 PM The full fractal looks like this: (https://copy.com/pwf8HxenE7E9) https://copy.com/pwf8HxenE7E9 (https://copy.com/pwf8HxenE7E9) The formula is: z = (alpha(beta*z^gamma - delta*z^epsilon) + zeta)^eta initial z = 0.75 alpha = location in the complex plane beta = 1 gamma = 3 delta = -1 epsilon = 4 zeta = 0.999999995 Zooming in: (https://copy.com/kJUEfUzP1YIp) https://copy.com/kJUEfUzP1YIp (https://copy.com/kJUEfUzP1YIp) and (https://copy.com/VFyc3Fk1V3Gm) https://copy.com/VFyc3Fk1V3Gm (https://copy.com/VFyc3Fk1V3Gm) Change zeta to 1 and the fractal becomes: (https://copy.com/YLYsDy3HG9vE) https://copy.com/YLYsDy3HG9vE (https://copy.com/YLYsDy3HG9vE) With zeta at 1 it starts getting a bit weird see http://www.fractalforums.com/new-theories-and-research/is-there-anything-novel-left-to-do-in-m-like-escape-time-fractals-in-2d/318/ (http://www.fractalforums.com/new-theories-and-research/is-there-anything-novel-left-to-do-in-m-like-escape-time-fractals-in-2d/315/) (reply 318). |