33 citations · 140 across the 13 of their papers we have counts for
14 papers
Loop Patterns Formed by Cellular Automata
Rolf Hoffmann, Mariusz Białecki
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cel…
An explanation of the shape of the universal curve of the Scaling Law for the Earthquake Recurrence Time Distributions
Mariusz Bialecki
This paper presents an explanation of a possible mechanism underlying the shape of the universal curve of Scaling Law for Earthquake Recurrence Time Distributions. The presented si…
Finite Random Domino Automaton
Mariusz Bialecki
Finite version of Random Domino Automaton (FRDA) - recently proposed a toy model of earthquakes - is investigated. Respective set of equations describing stationary state of the FR…
Motzkin numbers out of Random Domino Automaton
Mariusz Białecki
Motzkin numbers are derived from a special case of Random Domino Automaton - recently proposed toy model of earthquakes. An exact solution of the set of equations describing statio…
Ito equations out of domino cellular automaton with efficiency parameters
Zbigniew Czechowski, Mariusz Białecki
Ito equations are derived for simple stochastic cellular automaton with parameters and compared with results obtained from the histogram method. Good agreement for various paramete…
Three-level description of the domino cellular automaton
Zbigniew Czechowski, Mariusz Białecki
Inspired by the approach of kinetic theory of gases, a three-level description (microscopic, mesoscopic and macroscopic) of cellular automaton is presented. To provide an analytica…