A few Julia sets. Remember, each Julia set corresponds to a single point in the one-and-only Mandelbrot set.
The coloring is entirely arbitrary except for 2 things:
  1. The color has to do with how long the coordinates of the point takes to 'escape' off to infinity if you apply the basic Mandelbrot algorithm, which is to square the coordinates and add the coordinate of the original point. For simplicity (really!) treat each point's coordinates as a complex number, which means that a point with ordinary x-y-plane coordinates (a,b) will be treated as a + bi, where i means the square root of negative one. (What's that, you say? Negative one can't have a square root? You are so correct, as long as you restrict yourself to REAL numbers. But mathematicians can also talk about IMAGINARY numbers, and even COMPLEX numbers, which are the sum of a real number and an imaginary number.) If the result goes more than some set distance away from the origin after 3 moves, you color the point with one color. If it takes 4 moves, you pick a different color. If it takes 5 moves, you pick a different color; and so on. If the result NEVER goes more than that set distance from the origin, no matter how many iterations you perform, then you color the original point black.
  2. It had to look attractive to me.

  Julia Set #1 - The maelstrom of the pentapods

Julia set #1

The previous set suffered some pixel damage in a hard drive crash.

Image # 2 - Squished, reticulated, spiral galaxies

julia set #2
Actually, I think the following image is part of the Mandelbrot set.

Image #3 - The mandala of Mandelbrot

really cool

That's all for now.

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