Zobrazeno 1 - 10
of 105
pro vyhledávání: '"Barnsley, Michael F."'
Autor:
Bandt, Christoph, Barnsley, Michael F.
For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the formally stronger finite type property of Ngai and Wang. We show that an
Externí odkaz:
http://arxiv.org/abs/2404.04892
We review aspects of an important paper by Robert Strichartz concerning reverse iterated function systems (i.f.s.) and fractal blowups. We compare the invariant sets of reverse i.f.s. with those of more standard i.f.s. and with those of inverse i.f.s
Externí odkaz:
http://arxiv.org/abs/2302.10372
Publikováno v:
In Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena May 2024 182
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be fractals
Externí odkaz:
http://arxiv.org/abs/2002.03538
Autor:
Barnsley, Michael F, Vince, Andrew
The theory of fractal tilings of fractal blow-ups is extended to graph-directed iterated function systems, resulting in generalizations and extensions of some of the theory of Anderson and Putnam and of Bellisard et al. regarding self-similar tilings
Externí odkaz:
http://arxiv.org/abs/1805.00180
Autor:
Barnsley, Michael F, Vince, Andrew
New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings associated with fractal blow-ups of certain similitude iterated function systems (IFS). For each such IFS with attractor satisfying the open set condition, our construction produ
Externí odkaz:
http://arxiv.org/abs/1709.09325
We explore the chaos game for the continuous IFSs on topological spaces. We prove that the existence of attractor allows us to use the chaos game for visualization of attractor. The essential role of basin of attraction is also discussed.
Externí odkaz:
http://arxiv.org/abs/1410.3962
Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions themselves
Externí odkaz:
http://arxiv.org/abs/1309.0972
Autor:
Barnsley, Michael F., Vince, Andrew
Publikováno v:
SIGMA 11 (2015), 084, 21 pages
The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a class of
Externí odkaz:
http://arxiv.org/abs/1308.3819
Autor:
Barnsley, Michael F., Vince, Andrew
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.
Externí odkaz:
http://arxiv.org/abs/1209.6100