The emergence of specific properties, as in behavior, and the mechanisms that link these properties together into higher-order units referred to as patterns. The pattern itself resides at the level of an order parameter, and the mechanisms of pattern formation at that of a control parameter. Ubiquitous in both organic and organic systems, one example is the shell of the Nautilus mollusk that has a logarithmic spiral due to steady growth along the leading edge, and which retains the same form as the shell gets larger. Other examples include surface markings or motifs such as spots and stripes in many animals. Pattern formation arises as a consequence of self-organization processes subjected to constraints imposed by physical laws, but this tells us nothing about the mechanisms involved. Following the pioneering work of Alan M. Turing (1912-1954) on reaction-diffusion processes acting along gradients in morphogenetic fields, Hans Meinhardt and Alfred Gierer have proposed a model of pattern formation consisting of two ingredients: an activator and inhibitor, and in which the activator catalyzes its own formation while the inhibitor disrupts this process. For certain ratios of diffusion rates, this activator-inhibitor system develops a range of patterns found in nature. The question is whether the processes and mechanisms encapsulated by such models are a universal feature of morphogenesis. Another, and much more difficult, question, is how patterns are formed in developing behaviors, and one that was formed the key issue in the work by Arnold Gesell (1880-1961) on motor development. For some, answers are to be found in applications of irreversible thermodynamics and synergetics. Finally, the study of pattern formation is considered to be an example of an interdiscipline, drawing as it does on various combinations of interested parties from biochemistry, biology, ecology, fluid dynamics, mathematics and physics.
See Complexity, Control parameter, Emergence, Fractals, Interdiscipline, Irreversible thermodynamics, Mechanism, Morphogenesis, Morphogenetic field, Order parameter, Process, Self-organization, Synergetics