# Fractals/Iterations in the complex plane/sculpt

Techniques:

- Julia morphing - to sculpt shapes of Mandelbrot set parts ( zoom )
^{[1]}^{[2]}^{[3]} - Inflection
^{[4]}^{[5]} - shape stacking
^{[6]} - Navigating to a Leavitt Embedded Julia Set
^{[7]} - minibrots
- symmetry
- repetition
- Letteres in the Mandelbrot set

"The golden rule behind most of my images is the following. Its aspects can be used to do pretty much everything that you find in my gallery:
Given a location with a zoom level n, moving away from the center to a different center has the following effect:
The shape at zoom level n is doubled at zoom level 1,5n in such a way that the rotational symmetry becomes 2-fold.
At 1,75n the symmetry becomes 4-fold.
At 1,875n the symmetry becomes 8-fold.
...
In general: the zoom level increases in steps of 2^-1, 2^-2, 2^-3, ... and goes on forever. The symmetry increases by a factor 2 for every extra step. The limit of the sum of all of those steps 2^-1 trough 2^-n where n goes to infinity is 1, so after infinitely many steps we arrive at a finite zoom level. Indeed, at a depth of 2n, twice as deep as where we went off center, there is a small mandelbrot set, where the symmetry goes to infinity.
The rule itself has not been proven as far as I know and there are endless exceptions where it is not exact. Sometimes shapes appear a little earlier than the rule would predict, but the small mandelbrot set will never occur FURTHER than 2n. (I think I know what the inaccuracy is, by the way.)" Dinkydau^{[8]}

# Video[edit]

- FractalNet HD - Morphing Julia set 1 Michael Hogg
- Natural shapes discovered in the Mandelbrot set fractal by logicedges

# References[edit]

- ↑ automated_julia_morphing by Claude Heiland-Allen
- ↑ Julia morphing symmetry by Claude Heiland-Allen
- ↑ fractalforums : towards-a-language-for-julia-morphing
- ↑ fractalforums : show inflection
- ↑ fractalforums inflection-mappings
- ↑ Causality in Fractals - shapestacking explained by Chillheimer Chillheimer
- ↑ Navigating to a Leavitt Embedded Julia Set by Robert Munafo'
- ↑ fractalforums : deep-zooming-to-interesting-areas/