The nonlinearity of circle inversion causes some problems with the IFS approaches to generating limit sets. |
We illustrate Mandelbrot's method with an example, and begin by constructing some cirlces that belong to the limit set. |
Next we simplify the problem by inverting in another circle. |
Now,
we show that the limit set |
Similar arguments show the
limit set |
So the limit set is inside S1, and outside S2, S3, S4, and S5. We can say more. |
Continuing this idea quickly generates the limit set, to any desired accuracy. |
Return to circle inversion fractals.