4 papers
On the revolving structure of the Lévy dragon and its linear transforms
Miguel Gonzalez-Carriedo, Kiko Kawamura, Jonathan Leung +1
Lévy's Dragon Curve is a well-known self-similar fractal, notable for its ability to tile the complex plane. We review a representation of the curve as a set of points given by com…
Continuity of the natural dimension of piecewise linear iterated function systems
R. D. Prokaj, P. Raith
We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. We show that typically the natural dimension of these systems changes…
Special families of piecewise linear iterated function systems
R. D. Prokaj, K. Simon
This paper investigates the dimension theory of some families of continuous piecewise linear iterated function systems. For one family, we show that the Hausdorff dimension of the…
Piecewise linear iterated function systems on the line of overlapping construction
R. D. Prokaj, K. Simon
In this paper we consider Iterated Function Systems (IFS) on the real line consisting of continuous piecewise linear functions. We assume some bounds on the contraction ratios of t…