Related papers: Drip Paintings and Fractal Analysis
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…
Art is the ultimate expression of human creativity that is deeply influenced by the philosophy and culture of the corresponding historical epoch. The quantitative analysis of art is therefore essential for better understanding human…
Fractals have been at the heart of geophysical and geospatial studies in the recent past. We examine the emergent fractal character of water vapor distributions above the surface of the Earth as a function of both image resolution (number…
In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the…
We analyze the fractal dimension of melodic contours and pitch time series of classical music and folk music tunes. The fractal dimensions obtained from box counting and detrended fluctuation analysis show significant differences. They are…
It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for…
Ancient artworks obtained in archaeological excavations usually suffer from a certain degree of fragmentation and physical degradation. Often, fragments of multiple artifacts from different periods or artistic styles could be found on the…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
I report the results of the test, where the takers had to tell true masterpieces of abstract art from the fakes, produced by me. I describe each picture by the fraction of the test takers, who selected it as a masterpiece. When I compare…
It was demonstrated that there is a geometrical order in the structure of literature. Fractal geometry as a modern mathematical approach and a new geometrical viewpoint on natural objects including both processes and structures was employed…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal…
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…
This work proposes a texture descriptor based on fractal theory. The method is based on the Bouligand-Minkowski descriptors. We decompose the original image recursively into 4 equal parts. In each recursion step, we estimate the average and…
This work presents a differentiable rendering approach that allows latent fractal flame parameters to be learned from image supervision using gradient descent optimization. The approach extends the state-of-the-art in differentiable…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from the shape by applying a multiscale approach to the calculus of the fractal dimension of that shape. The fractal…