Two odometers in honeybees?

Two odometers in honeybees?

Although several studies have examined how honeybees gauge and report the distance and direction of a food source to their nestmates, relatively little is known about how this information is combined to obtain a representation of the position of the food source. In this study we manipulate the amount of celestial compass information available to the bee during flight, and analyse the encoding o...

Embedding Odometers in Cellular Automata

We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be be embedded in a gliders with reflecting walls cellular automaton, which one depending on the odometer, and (2) an odometer can be embedded in a cellular automaton with local rule xi 7→ xi + xi+1 mod n (i ∈ Z), where n depends on the odometer, if and only if it is “finitary.”

On-Line Odometers for Two-Sided Symbolic Dynamical Systems

Linear Recursive Odometers and Beta-expansions

The aim of this paper is to study the connection between different properties related to β-expansions. In particular, the relation between two conditions, both ensuring pure discrete spectrum of the odometer, is analysed. The first one is the so-called Hypothesis B for the G-odometers and the second one is denoted by (QM) and it has been introduced in the framework of tilings associated to Piso...

Odometers and Systems of Numeration

1. Introduction. Our starting point is the study of systems of numer-ation with respect to a general base from an arithmetical and a dynamical point of view. Let G = (G n) n≥0 be a strictly increasing sequence of positive integers with G 0 = 1. In the following such a sequence is called G-scale.