Title: Julia Set that looks like a Mandelbrot Set Post by: bugman on November 03, 2009, 07:34:44 PM This Julia set was created using the Modified Inverse Iteration Method (MIIM) for the formula z=z(z+1.2)².
I think it bears a remarkable resemblance to the Mandelbrot set. Which gets me thinking, I wonder if is there exists a formula for a Julia set that is exactly the same as the standard Mandelbrot set? If so, I imagine that would be a noteworthy identity for mathematicians. And it would open up the doors for creating inverse Mandelbrot sets (and possibly inverse 3D Mandelbrot sets!). Title: Re: Julia Set that looks like a Mandelbrot Set Post by: Dinkydau on November 06, 2009, 02:06:05 PM Isn't the mandelbrot set actually a Julia set?
Title: Re: Julia Set that looks like a Mandelbrot Set Post by: lkmitch on November 06, 2009, 03:48:02 PM Isn't the mandelbrot set actually a Julia set? No--for an iterated formula of the form z = f(z; c), a Julia set is a set of initial z values, whereas a Mandelbrot set is a set of c values. Title: Re: Julia Set that looks like a Mandelbrot Set Post by: David Makin on November 06, 2009, 08:37:36 PM Isn't the mandelbrot set actually a Julia set? No--for an iterated formula of the form z = f(z; c), a Julia set is a set of initial z values, whereas a Mandelbrot set is a set of c values. To put it another way - a Mandelbrot is a view of many different functions each with the same start value and a Julia is a view of a single function with many different start values. |