  Many natural phenomena evolve intermittently, with periods of tranquillity
interrupted by bursts of activity, rather than following a smooth gradual path.
Examples include earthquakes, volcanic eruptions, solar flares, gamma-ray
bursts, and biological evolution. Stephen Jay Gould and Niles Eldredge have
coined the term "punctuated equilibria" for this behavior. We argue that
punctuated equilibria reflects the tendency of dynamical systems to evolve
towards a critical state, and review recent work on simple models. A good
metaphoric picture is one where the systems are temporarily trapped in valleys
of deformable, interacting landscapes. Similarities with spin glasses are
pointed out. Punctuated equilibria are essential for the emergence of complex
phenomena. The periods of stasis allow the system to remember its past history;
yet the intermittent events permit further change.
