One of the most important features of biological life in all levels is its astounding diversity.
In this work we study the well-known game "Life" due to Conway analysing the statistics of cluster population, N(t), and cluster diversity, D(t). We have performed simulations on "Life" for dimensions d = 1 and 2 starting with an uncorrelated distribution of live and dead sites at t = 0. For d = 2 we study the effect of different neighbourhood relations in identifying and counting clusters. An interesting scaling relation connecting the maxima of N(t) and D(t) is found.
The game "Life" due to Conway [1,2] is possibly the most famous cellular automaton. It seems that "Life" captures in an allegorical sense some of the complex features of real (biological) life [3]. In nature, the term diversity occurs in several contexts, for instance in connection with forms [4], species [5], populations [6] and sizes [7]. For numerical studies on lattices the diversity of sizes is particularly appropriate. This work deals with extensive numerical simulations with the game "Life". Here we restrict ourselves to the study of the cluster size population and diversity [7,8]. New scaling relations are reported for the first time which are in part similar to those observed in many dissipative fragmentation dynamics of interest in physics, chemistry, biology and ecology [7,8].
Some aspects of the statistics of "Life" have been investigated recently [9-111. Bak, Chen and Creutz have suggested that "Life" would evolve into a self-organized critical state [12] characterized by spatial and temporal power laws [9]. Afterwards, Bennett and Bourzutschky [lo] showed that "Life" is subcritical, with large but finite relaxation time and extinction length. These authors argued that the conclusions attained in [9] were due to the use of relatively small (100 x 100) lattices. Bagnoli, Rechtman and Ruffo [ll] studied