Fractal graphics , curves and art

I’m presenting fractal images made with various fractal programs.

Simply put ,  fractals are  (mathematical) objects displaying self-similarity at different scales.

The images below show the Mandelbrot set , a set of complex numbers   obtained by iterating the equation z² = z + c , where c is a constant number.I used Mathematica and Fraqtive to create these images.

A set related to the Mandelbrot set is the Julia set :

The next slideshow contains seven fractal curves , five of which were  created with Apophys , a fractal flame editor , with some Photoshop. A fractal flame is an iterated function system class of fractals. Two more images were made with Fraqtive , a generator of the Mandelbrot family of fractals.

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The following slideshow has five images created with Mandelbulber , an application for rendering 3D Mandelbrot fractals (Mandelbulbs).The images are of the same fractal formula type (Aexion) with different views and different iteration modes.

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Here are two last images of 3 D surfaces made with Mandelbulber:

mandelbulb01

mandelb-quat02

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