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We extend a result regarding the Random Backward Iteration algorithm fordrawing Julia sets (known to work for certain rational semigroups containing anon-M\"obius element) to a class of M\"obius semigroups which includes certainsettings not yet been dealt with in the literature, namely, when the Julia setis not a thick attractor in the sense given in [David Fried, Sebastian. M.Marotta, and Rich Stankewitz, Complex dynamics of M\"obius semigroups, ErgodicTheory Dynam. Systems, 32(6):1889--1929, 2012].

Backward Iteration Algorithms for Julia sets of M\"obius Semigroups