Abstract
We extend a result regarding the Random Backward Iteration algorithm for drawing Julia sets (known to work for certain rational semigroups containing a non-Möbius element) to a class of Möbius semigroups which includes certain settings not yet been dealt with in the literature, namely, when the Julia set is not a thick attractor in the sense given in [David Fried, Sebastian. M. Marotta, and Rich Stankewitz, Complex dynamics of Möbius semigroups, Ergodic Theory Dynam. Systems, 32(6):1889--1929, 2012].
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