Let x is unstable
fixed point. In Fig 1. we take _{1}(c) = 1/2 + (1/4 - c)^{1/2}c = -2.5
and denote A = -x and _{1}D = x .
For real maps iterations of points _{1}|x| > x diverge to
infinity, therefore Julia set _{1}J(-2.5) Ì
[A,D]. Open interval (B,C) is mapped outside [A,D],
thus we throw away these points too. As since intervals
[A,B] and [C,D] are mapped onto [A,D], therefore we can
continue this process ad infinitum. Thus intervals double every iteration
and turn into separate points when number of iterations go to infinity.
You see these Cantor-like set on the |

Animated Cantor trip.

Here you can see yellow outline of the Cantor set in the Mandelbrot
and Julia midgets (the Cantor-like *J(-2.15)* set is shown for
comparison).

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