An approach to action selection in autonomous agents is presented. This approach is motivated by biological examples and the operation of the Random Iteration Algorithm on an Iterated Function System. The approach is illustrated with a simple three-mode behavior that allows a swarm of 200 computational agents to function as a global optimizer on a 30-dimensional multimodal cost function. The be...

If F and G are iterated function systems, then any infinite word W in the symbols F and G induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single C iterated function system H. We prove that under certain assumptions on F and G, the answer is no. This problem is motivated by the spectral theory of one-dimensional quasicrystals.

Motivated by the need for new mathematical tools applicable to the study of fractal point-cloud distributions, expectations of complex-valued functions defined over general ‘deterministic’ fractal domains are considered, following the development of a measure-theoretic foundation for their analysis. In particular, we wish to understand and evaluate separation moments as given by integrals of th...

LRIFS's (Language-Restricted Iterated Function Systems) generalize the original de nition of IFS's (Iterated Function Systems) by providing tools for restricting the sequences of applicable transformations.In this paper, we study an approach of LRIFS's based on matrices and graph theory. This enables us to generate a matrix which elements are attractors.

We survey some of the topological properties of the attractors of iterated function systems such as connectedness, arcwise connectedness and locally arcwise connectedness. We give necessary and sufficient conditions for the attractors of finite iterated function system (IFS) to be a connected sets and in the case when infinite iterated function systems (IIFS) are considered we give only some su...

The sequence {Fn} is called the iterated function system coming from the sequence f1, f2, f3, . . .; we abbreviate this to IFS. By Montel’s theorem (see for example [3]), the sequence Fn is a normal family, and every convergent subsequence converges uniformly on compact subsets of ∆ to a holomorphic function F . The limit functions F are called accumulation points. Therefore every accumulation ...