An Algorithm For The Construction of The Tight Span of Finite Subsets of The Manhattan Plane
We give a simple algorithm for the construction of the tight span of a finite subset of the Manhattan plane.
math.MG↗
arXiv subjects
Yunus Özdemir
Publications and source records attributed to Yunus Özdemir.
Graph-Directed Sprays and Their Tube Volumes via Functional Equations
The notion of sprays introduced by Lapidus and his co-workers has proved useful in the context of fractal tube formulas. In the present note, we propose a more general concept of sprays, where we allow several generators to make them more convenient for applications to graph-directed fractals. Using a simple functional equation satisfied by the volume of the inner $\varepsilon$-neighborhood of such a generalized spray, we establish a tube formula for them.
math.MG↗
Graph-Directed Fractal Interpolation Functions
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal interpolation function to the graph-directed case and prove that for a finite number of data sets there exist interpolation functions each of which interpolates corresponding data set in $\mathbb{R}^2$ such that the graphs of the interpolation functions are attractors of a graph-directed iterated function system.
math.MG↗