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Strongly-Fibred Iterated Function Systems and the Barnsley--Vince triangle
Krzysztof Leśniak, Nina Snigireva, Filip Strobin
We review the theory of semiattractors associated with non-contractive Iterated Function Systems (IFSs) and demonstrate its applications on a concrete example. In particular, we pr…
Fuzzy-set approach to invariant idempotent measures
Rudnei D. da Cunha, Elismar R. Oliveira, Filip Strobin
We provide a new approach to the Hutchinson-Barnsley theory for idempotent measures first presented in N. Mazurenko, M. Zarichnyi, Invariant idempotent measures, Carpathian Math. P…
Weakly contractive iterated function systems and beyond: A manual
Krzysztof Leśniak, Nina Snigireva, Filip Strobin
We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors an…
A multiresolution algorithm to approximate the Hutchinson measure for IFS and GIFS
Rudnei D. da Cunha, Elismar R. Oliveira, Filip Strobin
We introduce the discrete version of the Hutchinson--Barnsley theory providing algorithms to approximate the Hutchinson measure for iterated function systems (IFS) and generalized…
A multiresolution algorithm to generate images of generalized fuzzy fractal attractors
Rudnei D. da Cunha, Elismar R. Oliveira, Filip Strobin
We provide a new algorithm to generate images of the generalized fuzzy fractal attractors described in Oliveira-2017. We also provide some important results on the approximation of…
Connectedness of attractors of a certain family of IFSs
Filip Strobin, Jarosław Swaczyna
Let be a Banach space and be contractions. We investigate the set $$ C_{f,g}:=\{w\in X:\m{ the attractor of IFS }\F_w=\{f,g+w\}\m{ is connected}\}. $$ The…