A Two-dimensional Cellular Automaton Crystal with Irrational Density
نویسندگان
چکیده
We solve a problem posed recently by Gravner and Griffeath : to find a finite seed of 1's [GG] E ! for a simple -valued cellular automaton growth model on such that the occupied crystal after Ö!ß "× E 8 TM# 8 updates spreads with a two-dimensional asymptotic shape and a provably irrational density. Our solution exhibits an initial of 2,392 cells for Conway's Game of Life from which covers with asymptotic E E 8X ! 8 density , where . $ &
منابع مشابه
A Single Nonexpansive, Nonperiodic Rational Direction
A two-dimensional cellular automaton consists of a two-dimensional lattice of sites, each of which takes on a finite number of values, and a cellular automaton map. The cellular automaton map updates the value at each site a " Ÿ2 using a translation invariant rule that only depends on the values at the sites in some finite neighborhood of a. A number of global properties of a two-dimensional ce...
متن کاملPackard Snowflakes on the von Neumann Neighborhood
In 1984, Packard [1] introduced simple planar cellular automata to emulate the growth of snow crystals. These Packard Snowflakes have since been popularized by S. Wolfram and others, most recently in [2]. The present paper provides a rigorous analysis of the simplest examples: those with nearest neighbor interaction on the two-dimensional integers. In each case we determine the asymptotic densi...
متن کاملTwo-Dimensional Traffic Rules and the Density Classification Problem
The density classification problem is the computational problem of finding the majority in a given array of votes, in a distributed fashion. It is known that no cellular automaton rule with binary alphabet can solve the density classification problem. On the other hand, it was shown that a probabilistic mixture of the traffic rule and the majority rule solves the one-dimensional problem correct...
متن کاملTwo-dimensional cellular automaton model of traffic flow with open boundaries.
A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and average velocity have flicker noises in a jamming phase. The low density behavior are discussed with simple jam-free approximation. 64.60.Cn, 05.70.Ln Typeset...
متن کاملA Cellular Automaton Based Algorithm for Mobile Sensor Gathering
In this paper we proposed a Cellular Automaton based local algorithm to solve the autonomously sensor gathering problem in Mobile Wireless Sensor Networks (MWSN). In this problem initially the connected mobile sensors deployed in the network and goal is gather all sensors into one location. The sensors decide to move only based on their local information. Cellular Automaton (CA) as dynamical sy...
متن کامل