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Self-organization
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Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. T
Self-organization in micron-sized Nb3O7(OH) cubes during a hydrothermal treatment at 200 °C. Initially amorphous cubes gradually transform into ordere
Self-organization in micron-sized Nb3O7(OH) cubes during a hydrothermal treatment at 200 °C. Initially amorphous cubes gradually transform into ordered 3D meshes of crystalline nanowires as summarized in the model below.
Birds flocking (boids in Blender), an example of self-organization in biology
Birds flocking (boids in Blender), an example of self-organization in biology
Chaos theory
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Chaos theory is a branch of mathematics and an interdisciplinary area of scientific study. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to in
Self-organization
…over all the components of the system. As such, the organization is typically robust and able to survive or self-repair substantial perturbation. Chaos theory discusses self-organization in terms of islands of predictability in a sea of chaotic unpredictability. Self-organization is a phenomenon that occurs…
The Lorenz attractor displays chaotic behavior. These two plots demonstrate sensitive dependence on initial conditions within the region of phase spac
The Lorenz attractor displays chaotic behavior. These two plots demonstrate sensitive dependence on initial conditions within the region of phase space occupied by the attractor.
Turbulence in the tip vortex from an airplane wing. Studies of the critical point beyond which a system creates turbulence were important for chaos th
Turbulence in the tip vortex from an airplane wing. Studies of the critical point beyond which a system creates turbulence were important for chaos theory, analyzed for example by the Soviet physicist Lev Landau, who developed the Landau-Hopf theory of turbulence. David Ruelle and Floris Takens later predicted, against Landau, that fluid turbulence could develop through a strange attractor, a main concept of chaos theory.
A Conus textile shell, similar in appearance to Rule 30, a cellular automaton with chaotic behaviour
A Conus textile shell, similar in appearance to Rule 30, a cellular automaton with chaotic behaviour