Related papers: Fractal Transformations in 2 and 3 Dimensions
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
We review the time evolution of wavepackets at the metal-insulator transition in two- and three-dimensional disordered systems. The importance of scale invariance and multifractal eigenfunction fluctuations is stressed. The implications of…
Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D topological system can transform under symmetry in a fractional way. For example in fractional quantum Hall systems, excitations can carry fractional…
A study of the use of fractals in top non-leptonic decays for the sake of discrimination against background is presented. Preliminary results show that fractals may provide a useful check for top event enrichment techniques.
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
Recently, a general tool called a holographic transformation, which transforms an expression of the partition function to another form, has been used for polynomial-time algorithms and for improvement and understanding of the belief…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
Fast Fourier transforms are used to develop algorithms for the fast generation of correlated Gaussian random fields on d-dimensional rectangular regions. The complexities of the algorithms are derived, simulation results and error analysis…
We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
This paper presents an iterative inversion algorithm for computed tomography image reconstruction that performs well in terms of accuracy and speed using limited data. The computational method combines an image domain technique and…
We analyze examples of projected two dimensional fractals for the case where the objects studied have a Schechter luminosity function. Our results indicate that two dimensional catalogues of sources could be of value in detecting the…
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension.…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
The fully covariant formulation of transformation optics is used to find the configuration of a cloaking device operating in an expanding universe modelled by a Friedmann-Lema\^itre-Robertson-Walker spacetime. This spacetime cloak is used…
Iterated function systems (IFS) can be a surprisingly useful tool for studying structure in data. Here we present results stemming from a 2013 computational study by the author using IFS. The results include fractal patterns that reveal…
The Fractional Fourier Transform (FRFT) has been playing a unique and increasingly important role in signal and image processing. In this letter, we investigate the property of frequency shift in two-dimensional FRFT (2D-FRFT) domain. It is…
We discuss transformations on matrices that preserve the effective spectrum and/or the effective spectral radius.
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
A multifractal analysis (MFA) is performed on three-dimensional grayscale images associated with natural porous structures (soil samples). First, computed tomography (CT) scans are carried out on the samples to generate 3D grayscale images.…