We provide a formal proof of equivalence between the class of fractals created by Recursive Turtle Programs (RTP) and Iterated Affine Transformations (IAT). We begin by reviewing RTP ( a geometric interpretation of non-bracketed L-systems with a single production rule) and IAT (Iterated Function Systems restricted to affine transformations). Next, we provide a simple extension to RTP that gener...

We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems. Under assumptions that include, for example, iterated function systems, but that exclude stochastic differ...

Visualization provides powerful tools for the investigation of dynamical systems. The application of various visualization techniques to complex and chaotic dynamical systems is discussed. The interactive specification and modification of strange attractors allow an easier understanding of the underlying dynamics. Graphical time series analysis visualizes time series and phase space reconstruct...

in this paper, we study l1 -solutions of the following two-direction poly-scale refinement equationwe prove that the vector space of all l1 -solutions of the above equation is at most one-dimensional andconsists of compactly supported functions of constant sign. we also show that any- l1 solution of the aboveequation is either positive or negative on its support under a special assumption. with...

Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. And contractivity functions in IFS has iterated systems. If are contractions, then is guaranteed a unique attractor. Recently, however, there an interest what occurs attractor at boundary between contractvity expansion IFS. That subject this paper. For family $F_t...

In this paper we aim to obtain the attractors with assistance of a finite family generalized contractive mappings, which belong special class mappings defined on partial metric space. Consequently, variety results for iterated function systems satisfying different set conditions are acquired. We present some examples in support proved herein. Our generalize, unify and extend exist current liter...

Large video files processing involves a huge volume of data. The codec, storage systems and network needs resource utilization, so it becomes important to minimize the used memory space time distribute these videos over Internet using compression techniques. Fractal image falls under category lossy compression. It gives best results when for natural images.
 This paper presents an efficien...