Related papers: A fractal set from the binary reflected Gray code
We explore a novel link between two seemingly disparate mathematical concepts: Egyptian fractions and fractals. By examining the decomposition of rationals into sums of distinct unit fractions, a practice rooted in ancient Egyptian…
The fractal property stipulates that the same physical laws apply for different scales of a given physics. This property is applied to particles and nuclei, in order to study the possibility to use it to help for determination of unknown…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…
A bitset is a set that encodes for a binary number. Bitsets are at the basis of a beautiful theory of recombination with n-loci and here we begin from scratch and advance to include the derivation of the fundamental results about the…
Fractal Clifford Spaces (FCS) may be considered as a challenging approach to the unification of micro-physics and macro-physics. Trajectories of these manifolds are described by different poly-vectors describing paths and their deviation…
Prime number related fractal polygons and curves are derived by combining two different aspects. One is an approximation of the prime counting function build on an additive function. The other are prime number indexed basis entities taken…
We apply some methods and technique of complex dynamics to study the set of symmetries of attractors of holomorphic Iterated Function Systems (IFS), as well as relations between IFS sharing the same attractor.
In this paper we will introduce the methodology of analysis of the convex hull of the attractors of iterated functional systems (IFS) - compact fixed sets of self-similarity mapping. The method is based on a function which for a direction,…
In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals.…
Fractals offer the ability to generate fascinating geometric shapes with all sorts of unique characteristics (for instance, fractal geometry provides a basis for modelling infinite detail found in nature). While fractals are non-euclidean…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
The fragmentation processes of exchangeable partitions have already been studied by several authors. In this paper, we examine rather fragmentation of exchangeable compositions, that means partitions of $\mathbb{N}$ where the order of the…
We investigate the geometric properties displayed by the magnetic patterns developing on a two-dimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout…
I describe a mathematical framework for the efficient processing of the very large sets of Feynman diagrams contributing to the scattering of many particles. I reexpress the established numerical methods for the recursive construction of…
Fractal geometry is the study of sets which exhibit the same pattern at multiple scales. Developing tools to study these sets is of great interest. One step towards developing some of these tools is recognizing the duality between…
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
Large light deflection angles are produced in the strong gravitational field regions around neutron stars and black holes. In the case of binary systems, part of the photons emitted from the companion star towards the collapsed object are…
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…