Pattern formation today.

Patterns are orders embedded in randomness. They may appear as spatial arrangements or temporal series, and the elements may appear identical or with variations. Patterns exist in the physical world as well as in living systems. In the biological world, patterns can range from simple to complex, forming the basic building blocks of life. The process which generates this ordering in the biological world was termed pattern formation. Since Wolpert promoted this concept four decades ago, scientists from molecular biology, developmental biology, stem cell biology, tissue engineering, theoretical modeling and other disciplines have made remarkable progress towards understanding its mechanisms. It is time to review and re-integrate our understanding. Here, we explore the origin of pattern formation, how the genetic code is translated into biological form, and how complex phenotypes are selected over evolutionary time. We present four topics: Principles, Evolution, Development, and Stem Cells and Regeneration. We have interviewed several leaders in the field to gain insight into how their research and the field of pattern formation have shaped each other. We have learned that both molecular process and physico-chemical principles are important for biological pattern formation. New understanding will emerge through integration of the analytical approach of molecular-genetic manipulation and the systemic approach of model simulation. We regret that we could not include every major investigator in the field, but hope that this Special Issue of the Int. J. Dev. Biol. represents a sample of our knowledge of pattern formation today, which will help to stimulate more research on this fundamental process.