All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional
Barbara Wolnik , Bernard De Baets
AbstractA binary number-conserving cellular automaton is a discrete dynamical system that models the movement of particles in a d-dimensional grid. Each cell of the grid is either empty or contains a particle. In subsequent timesteps the particles move between the cells, but in one cell there can be at most one particle at a time. In thispaper, the von Neumann neighborhood is considered, which means that in each time step a particle can moveto an adjacent cell only. It is proven that regardless of the dimensiond, all of these cellular automata are trivial,as they are intrinsically one-dimensional. Thus, for givend, there are only 4d+1 binary number-conserving cellular automata with the von Neumann neighborhood: the identity rule and the shift and traffic rules in each ofthe 2d possible directions.
|Journal series||Physical Review E, ISSN 1539-3755, (N/A 140 pkt)|
|Publication size in sheets||0.50|
|Keywords in English||multi-dimensional cellular automata, number conservation|
|ASJC Classification||; ;|
|Score||= 140.0, 27-07-2020, ArticleFromJournal|
|Publication indicators||= 1.000; = 1.000; : 2016 = 0.896; : 2018 = 2.353 (2) - 2018=2.380 (5)|
|Citation count*||1 (2020-06-30)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.