We consider classes of sets of r-adic expansions of reals speciied by means of the theory of formal languages or automata theory. It is shown how these speciications are used to calculate the Hausdorr dimension and Hausdorr measure of such sets. Since the appearence of Mandelbrot's 11 book \Fractals, Form, Chance and Dimen-sion" Fractal Geometry as a means providing a theory describing many of ...

AIM To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method. METHODS This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding t...

Keywords: fractal geometry, fractional derivative, fractional Fourier transform, fractional power of a matrix, self similarity, complex partial differential equation, broadband ultrasound, frequency-dependent attenuation, time domain. 1. Backgrounds The rational behind this model is schematically illustrated below: Fractal geometry (irregular soft tissues) → Fractional Fourier transform (freque...

We compare the Grushin geometry to Euclidean geometry, through quasisymmetric parametrization, bilipschitz parametrization and bilipschitz embedding, highlighting the role of the exponents and the fractal nature of the singular hyperplanes in Grushin geometry. Consider in Rn a system of diagonal vector fields Xj = λj(x) ∂ ∂xj , j = 1, . . . , n,

One of the central goals of ecology is to predict the distribution and abundance of organisms. Here, we show that, in ecosystems of high biodiversity, the outcome of multispecies competition can be fundamentally unpredictable. We consider a competition model widely applied in phytoplankton ecology and plant ecology in which multiple species compete for three resources. We show that this competi...

This paper proposes a method for the rapid prototyping (RP) of self-similar objects. RP technology makes available the physical generation of a solid object. However, the contemporary design capability of a computer-aided design (CAD) system can atmost use the non-uniform rational B-spline (NURBS) modelling method. When the design has a very complicated shape with self-similarity, contemporary ...

Low profile antenna in communication is a new methodology. Fractal geometry is a methodology through which size reduction is achieved. A Self-similar fractal antenna using multicantor technique is proposed and experimentally studied. Space-filling cantors and self-similarity properties of fractal geometry have been adopted in the proposed antenna to miniaturize the size of antenna. The antenna ...

With regards to the big agglomerations and especially the cities, the constructed surface has often got an irregular shape, in spite of the efforts of the urbanists to promote more compact shapes. The internal spatial order of the big agglomerations is a matter of the fractal geometry. This article shows the interest of applying the fractal geometry in cities and in networks of communication of...

The fractal dimensions of FeZSM-5 zeolites were used to characterize the change in their geometry depending on different postsynthesis treatments. The fractal dimension values were estimated from the Dubinin–Astakhov isotherms of nitrogen adsorption and related to the activity of these zeolites in the benzene hydroxylation to phenol by nitrous oxide. The zeolites had two different iron contents...

The self-similarity of Indonesian Borobudur Temple is observed through the dimensionality of stupa that is hypothetically closely related to whole architectural body. Fractal dimension is calculated by using the cube counting method and found that the dimension is 2.325, which is laid between the two-dimensional plane and three dimensional space. The applied fractal geometry and self-similarity...