Related papers: Fractal surfaces from simple arithmetic operations
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…
Arguments for black hole formation in collisions of high-energy particles have rested on the emergence of a closed trapped surface in the classical geometry of two colliding Aichelburg-Sexl solutions. Recent analysis has, however, shown…
When a finite volume of etching solution is in contact with a disordered solid, complex dynamics of the solid-solution interface develop. If the etchant is consumed in the chemical reaction, the dynamics stop spontaneously on a self-similar…
A conformal map from a Riemann surface to the Euclidean four-space is explained in terms of its twistor lift. A local factorization of a differential of a conformal map is obtained. As an application, the factorization of a differential…
We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we…
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…
We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes…
Predicting the growth of large cracks in brittle materials is a fundamental unresolved problem in fracture mechanics. Under out-of-plane shear loading, an initially planar crack may fragment into multiple cracks, forming an echelon crack…
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
Thin elastic solids are easily deformed into a myriad of three-dimensional shapes, which may contain sharp localized structures as in a crumpled candy wrapper, or have smooth and diffuse features like the undulating edge of a flower.…
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…
Using the moving frame and invariants, any discrete curve in $\R^3$ could be uniquely identified by its centroaffine curvatures and torsions. In this paper, depending on the affine curvatures of the fractal curves, such as Koch curve and…
We study a theoretical model of mud cracks, that is, the fracture patterns resulting from the contraction with drying in a thin layer of a mixture of granules and water. In this model, we consider the slip on the bottom of this layer and…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
Numerical simulations of assemblies of grains under cyclic loading exhibit ``granular ratcheting'': a small net deformation occurs with each cycle, leading to a linear accumulation of deformation with cycle number. We show that this is due…
We study numerically the growth of a crack in an elastic medium under the influence of a travelling shockwave. We describe the implementation of a fast algorithm which is perfectly suited for a data parallel computer. Using large scale…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
A fractal bears a complex structure that is reflected in a scaling hierarchy, indicating that there are far more small things than large ones. This scaling hierarchy can be effectively derived using head/tail breaks - a clustering and…
Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…
We use computer simulations and simple theoretical models to analyze the morphologies that result when rod-like particles end-attach onto a curved surface, creating a finite-thickness monolayer aligned with the surface normal. This geometry…