Related papers: Abstract art generated by Thue-Morse correlation f…
Studying and comparing arithmetic properties of a given automatic sequence and the sequence of coefficients of the composition inverse of the associated formal power series (the formal inverse of that sequence) is an interesting problem.…
This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…
The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…
Quasi-crystals are aperiodic structures that present crystallographic properties which are not compatible with that of a single unit cell. Their revolutionary discovery in a metallic alloy, less than three decades ago, has required a full…
The pair correlations of the Thue--Morse sequence and system are revisited, with focus on asymptotic results on various means. First, it is shown that all higher-order correlations of the Thue--Morse sequence with general real weights are…
Abstract continued Thiele type fraction has been constructed, which is an interpolation one for nonlinear operator acting from linear topological space X to algebra Y with a unit. In particular cases it changes into both a classic Thiele…
In this paper the problem of the theory of a quasicrystal structures - the determination of coordinates of each atom of quasicrystal in analytical form - is solved. Within the framework of the proposed model a periodic crystal can be…
We present the sign-problem-free quantum Monte Carlo study of the half-filled Hubbard model on two-dimensional quasicrystals, revealing how specific aperiodic geometries fundamentally dictate quantum criticality. By comparing the Penrose…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation…
This paper proposes a way to understand neural network artworks as juxtapositions of natural image cues. It is hypothesized that images with unusual combinations of realistic visual cues are interesting, and, neural models trained to model…
An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congruences include paradoxical decompositions and $n$-divisibility…
Our study delves into the fusion of abstract art interpretation and text-to-image synthesis, addressing the challenge of achieving precise spatial control over image composition solely through textual prompts. Leveraging the capabilities of…
Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three…
Linearly repetitive cut and project sets are mathematical models for perfectly ordered quasicrystals. In a previous paper we presented a characterization of linearly repetitive cut and project sets. In this paper we extend the classical…
We present a generative model for complex free-form structures such as stroke-based drawing tasks. While previous approaches rely on sequence-based models for drawings of basic objects or handwritten text, we propose a model that treats…
We define the Thue-Morse transform T on a class of infinite binary words. It sends the alternating word a_0 = 010101... to the Thue-Morse sequence. We then study its orbit a_m = T^m(a_0) as well as the sequences u_m and v_m giving…
We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth…
In this paper, we propose a general mechanism for the existence of quasicrystals in spatially extended systems (partial differential equations with Euclidean symmetry). We argue that the existence of quasicrystals with higher order…
We define the arithmetic self-similarity (AS) of a one-sided infinite sequence sigma to be the set of arithmetic progressions through sigma which are a vertical shift of sigma. We study the AS of several famlies of sequences, viz.…