Related papers: Langton's Ant from the Ant's referential
Multiple sequence alignment is a key process in today's biology, and finding a relevant alignment of several sequences is much more challenging than just optimizing some improbable evaluation functions. Our approach for addressing multiple…
We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only…
The structure of a previously developed representation of the Leech lattice, $\Lambda_{24}$, is exposed to further light with this unified and very simple construction.
We consider two-layers of immiscible liquids confined between an upper and a lower rigid plate. The dynamics of the free liquid-liquid interface is described for arbitrary amplitudes by a single evolution equation derived from the basic…
The electrostatics of 2D system with complicated inner boundary is studied. The object which we call "monster" is built by an iterative process of multiple conformal mapping of the circle exterior. The procedure leads to the figures built…
We perform a multifractal analysis of the evolution of London's street network from 1786 to 2010. First, we show that a single fractal dimension, commonly associated with the morphological description of cities, does not su ce to capture…
Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate…
We investigate the organization of traffic flow on preexisting uni- and bidirectional ant trails. Our investigations comprise a theoretical as well as an empirical part. We propose minimal models of uni- and bi-directional traffic flow…
In this report, we introduce the elephant random walk on the triangular lattice over $R^2$ incorporating directions by extending the model developed in \cite{baur2016elephant}. We study the behavior of the walk by finding the appropriate…
We perform intensive computations of Generalised Langton's Ants, discovering rules with a big number of highways. We depict the structure of some of them, formally proving that the number of highways which are possible for a given rule does…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We study a class of minimal geometric partial differential equations that serves as a framework to understand the evolution of boundaries between states in different pattern forming systems. The framework combines normal growth, curvature…
The division of labor (DOL) and task allocation among groups of ants living in a colony is thought to be highly efficient, and key to the robust survival of a colony. A great deal of experimental and theoretical work has been done toward…
We investigate a driven diffusive lattice gas model with two oppositely moving species of particles. The model is motivated by bi-directional traffic of ants on a pre-existing trail. A third species, corresponding to pheromones used by the…
Animal movement exhibits complex behavior which can be influenced by unobserved environmental conditions. We propose a model which allows for a spatially-varying movement rate and spatially-varying drift through a semiparametric potential…
We study the optical response of a 2D square lattice of atoms using classical electrodynamics. Due to dipole-dipole interactions, the lattice atoms polarize as if the lattice were an atom with up to three resonance frequencies, with…
Generalising recent studies on the sawtooth lattice, a two-spin variant of the model is considered. Numerical studies of the energy spectra and the relevant spin correlations in the problem are presented. Perturbation theory analysis of the…
A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is…
A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35, L573 (2002)}), motivated by the motions of ants in a trail, is investigated in detail in this paper. The flux of ants in this model is sensitive to the probability…
Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling…