Title: Spring Garden IXe Post by: Pauldelbrot on August 15, 2012, 10:04:52 PM Spring Garden IXe
(http://nocache-nocookies.digitalgott.com/gallery/12/511_15_08_12_10_04_51.jpeg) http://www.fractalforums.com/index.php?action=gallery;sa=view;id=12253 A tiny minibrot is set like a jewel in the middle of a pattern of three basins, in this penultimate zoom of the Spring Garden e branch. Title: Re: Spring Garden IXe Post by: cKleinhuis on August 15, 2012, 10:16:31 PM is that area around due to low iteration ?!
i somehow dont like the gardening pics that much, although this minibrot looks promising! this is plain z^2 mandelbrot ?! Title: Re: Spring Garden IXe Post by: Pauldelbrot on August 15, 2012, 10:51:43 PM is that area around due to low iteration ?! i somehow dont like the gardening pics that much, although this minibrot looks promising! this is plain z^2 mandelbrot ?! Nope, it's f(z) = az^2(z - c)/(1 - cz) + b which has fixed basins at zero (pink) and infinity (blue) and up to two parameter-dependent basins (large purple areas and the minibrot, respectively). That's the same system that produces the Herman rings under other circumstances. Title: Re: Spring Garden IXe Post by: Pauldelbrot on August 15, 2012, 10:54:55 PM Actually, that's strictly true only if b = 0. When b is moved off zero, zero ceases to be a superattracting fixed point -- there's still an attractor, and it remains near zero, but it's no longer superattracting and no longer exactly on zero. In this instance, b is a very tiny nonzero number, not to get new fractal shapes but purely to stop that attractor from superattracting so that the convergent smooth coloring algorithm will work properly in its basin. |