9.D. Animations

Changing the circles certainly can change the limit set.

A simple example is made from five circles, with four constant and the fifth shrinking.

These three animations illustrate the idea of fractal motion seen in the first example.

In all three, the fixed circles have radius 1 and centers at (1, 1), (-1, 1), (-1, -1), and (1, -1).

In the one moving circle animation there is a single moving circle, of constant radius, staying tangent to one or two of the fixed circles.

In the two moving circles animation there are two moving circles, of varying radius, staying tangent to one or two of the fixed circles and to one another.

In the four moving circles animation there are four moving circles, of varying radius, staying tangent to one or two of the fixed circles and to two of the moving circles.

Return to circle inversion fractals.

In the one moving circle animation there is a single moving circle, of constant radius, staying tangent to one or two of the fixed circles.
In the two moving circles animation there are two moving circles, of varying radius, staying tangent to one or two of the fixed circles and to one another.
In the four moving circles animation there are four moving circles, of varying radius, staying tangent to one or two of the fixed circles and to two of the moving circles.