相关论文: Langton's Ant from the Ant's referential

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…

A few of ant robots are dropped to a labirynth, formed by a square lattice with a small number of nodes removed. Ants move according to a deterministic algorithm designed to explore all corridors. Each ant remembers the shape of corridors…

The virtual ant introduced by C. Langton has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit with the trajectory of a single ant. This proves the P-hardness…

Condensed active matter is exemplary for its capacity to morph and exhibit internal flows despite remaining cohered. To facilitate understanding of this ability, we investigate the cause of finger-like protrusions that emerge from…

In this paper we prove an existence theorem concerning linear forms of a given Diophantine type and apply it to study the structure of the spectrum of lattice exponents.

Colonies of ants are systems of interacting living organisms in which interactions between individuals and their environment can produce a reliable performance of a complex tasks without the need for centralised control. Particularly…

We provide a relation which describes how the entanglement of two d-level systems evolves as either system undergoes an arbitrary physical process. The dynamics of the entanglement turns out to be of a simple form, and is fully captured by…

Using a simple model for the trail formation of ants, the relation between i)the schedule of feeding which represents the unsteady natural environment, ii)emerging patterns of trails connecting a nest with food resources, and iii)the…

We describe the spectrum of ordinary Diophantine exponents for $d$-dimensional lattices. The result reduces the problem to two-dimensional case and uses argument of metric theory.

A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter. At a discrete level, the evolution has a "checkerboard" structure and its…

A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…

There is great potential if we understand how nature functions, particularly the animals taking down from the ant to the larger animals. In this paper we will make an attempt to learn about ants colonization processing by studying their…

We present two generalised ants (LLRRRL and LLRLRLL) which admit both highway behaviours and other kinds of emergent behaviours from initially finite configurations. This limits the well known Highway conjecture on Langton's ant as it shows…

We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…

Switching interacting particle systems studied in probability theory are the stochastic processes of hopping particles on a lattice made up of slow and fast particles, where the switching between these types of particles occurs randomly at…

A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…

We introduce a method for translating any upper bound on the percolation threshold of a lattice $G$ into a lower bound on the exponential growth rate $a(G)$ of lattice animals and vice-versa. We exploit this in both directions. We improve…

Diffusion limited aggregation (DLA) is a well studied phenomenon in which diffusing particles cumulatively aggregate on a starting fixed seed point, forming a pattern which is fractal in structure. Here we report an interesting DLA process…

The temporal evolution of the entanglement between two qubits evolving by random interactions is studied analytically and numerically. Two different types of randomness are investigated. Firstly we analyze an ensemble of systems with…

The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of…