Fractals are geometric shapes and patterns that may repeat their geometry at smaller or
larger scales. It is well established that fractals can describe shapes and surfaces that …

This collaborative volume presents recent trends arising from the fruitful interaction between
the themes of combinatorics on words, automata and formal language theory, and number …

Iterated function systems have been at the heart of fractal geometry almost from its origins.
The purpose of this expository article is to discuss new research trends that are at the core of …

We consider the disklikeness of the planar self-affine tile $ T $ generated by an integral
expanding matrix $ A $ and a consecutive collinear digit set ${\mathcal {D}}=\{0, v …

We consider a class of planar self-affine tiles T that are generated by the lower triangular
expanding matrices and the product-form digit sets. We give necessary and sufficient …

A simple, yet unifying method is provided for the construction of tilings by tiles obtained from
the attractor of an iterated function system (IFS). Many examples appearing in the literature …

Finite automata were used to determine multiple addresses in number systems and to find
topological properties of self-affine tiles and finite type fractals. We join these two lines of …

We study the structure of the digit sets ${\mathcal D} $ for the integral self-similar tiles $ T
(b,{\mathcal {D}}) $(we call such a ${\mathcal D} $ a tile digit set with respect to $ b $). So far …

TI Zaitseva, V. Yu. Protasov, “Self-affine $2$-attractors and tiles”, Mat. Sb., 213:6 (2022), 71–110;
Sb. Math., 213:6 (2022), 794–830 Sbornik: Mathematics RUS ENG JOURNALS PEOPLE …

Real-world applications now deal with enormous amounts of data, especially in the area of
high dimensional features. In the present study, we provide an approach for the rough set …