Related papers: On the Sierpinski triangle and its generalizations
The generalization of the the Yang-Baxter relation is proposed. In this generalization the spectral parameters of the particles change after the scattering. The corresponding algebraic structures are discussed. The corresponding action of…
In the present paper we explore a way to represent numbers with respect to the base $-\frac32$ using the set of digits $\{0,1,2\}$. Although this number system shares several properties with the classical decimal system, it shows remarkable…
In this paper we introduce a generalization of palindromic continued fractions as studied by Adamczewski and Bugeaud. We refer to these generalized palindromes as $m$-palindromes, where $m$ ranges over the positive integers. We provide a…
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in…
In this paper, we give a few results on the local behavior of harmonic functions on the Sierpinski triangle - more precisely, of their restriction to a side of the triangle. First we present a general formula that gives the H\"older…
We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…
We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.
Fractal structure emerges spontaneously from the chemical cross\-linking of monomers into hydrogels, and has been directly linked to power law visco\-elasticity at the gel transition, as recently demonstrated for isostatic…
In this paper we shall introduce some nonmeasurable and completely nonmeasurable subsets of the plane with various additional properties, e.g. being Hamel basis, intersecting each line in a strong Luzin / Sierpi\'nski set. Also some…
Recently, attempts have been made to take into account the fractal properties of seismicity when mapping the long-term rate of earthquakes. The paper touches upon the theoretical aspects of fractality and provides a critical analysis of its…
This article is devoted to sets having the Moran structure. The main attention is given to topological, metric, and fractal properties of certain sets whose elements have restrictions on using digits or combinations of digits in own…
We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account…
The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective…
We introduce a model of interacting bosons exhibiting an infinite collection of fractal symmetries -- termed "Pascal's triangle symmetries" -- which provides a natural $U(1)$ generalization of a spin-(1/2) system with Sierpinski triangle…
The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies.…
This work explores new arithmetic and combinatorial structures arising from the interplay between Farey-type graphs, Fibonacci expansions, and operadic constructions. We introduce Fibonadic numbers, defined as an inverse limit under the…
This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…
Tsallis q-extension of statistics and fractal generalization of dynamics are two faces of the same physical reality, as well as the Kernel modern complexity theory. The fractal generalization dynamics is based at the multiscale -…