We explore when the chaos game renders a quasi attractor of an iterated function system (IFS); we emphasize the role of the set in which the chaos game is initialized. For IFS with lower semicontinuous Hutchinson-Barnsley operator we find that these initial points necessarily belong to the largest invariant set of the weak basin of the attractor. Under additional assumptions, namely the attractor is a stable small attractor and the space compact, we find that the probabilistic chaos game with initial points in the largest invariant set of the weak basin does in fact render the attractor. We note that this result applies to IFS which contain discontinuous functions. Under the same additional assumptions we provide the same conclusion for the disjunctive chaos game played with an evenly continuous IFS (this is the topological version of equicontinuous IFS).

我们探讨了混沌游戏何时呈现出迭代功能系统（IFS）的准吸引子。我们强调混沌游戏在其中初始化的场景的作用。对于具有较低半连续Hutchinson-Barnsley算符的IFS，我们发现这些初始点必然属于吸引子的弱盆地的最大不变集。在另外的假设下，即吸引子是一个稳定的小吸引子，并且空间紧凑，我们发现在弱盆地的最大不变集合中具有初始点的概率混沌博弈确实可以使吸引子成为现实。我们注意到，此结果适用于包含不连续函数的IFS。