fractalforums.com - Julia Set that looks like a Mandelbrot Set

bugman

Iterator

Posts: 122

Julia Set that looks like a Mandelbrot Set

« 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!).

Julia Set that looks like a Mandelbrot Set.jpg (13.54 KB, 276x276 - viewed 134 times.)
« Last Edit: November 03, 2009, 09:15:01 PM by bugman »	Logged

Dinkydau

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Posts: 132

1337

Re: Julia Set that looks like a Mandelbrot Set

« Reply #1 on: November 06, 2009, 02:06:05 PM »

Isn't the mandelbrot set actually a Julia set?


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I am not an old man, I am not a genius, I am not engaged in maths 24/7, I just think fractals are beautiful!

lkmitch

Conqueror

Posts: 69

Re: Julia Set that looks like a Mandelbrot Set

« Reply #2 on: November 06, 2009, 03:48:02 PM »

Quote from: Dinkydau on November 06, 2009, 02:06:05 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.


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David Makin

Global Moderator
Fractal Supremo

Posts: 1202

Re: Julia Set that looks like a Mandelbrot Set

« Reply #3 on: November 06, 2009, 08:37:36 PM »

Quote from: lkmitch on November 06, 2009, 03:48:02 PM

Quote from: Dinkydau on November 06, 2009, 02:06:05 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.


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