In a large class of cellular automata a unique ''parent'' particle of the previous state can be assigned to each particle of the present state. This allows us to define families and study their evolution and extinction in one-dimensional cellular automata. The size density of families is found to tend towards a universal function for large times. The evolution of the average family size, proportional to t, is strongly related to the ordering mechanism found by Grassberger [Phys. Rev. A 28, 3666 (1983)].
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics