Scale-invariant cascades in turbulence and evolution

In this dissertation, I present work addressing three systems which are traditionally considered to be unrelated: turbulence, evolution, and social organization. The commonality between these systems is that in each case, microscopic interaction rules give rise to an emergent behavior that in some way makes contact with the macroscopic scale of the problem. The open-ended evolution of complexity in evolving systems is analogous to the scale-free structure established in turbulent flows through local transportation of energy. In both cases, an invariance is required for the cascading behavior to occur, and in both cases the scale-free structure is built up from some initial scale from which the behavior is fed.;In turbulence, I examine the case of two-dimensional turbulence in order to support the hypothesis that the friction factor and velocity profile of turbulent pipe flows depend on the turbulent energy spectrum in a way unpredicted by the classic Prandtl theory. By simulating two-dimensional flows in controlled geometries, either an inverse energy cascade or forward enstrophy cascade can be produced. The friction factor scaling of the flow changes depending on which cascade is present, in a way consistent with momentum transfer theory and roughness-induced criticality.;In the problem of evolution, I show that open-ended growth of complexity can be obtained by ensuring that the evolutionary dynamics are invariant with respect to changes in complexity. Finite system size, finite point mutation rate, and fixed points in the fitness landscape can all interrupt this cascade behavior, producing an analogue to the integral scale of turbulence. This complexity cascade can exist both for competing and for symbiotic sets of organisms. Extending this picture to the qualitatively-different levels of organization of real lifeforms (viruses, unicellular, biofilms, multicellular) requires an understanding of how the processes of evolution themselves evolve. I show that a separation of spatial or temporal scales can enhance selection pressure on parameters that only matter several generations down the line. Because of this, I conclude that the prime candidates for the emergence of novel evolutionary mechanisms are biofilms and things living in oscillating environments.;Finally, in the problem of social organization, I show that different types of control hierarchies - leaders or communal decision making - can emerge depending on the relationship between the environment in which members of the social group act and the development and exchange of information.