4. Pattern Formation

Patterns in complex systems are manifest in temporal and spatial differences or gradients. These gradients can drive the flow of information, energy, and material, leading to the ability of a system to perform work. This chapter discusses how patterns form and the critical role they play in the development and maintenance of complex systems. Symmetry breaking is used to illustrate how patterns can emerge between completely heterogeneous (well-mixed) and homogeneous states. Benard cells and the Ising model are used to illustrate two canonical pathways to pattern formation. Turing patterns are introduced to describe spirals, spots, and stripes as well as growth and differentiation. Patterns in time are also addressed as events that can repeat or synchronize, with applications to swimming, walking, and flying as well as political and financial cycles. With these grounding concepts, fractals as patterns in space, strange attractors as patterns in phase space, autocatalytic sets as logical patterns, and power laws are introduced. More speculative connections are made to patterns in evolution and how a self might be a kind of pattern. The chapter concludes with questions for either reflection or group discussion as well as resources for further exploration.