Related papers: Sideways on the highways
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…
We present a short note on the dynamics of the LLLR generalised Langton's ant. We describe two different asymptotic behaviours for the LLLR ant.
Motivated by recent experimental work of Burd et al., we propose a model of bi-directional ant-traffic on pre-existing ant-trails. It captures in a simple way some of the generic collective features of movements of real ants on a trail.…
The automaton known as `Langton's ant' exhibits a dynamical transition from a disordered phase to an ordered phase where the particle dynamics (the ant) produces a regular periodic pattern (called `highway'). Despite the simplicity of its…
Many insects like ants communicate chemically via chemotaxis. This allows them to build large trail systems which in many respects are similar to human-build highway networks. Using a recently proposed stochastic cellular automaton model we…
The evolution of the Langton's ant on a 2D lattice is studied from the "ant's framework". The aim of this article is twofold. Firstly, to see if one can explain the emergent behaviour of the ant as an analogous sytem of a particle crossing…
This paper addresses the problem of existence of generalized Landsberg structures on surfaces using the Cartan-K\"ahler Theorem and a Path Geometry approach.
The road colouring theorem characterizes the class of strongly connected directed graphs with constant out-degree that admit a synchronizing road colouring. The subject of this paper is a pair of related conjectures that generalize the road…
The fourfold research proposal regards in particular: critical oriented percolation; random walk limit laws; neural networks with long-range connections; the ant in a labyrinth.
We clarify and generalize the ant on a rubber rope paradox, which is a mathematical puzzle with a solution that appears counterintuitive. In this paper, we show that the ant can still reach the end of the rope even if we consider the step…
We report experimental results on unidirectional traffic-like collective movement of ants on trails. Our work is primarily motivated by fundamental questions on the collective spatio-temporal organization in systems of interacting motile…
The paper consists of two parts. In the first part we review recent work on limit theorems for random walks in random environment (RWRE) on a strip with jumps to the nearest layers. In the second part, we prove the quenched Local Limit…
We obtain new average results on the conjectures of Lang-Trotter and Sato-Tate about elliptic curves.
Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the…
In this paper we consider finitary symmetric random walks on groups. We construct new possible asymptotics for the drift. We show that the drift can be very close to linear ant yet sublinear. We also give estimates for entropy growth of…
In this note we observe that Arnold conjecture for the Hamiltonian maps still holds on weighted projective spaces $\CP^n({\bf q})$, and that Arnold conjecture for the Lagrange intersections for $(\CP^n({\bf q}), \RP^n({\bf q}))$ is also…
Efficient transportation, a hot topic in nonlinear science, is essential for modern societies and the survival of biological species. Biological evolution has generated a rich variety of successful solutions, which have inspired engineers…
We consider a persistent random walk on an inhomogeneous environment where the reflection probability depends only on the distance from the origin. Such an environment is the result of an average over all realizations of disorder of a…
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…
The generalized Andrews-Curtis Conjecture expects that finite PLCW 2-complexes which are simple-homotopy equivalent, can be 3-deformed into each other. If in addition subcomplexes are required to be kept fix during the deformation, this is…