Related papers: Fractal and Multi-Scale Fractal Dimension analysis…
This study builds a bridge between two well-studied but distant topics: fractal dimension and Discrete Global Grid System (DGGS). DGGSs are used as covering sets for geospatial vector data to calculate the Minkowski-Bouligand dimension.…
We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a…
We consider two models (A and B) which can describe both two dimensional fragmentation and stochastic fractals. Model A exhibits multifractality on a unique support when describing a fragmentation process and on one of infinitely many…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…
Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to consider, and part of the richness of the subject is in…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
The improved city clustering algorithm can be used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the urban measurements within the variable boundaries follow allometric…
Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
This paper serves as a complementary material to a poster presented at the XXXVI Dynamics Days Europe in Corfu, Greece, on June 6th-10th in 2016. In this study, fractal dimension ($D$) of two types of self-affine signals were estimated with…
This chapter deals with error and uncertainty in data. Treats their measuring methods and meaning. It shows that uncertainty is a natural property of many data sets. Uncertainty is fundamental for the survival os living species, Uncertainty…
Tissues are fractal due to its self-similar structure, and the fractal dimension change with the abnormalities such as in disease like cancer. The optical imaging of thin slices of tissue using transmission microscopy can produce an…
Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by…
Fractal plays an important role in nonlinear science. The most important parameter to model fractal is fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, given a mass function…
We establish a correspondence between Pavlovian conditioning processes and fractals. The association strength at a training trial corresponds to a point in a disconnected set at a given iteration level. In this way, one can represent a…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
A gray-level image texture descriptors based on fractal dimension estimation is proposed in this work. The proposed method estimates the fractal dimension using probability (Voss) method. The descriptors are computed applying a multiscale…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The…