Related papers: Mathematical model for fractal manifold
A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first…
The question of a possible excitation and emergence of fractional type dynamics, as a more realistic framework for understanding emergence of complex systems, directly from a conventional integral order dynamics, in the form a continuous…
In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…
It is argued that in the case of a smooth transition across a (dilaton-driven) curvature bounce the growing mode of the vector fluctuations matches continuously with a decaying mode at later times. Analytical examples of this observation…
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This…
Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules.…
The subject of this note is the mixed Katugampola fractional integral of a bivariate function defined on a rectangular region in the Cartesian plane. This is a natural extension of the Katugampola fractional integral of a univariate…
This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…
In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base…
This paper is a sharp and focussed exploration of the Fibonacci substitution and the mathematical entity it gives rise to, the Fibonacci word. Our investigations are both of an algebraic and a geometric nature. Indeed, it is the combination…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
In this paper we use fractal geometry to investigate boundary aspects of the first homology group for finite coverings of the modular surface. We obtain a complete description of algebraically invisible parts of this homology group. More…
We discuss a variation of Takagi curves based, however, more on algebraic than geometric principles. Namely, we construct functions of loops in a special binary representation. The graph of these functions usually has chaotic and fractal…
In the context of a noncommutative differential calculus on the algebra of real valued functions of an $n$-dimensional manifold $M$, a commutative and associative product of 1-forms is naturally defined. Ordinary differential calculus…
In the framework of nonassociative geometry (hep-th/0003238) a unified description of continuum and discrete spacetime is proposed. In our approach at the Planck scales the spacetime is described as a so-called "diodular discrete structure"…
Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer…
We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…
Precise analyses of the statistical and scaling properties of galaxy distribution are essential to elucidate the large-scale structure of the universe. Given the ongoing debate on its statistical features, the development of statistical…
We set up a geometrical theory for the study of the dynamics of reducible Pisot substitutions. It is based on certain Rauzy fractals generated by duals of higher dimensional extensions of substitutions. We obtain under certain hypotheses…