Complex Systems

Uncertain Density Balance Triggers Scale-Free Evolution in Game of Life Download PDF

Tomoko Sakiyama
Graduate School of Natural Science and Technology
Okayama University
Okayama, 700-8530, Japan
tmk.sakiyama@gmail.com

Yukio-Pegio Gunji
Department of Intermedia Art and Science
School of Fundamental Science and Engineering
Waseda University, Tokyo, Japan

Abstract

Since Conway proposed the Game of Life, it has attracted researchers' attention due to complex "life" evolutions despite simple rules. It is known that the Game of Life exhibits self-organized criticality, which might be related to scale-free evolutions. Despite the interesting phenomenon of self-organized criticality, the Game of Life turns to steady states within several generations. Here, we demonstrate a new version of the Game of Life in which cells tried to stay "alive" even though neighboring sites were over- or underpopulated. These rule changings enabled the system to show scale-free evolutions for many generations.