Circle Inversion Fractals

Circle Inversion Driven IFS

As illustrated in Overlapping Circles, section D, the limit set can be quite complicated when the inverting circles overlap because inversion from inside to outside of a circle is an expansion.

One way to deal with the problems resulting from expansion is the restricted limit set, section H, in which we never invert from inside to outside of the circle.

The nonlinearity of inversion can make difficult the task of determining which combinations of inversions are forbidden.

Driven IFS provides a more uniform way of visualizing these restrictions.

First we modify the standard notion of driven IFS to simplify the task of parsing these pictures.
Example 1
Example 2
Finally, here is an animation illustrating the change of the driven IFS as one of the inverting circles enlarges.

Return to circle inversion fractals.