Related papers: Fractal Transformations in 2 and 3 Dimensions
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory…
The image fractal analysis is actively used in all science branches. In particular in materials science the fractal analysis is applied to study microstructure of deformed metals because its structure can be interpreted as the fractal…
The paper presents a novel concept of a 3D structural metasurface with mechanically morphing capability that can be used as a transmit- or reflect-array to manipulate electromagnetic beams for applications in RF sensing and communications…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
Simulations of light scattering off an extreme ultraviolet lithography mask with a 2D-periodic absorber pattern are presented. In a detailed convergence study it is shown that accurate results can be attained for relatively large 3D…
Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…
Based on the Riemann- and Caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higher dimensional representation of a fractional rotation group with mixed…
In this third decade of systems engineering in the twenty-first century, it is important to develop and demonstrate practical methods to exploit machine-readable models in the engineering of systems. Substantial investment has been made in…
We consider two models (A and B) which can describe both two dimensional fragmentation and stochastic fractals. Model A exhibits multifractality on a unique support when describing a fragmentation process and on one of infinitely many…
We survey and investigate some computational aspects of the Fourier-Mukai transform.
The fractal dimension provides a statistical index of object complexity by studying how the pattern changes with the measuring scale. Although useful in several classification tasks, the fractal dimension is under-explored in deep learning…
When information is spatially repeated in self-similar fractal beam patterns, only a portion of the diffracted beam is needed to reconstruct the kernel data. What is unique to a fractal-encoding scheme is that the image demultiplexing…
The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…
Fractional programming (FP) is a branch of mathematical optimization that deals with the optimization of ratios. It is an invaluable tool for signal processing and machine learning, because many key metrics in these fields are fractionally…
We develop the theory of fractal homeomorphisms generated from pairs of overlapping affine iterated function systems.
By using Jet Calculus as a consistent framework to describe multiparton dynamics we explain the peculiar evolution equation of fracture functions by means of the recently introduced extended fracture functions.
Fractals are self-similar recursive structures that have been used in modeling several real world processes. In this work we study how "fractal-like" processes arise in a prediction game where an adversary is generating a sequence of bits…
Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases…
Despite much interest and progress in optical spatial cloaking, a three-dimensional (3D), transmitting, continuously multidirectional cloak in the visible regime has not yet been demonstrated. Here we experimentally demonstrate such a cloak…