相关论文: Borobudur was Built Algorithmically

Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…

We show that any order isomorphism between ordered structures of associative unital JB-subalgebras of JBW algebras is implemented naturally by a Jordan isomorphism. Consequently, JBW algebras are determined by the structure of their…

Trees in works of art have stirred emotions in viewers for millennia. Leonardo da Vinci described geometric proportions in trees to provide both guidelines for painting and insights into tree form and function. Da Vinci's Rule of trees…

In this article, we present a novel box-covering algorithm for analyzing the fractal properties of complex networks. Unlike traditional algorithms that impose a predetermined box size, our approach assigns nodes to boxes identified by their…

Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…

We analyze the fractal dimension of open clusters using 3D spatial data from Gaia DR3 for 93 open clusters from Pang et al. (2024) and 127 open clusters from Hunt & Reffert (2024) within 500 pc. The box-counting method is adopted to…

The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…

Crystal structure prediction has been a subject of topical interest, but remains a substantial challenge, especially for complex structures as it deals with the global minimization of the extremely rugged high-dimensional potential energy…

Intricate patterns in abstract art many times can be wrongly characterized as being complex. Complexity can be an indicator of the internal dynamic of the whole system, regardless of the type of system in question, including art creation.…

In this report we present experimental results using \emph{Haussdorf-Besicovich} fractal dimension for performing morphological galaxy classification. The fractal dimension is a topological, structural and spatial property that give us…

We face a need of discovering a pattern in locations of a great number of points in a high-dimensional space. Goal is to group the close points together. We are interested in a hierarchical structure, like a B-tree. B-Trees are…

Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant…

A conjecture for the dimension and the character of the homogenous components of the free Jordan algebras is proposed. As a support of the conjecture, some numerical evidences are generated by a computer and some new theoretical results are…

We construct Jordan arcs of prescribed conformal dimension which are minimal for conformal dimension. These curves are used to design fractal rugs, similar to Rickman's rug, that are also minimal for conformal dimension. These fractal rugs…

In this paper, we propose to enumerate all different configurations belonging to a specific class of fractals: A binary initial tile is selected and a finite recursive tiling process is engaged to produce auto-similar binary patterns. For…

Given a triangulation of a closed topological cube, we show that (under some technical condition) there is an essentially unique tiling of a rectangular parallelepiped by cubes, indexed by the vertices of the triangulation. Moreover, i -…

In this paper we try to find examples of integrable natural Hamiltonian systems on the sphere $S^2$ with the symmetries of each Platonic polyhedra. Although some of these systems are known, their expression is extremely complicated; we try…

The Cantor set complementary to the Devil's Staircase associated with the Circle Map has a fractal dimension d approximately equal to 0.87, a value that is universal for a wide range of maps, such results being of a numerical character. In…

We relate the fractal dimension of the backbone, and the spectral dimension of Eden trees to the dynamical exponent z. In two dimensions, it gives fractal dimension of backbone equal to 4/3 and spectral dimension of trees equal to 5/4. In…

Each closed oriented 3-manifold $M$ is naturally associated with a set of integers $D(M)$, the degrees of all self-maps on $M$. $D(M)$ is determined for each torus bundle and torus semi-bundle $M$. The structure of torus semi-bundle is…