Julia Set that looks like a Mandelbrot Set

[bugman]

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!).

[Dinkydau]

Isn't the mandelbrot set actually a Julia set?

[lkmitch]

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.

[David Makin]

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.