We explore the performance of applying fractal coding on audio data. Some conventional fractal coding problems have been studied with audio data to provide an overview on this subject. A review of fractal coding is presented. We implement a fractal audio coding scheme to carry out the experiments. The performance of the scheme can be controlled by a number of different parameters, including map...

WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. Fi...

The paper presents a novel interactive application created in the C# programming language under the Microsoft Visual Studio environment: its introduction, theoretical grounds and application. The application allows generating two-dimensional fractals defined by iterated function systems and performing their arbitrary affine transformation. Most importantly, this transformations are easily contr...

The scope of this article is to identify the parameters bivariate fractal interpolation surfaces by using convex hulls as bounding volumes appropriately chosen data points so that resulting (graph of) function provides a closer fit, with respect some metric, original points. In way, when are chosen, one can approximate shape every rough surface. To achieve this, we first find hull each subset i...

In this paper, the newly developed fractal-fractional differential and integral operators are used to analyze dynamics of chaotic system based on image encryption. The problem is modeled in terms classical order nonlinear, coupled ordinary equations that then generalized through operator Mittag-Leffler kernel. addition that, some theoretical analyses, such as model equilibria, existence, unique...

The topic of airway-parenchymal interdependence (API) is of great importance to those interested in identifying factors that influence airway patency. A carefully designed experiment has raised questions about the classical concept of API. This paper proposes a new mechanism of API. The pulmonary lobe is an aggregated body consisting of many Miller’s lobular polyhedrons and a fractal bronchial ...

BACKGROUND Placentas are generally round/oval in shape, but "irregular" shapes are common. In the Collaborative Perinatal Project data, irregular shapes were associated with lower birth weight for placental weight, suggesting variably shaped placentas have altered function. METHODS (I) Using a 3D one-parameter model of placental vascular growth based on Diffusion Limited Aggregation (an accep...

In his groundbreaking work, ‘The Fractal Geometry of Nature’ (Mandelbrot, 1982), Benoit Mandelbrot described how fractals could account for a long list of natural forms ranging from trees to coastlines. Two recent studies in Science and The EMBO Journal have suggested that chromatin and the nucleoplasmic space surrounding it should be added to the fractal list. Fractals are ‘self-similar’, mean...

Highly nonlinear behaviour of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing quantum cellular automata [1] or their real-valued analogues. It is shown that the combination of two operations, i.e. i) enhancement of a site’s value when fulfilling a feedback condition and ii) normalization of the system after each time step, pr...