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:
- 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.
- It had to look attractive to me.
Julia Set #1 - The maelstrom of the pentapods
The previous set suffered some pixel damage in a hard drive crash.
Image # 2 - Squished, reticulated, spiral galaxies
Actually, I think the following image is part of the
Image #3 - The mandala of Mandelbrot
That's all for now.