Barnsley, Michaelvince, Andrew2015-12-100143-3857http://hdl.handle.net/1885/63880The main theorem of this paper establishes conditions under which the 'chaos game' algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non-contractive iterated function systems, and under weaker conditions on the random orbit of the chaos game than obtained previously.201110.1017/S01433857100004282015-12-10