Leader Election without Compass in Some Hyperbolic and Euclidean Cellular Automata

(The other is majority consensus, and is discussed in the related work.) In leader election, each agent starts from the same state and the protocol must, eventually, stabilize to

The behaviour of this rule is known for fully asynchronous updating [3], that is, when only cell is selected randomly at each time step, but it is an open problem to determine

Second, we establish that for a large class of linear CA, diffusion of diamonds is equivalent to randomiza- tion (a large class of probability measures converge weakly towards

Our main result is that under the action of such an automaton any shift–ergodic measure converges in Ces` aro mean, assuming equicontinuity points have measure 1; the limit measure

Indeed, if we start with a circular list of n + 1 numbers and eliminate the player with the largest number, then the remaining n numbers form a linear list, and the peaks in this

Let Σ be the input alphabet of our automaton, we define the patch word associated to a proper patch as the word w c = w Γ w Σ , where w Γ ∈ Γ ∗ is the border word of the patch, and

Assuming no chirality, a swarm of robots is able to deterministi- cally agree on the same leader if and only if there exists a radius ρ such that W (ρ) is a 0-symmetric

The second result is the construction of n-noids in Hyperbolic space: genus 0, embedded, constant mean curvature surfaces with n Delaunay ends.. Keywords: Constant Mean