fractal [liquid geometry]

A fractal walk, based on the Mandelbrot set, that penetrates the magic within, traversing the rhizomatic complexity of images at increasingly smaller scales, exponentially enlarged on a round trip. Any math lover knows the beauty of fractals through a static zoom, however, adding movement, rhythm and melody to the formula (nothing better than AI to make an algorithm work with new algorithms) allows it to become a new and exciting experience. This is an incredibly simple formula that generates infinite complexity: zeta sub n+1 equals zeta sub n squared plus c, with an initial condition that zeta sub zero equals zero. To generate the image, you choose a point c = (x, y) in a complex plane and start by assigning z the value 0. You repeat this many times (e.g., 100–1000 iterations). If z is less than 2, you paint it black (it's in the Mandelbrot set). If z is greater than 2, c is outside the set, and you assign the pixel a color based on how many iterations it took to escape (escape velocity).