11 citations · 32 across the 11 of their papers we have counts for
12 papers
Split square and split carpet as examples of non-metrizable IFS attractors
Krzysztof Leśniak, Magdalena Nowak
We define two non-metrizable compact spaces and show that they are attractors of iterated function systems. Both of them, the split square and the split carpet, are constructed usi…
Pointwise attractors which are not strict
Magdalena Nowak
We deal with the finite family of continuous maps on the Hausdorff space. A nonempty compact subset of such space is called a strict attractor if it has an open n…
Peano continua with self regenerating fractals
Magdalena Nowak
We deal with the question of Masayoshi Hata: is every Peano continuum a topological fractal? A compact space is a topological fractal if there exists a finite fam…
Embedding fractals in Banach, Hilbert or Euclidean spaces
Taras Banakh, Magdalena Nowak, Filip Strobin
By a metric fractal we understand a compact metric space endowed with a finite family of contracting self-maps of such that . I…
Counterexamples in theory of fractal dimension for fractal structures
Magdalena Nowak, Manuel Fernández-Martínez, Miguel Angel Sánchez-Granero
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate…
Counterexamples for IFS-attractors
Magdalena Nowak, Manuel Fernandez-Martinez
In this paper, we deal with the part of Fractal Theory related to finite families of (weak) contractions, called iterated function systems (IFS, herein). An attractor is a compact…