Related papers: Self-similar resistive circuits as fractal-like st…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
Fractal structure emerges spontaneously from the chemical cross\-linking of monomers into hydrogels, and has been directly linked to power law visco\-elasticity at the gel transition, as recently demonstrated for isostatic…
We investigate the iterative construction of discrete Laplacians on 2D square lattices, revealing emergent fractal-like patterns shaped by modular arithmetic. While classical 2222-style iterations reproduce known structures such as the…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
This paper answers a long-standing open question in tile-assembly theory, namely that it is possible to strictly assemble discrete self-similar fractals (DSSFs) in the abstract Tile-Assembly Model (aTAM). We prove this in 2 separate ways,…
A model, plane symmetric, 3-D potential, which preserves some features of galactic problems,is used in order to examine the phase space structure through the study of the properties of orbits crossing perpendicularly the plane of symmetry.…
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, but largely open for fractal drums in larger dimensions. To…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical estimates…
In this paper we study the diffusely observed occurrence of Fractality and Self-organized Criticality in mechanical systems. We analytically show, based on a prototypical compressed tensegrity structure, that these phenomena can be viewed…
The problem of the vortex structure in the lattice modele of superconductors has been reduced to the nonlinear map problem characteristic for the fractal theory.
Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we…
We establish a correspondence between Pavlovian conditioning processes and fractals. The association strength at a training trial corresponds to a point in a disconnected set at a given iteration level. In this way, one can represent a…
We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond…
Self-organized spatial plasma structures exhibit many similarities with Turing structures obtained in biology and chemistry. Using an analytical mesoscopic approach it is shown that plasma balls of fire belong to the same class of Turing…
Electrical circuits offer a unique platform to explore physical phenomena, from topology to non-Hermitian effects. Investigations of the fundamental properties of this metamaterial platform are crucial to distinguish observed/measured…
The Stretched Sierpinski Gasket is a non-self-similar set but it still exhibits very high symmetry. In an earlier work we calculated the leading term for the eigenvalue counting function for operators coming from resistance forms that were…
Iterated Function Systems (IFSs) have been at the heart of fractal geometry almost from its origin, and several generalizations for the notion of IFS have been suggested. Subdivision schemes are widely used in computer graphics and attempts…
In this paper, we identify two fractals if and only if they are biLipschitz equivalent. Fix ratio $r,$ for dust-like graph-directed sets with ratio $r$ and integer characteristics, we show that they are rigid in the sense that they are…
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…