Abstract: The inversion problem between Mandelbrot and Julia sets is discussed in this
paper. Providing the inversions of arbitrary point on extended complex plane to iterative functions,
it obtains two kinds of conjugate function of the iterative function drawing Julia and Mandelbrot
sets. The Julia and Mandelbrot sets for the two kinds of conjugate function, are exactly the
inversion figures of original ones. Using the escape time algorithm, it draws the inversion figures
of Julia and Mandelbrot sets.

Key words: fractal, inversion figure, escape time algorithm, Julia set, Mandelbrot set