Fractals have gained great attention from researchers due to their wide applications in engineering and applied sciences. Especially, several topics of sciences, the iterated function systems theory has important roles. As is well known, examples fractals are derived fixed point for suitable operators spaces with complete or compact structures. In this article, a new generalization Hausdorff di...

We consider a class of iterated function systems (IFSs) of contracting similarities of Rn, introduced by Hutchinson, for which the invariant set possesses a natural Hölder continuous parameterization by the unit interval. When such an invariant set is homeomorphic to an interval, we give necessary conditions in terms of the similarities alone for it to possess a quasisymmetric (and as a corolla...

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...

Images are created using probabilistic iterated function systems that involve both affine transformations of the plane and isometries of hyperbolic geometry. Figures of attractors with striking hyperbolic symmetry are the result.

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to c...

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to c...