Related papers: Fractal surfaces from simple arithmetic operations
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 surface of metal, glass and plastic objects is often characterized by microscopic scratches caused by manufacturing and/or wear. A closer look onto such scratches reveals iridescent colors with a complex dependency on viewing and…
In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show…
Post mortem analysis of fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveal self affine graphs with an anomalous scaling exponent $\zeta\approx 0.8$. Attempts to use elasticity theory…
We investigate the formation of trapped surfaces in cosmological spacetimes, using constant mean curvature slicing. Quantitative criteria for the formation of trapped surfaces demonstrate that cosmological regions enclosed by trapped…
We consider a plate made from an isotropic but brittle elastic material, which is used to span a rigid aperture, across which a small pressure difference is applied. The problem we address is to find the structure which uses the least…
The cosmic web is one of the most complex systems in nature, consisting of galaxies and clusters of galaxies joined by filaments and walls, leaving large empty regions called cosmic voids. The most common method of describing the web is a…
A simple multifractal coarsening model is suggested that can explain the observed dynamical behavior of the fractal dimension in a wide range of coarsening fractal systems. It is assumed that the minority phase (an ensemble of droplets) at…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
Causal shadows are bulk space-time regions between the entanglement wedges and the causal wedges, their existence encodes deep aspects of the entanglement wedge reconstruction in the context of subregion duality in AdS/CFT. In this paper,…
The quotient singularities of dimensions two and three obtained from polyhedral groups and the corresponding binary polyhedral groups admit natural resolutions of singularities as Hilbert schemes of regular orbits whose exceptional fibres…
The free volume comprised between rough surfaces in contact governs the fluid/gas transport properties across networks of cracks and the leakage/percolation phenomena in seals. In this study, a fundamental insight into the evolution of the…
In this paper, we propose to enumerate all different configurations belonging to a specific class of fractals: A binary initial tile is selected and a finite recursive tiling process is engaged to produce auto-similar binary patterns. For…
As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility.…
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…
We study in this work the properties of the $Q_{mf}$ network which is constructed from an anisotropic partition of the square, the multifractal tiling. This tiling is build using a single parameter $\rho$, in the limit of $\rho \to 1$ the…
We used nonequilibrium molecular dynamics simulations to study the shear deformation of metallic composites composed of alternating layers of Cu and Au. Our simulations reveal the formation of "vortices" or "swirls" if the bimaterial…
Cutting mozzarella with a dull blade results in poorly shaped slices: the process occurs in a configuration so deformed as to yield unexpectedly curved surfaces. We study the rich morphogenetics arising from such process through the example…
Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter \lambda of the system is modified. Complex patterns on the plane are visualised as a consequence of basins'…
We have discovered a new fractal pattern, coffee exhibits on a horizontal surface, with a fractal dimension $1.88 \pm 0.06$, when a heavy coffee droplet interacts with the surface of lighter milk. Parts of coffee pattern on the surface…