Title: मण्डलबेथ (maṇḍalabeth) 3D analog of the mandelbrot set Post by: bethchen on December 13, 2010, 01:46:27 PM नमस्ते! (i bow to you!)
please feel free to check out the मण्डलबेथ (maṇḍalabeth), new 3D fractal with various symmetry groups. http://www-personal.umich.edu/~bethchen/mandalabeth/ actually, it's a 3D analog of the mandelbrot set! the standard 2D generating function (over the standard unit circle) gives you the usual 2D mandelbrot set. the 3D generating function (over a bouquet of rings) is the sum of 2D generating functions (over each ring), where the function is conjugated by the isometry (between the ring & standard unit circle) & its inverse. if the power–1 is a multiple of the natural symmetry of the bouquet of rings, then the 3D fractal will have the same symmetry group as the bouquet of rings. i invite you to explore these new worlds, and have fun drawing lots of pretty pictures! bethchen@umich.edu Title: Re: मण्डलबेथ (maṇḍalabeth) 3D analog of the mandelbrot set Post by: jehovajah on January 25, 2011, 03:35:26 AM I bow to you, also and welcome you to the forum! Maybe you want to introduce yourself in the meet and greet? Thank you so much for the Formulae in the appendix of your pdf. |