Related papers: Fractal Patterns in Music
Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle. The former is the measure of the jaggedness of the curves while…
While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is…
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the…
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To…
Categorization is crucial for content description in archiving of music signals. On many occasions, human brain fails to classify the instruments properly just by listening to their sounds which is evident from the human response data…
Trees in works of art have stirred emotions in viewers for millennia. Leonardo da Vinci described geometric proportions in trees to provide both guidelines for painting and insights into tree form and function. Da Vinci's Rule of trees…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
We examine the fractal structure of the physical universe from the large scale to the smallest scale, including the phenomenon of fractal scaling. This is explained in terms of a stochastic underpinning for the laws of physics. A picture in…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
The foundation of the theory presented here has already been proved to be effective for the case of curves belonging to the Koch family. The present paper extends the investigation to more complex curves, namely randomly generated curves…
The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…
This paper addresses the problem of cross-modal musical piece identification and retrieval: finding the appropriate recording(s) from a database given a sheet music query, and vice versa, working directly with audio and scanned sheet music…
Music contains hierarchical structures beyond beats and measures. While hierarchical structure annotations are helpful for music information retrieval and computer musicology, such annotations are scarce in current digital music databases.…
This paper deals with an estimating of the Fractal Dimension of a hydrometeorology variables like an Air temperature or humidity at a different sites in a landscape (and will be further evaluated from the land use point of view). Three…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
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…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…