Abstract
Dekking and Meester defined six phases for a subclass of random Cantor sets consisting of those generated by Bernoulli random substitutions. They proved that the random Sierpinski carpet passed through all these phases asp tended from 0 to 1, but the were not able to prove the existencne of phase V in the Mandelbrot percolation process. In this paper, we accomplish the proof by improving their methods.
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