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Lol, detractors of fractal art say just that: you press a button and the image come out
Don't take all I say as absolute truth, because I only rely on my experience, but the process is this one (more or less):
- some good programmer (with good knowledge of fractal math) writes a software capable to render images of fractal formulas; in this case the software is really great and it shows 3D images based on different fractal formulas which can be mixed in many ways
- some good people add new fractal formulas to the software, making the possibilities more and more interesting
- you download the (free) software, choose your formulas and their parameters. You can keep changing formulas of parameters and navigating in the 3D environment until you see something you like (in my opinion this is already where your artistic soul comes to life). For me, this is where my fantasy matches the image and the idea takes life
- you make small tuning on the image... to remove noise, to make more interesting shapes, to add details, to have a better viewpoint from a virtual camera, to properly zoom in it etc
- you add depth, fog, shadows, lights and colors
- if needed you add more shadows, reflections, transparency etc.
- if needed you set better luminosity/contrast/colors etc in post production. Or you add a sky, or you change the fractal to make a fractal manipulation
So: yes, you choose equations and the program makes shapes similar to this one; but without your personal touch and artistic choices they don't look exactly like this one