Fractals Everywhere, Second Edition covers the fundamental approach to fractal geometry
through iterated function systems. This 10-chapter text is based on a course called" Fractal …

Let a data set {(xi, yi)∈ I× R; i= 0, 1,⋯, N} be given, where I=[x 0, x N]⊂ R. We introduce
iterated function systems whose attractors G are graphs of continuous functions f∶ I→ R …

The goal of science is to understand why things are the way they are. By emulating the logic
of nature, computer simulation programs capture the essence of natural objects, thereby …

Consider a discrete-time Markov process on a locally compact metric space X obtained by
randomly iterating Lipschitz maps wl,..., w~; the probability p~(x) of choosing map w~ at each …

Interpolation functions f:0,1→R of the following nature are constructed. Given data
\left{\left(t_n,x_n\right)∈0,1*R:n=0,1,2,⋯,N\right\} with 0=t_0<t_1<⋯<'t_N=1, f obeys …

In this paper, two iterated function system (IFS) models are explored for the representation of
single-valued discrete-time sequences: the self-affine fractal model and the piecewise self …

New developments in computer science, biology, mathematics and physics offer possibilities
to obtain deeper understanding of growth and forms of organisms. It is now possible to carry …

What is computer graphics and what are the conceptual tasks of research in this area? To
the average person the term still conveys more or less the design of-gos and the …

Fractal geometry has been widely applied in computer graphics to visually represent natural
objects, which cannot be easily represented by Euclidean geometry. Other than visual …

A new class of iterated function systems is introduced, which allows for the computation of
non-compactly supported invariant measures, which may represent, for example, greytone …