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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.
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Feedback can give rise to incredibly complex behaviors. The Mandelbrot set (black) within a continuously colored environment is plotted by repeatedly
Feedback can give rise to incredibly complex behaviors. The Mandelbrot set (black) within a continuously colored environment is plotted by repeatedly feeding back values through a simple equation and recording the points on the imaginary plane that fail to diverge.