The importance of being discrete: Life always wins on the surface

Nadav M. Shnerb, Yoram Louzoun, Eldad Bettelheim, Sorin Solomon

Research output: Contribution to journalArticlepeer-review

155 Scopus citations


Many systems in chemistry, biology, finance, and social sciences present emerging features that are not easy to guess from the elementary interactions of their microscopic individual components. In the past, the macroscopic behavior of such systems was modeled by assuming that the collective dynamics of microscopic components can be effectively described collectively by equations acting on spatially continuous density distributions. It turns out that, to the contrary, taking into account the actual individual/discrete character of the microscopic components of these systems is crucial for explaining their macroscopic behavior. In fact, we find that in conditions in which the continuum approach would predict the extinction of all of the population (respectively the vanishing of the invested capital or the concentration of a chemical substance, etc.), the microscopic granularity insures the emergence of macroscopic localized subpopulations with collective adaptive properties that allow their survival and development. In particular it is found that in two dimensions 'life' (the localized proliferating phase) always prevails.

Original languageEnglish
Pages (from-to)10322-10324
Number of pages3
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number19
StatePublished - 12 Sep 2000
Externally publishedYes


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