Adding Examples to Math Paper

Question

I'm writing a paper on the Mandelbrot set and want to add some examples of iteration to it to show values that are members of the set and to show values that are not members of the set. What's the cleanest way of doing this?

Answer 1

First :

• $c:abs(c)>2$ is not a member, because critical point z=0 is escaping to infinity under $f_c(z)$ on dynamic plane = it's orbit is unbounded
• $c:abs(c)<2$ maybe is a member. One have to check it.

HTH

Answer 2

The have very nice looking graphics of the boundary of mandelbrot sets that nicely illustrate these things. Why not simply choose a suitable region that shows inside and outside and the complex pattern of near misses ? You can pick a few values that are close together to show how small differences can push it outside or inside the boundary.

It has the advantage of giving students a visual hook to get snared on.