More Julia sets

We now move in the other direction, towards the circular disk attached to the left of the main cardoid. Recall that the interior of this disk is the region in which there is an attracting orbit of period two. We need a word on the Julia sets. It turns out that images of the Julia sets are harder to compute than for the Mandelbrot set. (Difficulties with parts of the Mandelbrot set are discussed in the next page.) Some Julia sets look like they have lines that should join. They probably do, but the program that computed the images could not pick them up.

c=-0.5+0i.
The circle distorts in another direction.
8.

c=-0.75+0i.
At the point of tangency of the main cardioid and the disk to the left, the Julia set is a collection of tangent distorted circles.
9.

c=-1+0i.
At the center of the disk to the left, the lines in the Julia set are no longer tangent.
10.

c=0+.5i.
Moving vertically introduces twist into the picture. There is still symmetry about the origin, but symmetry about the axes is lost.
11.

c=-0.125+0.65i.
At the tangency between the main cardioid and the disk at the top. This can be compared to image 9 above.
12.

Forward to What is the Mandelbrot set - Page IV (12 embedded images).
Back to What is the Mandelbrot set - Page II (14 embedded images).
Back to The Mandelbrot Set and Julia Sets.

Return to A Few Bits of Mathematics.
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