Self-organisation and the emergence of macroscopic behaviour. This figure shows a simple example of self-organisation using sixteen (Lorenz) oscillators that have been coupled to each other, so that each oscillator (with three microscopic states) sees the other oscillators. This is an example of a globally coupled map, where the dynamics of each oscillator conform to a classical Lorenz system. The equations of motion are provided in the left panel for each microstate, , whose average constitutes a macrostate . Each oscillator has its own random fluctuations and speed . The upper right panel shows the evolution of the microstates (dotted lines) and the macrostates (solid lines) over 512 time steps of one 1/32 second. The lower right panel, shows the first two macrostates plotted against each other to show the implicit attractor that emerges from self-organisation. The lower left panel shows the implicit synchronisation manifold by plotting the first states from successive pairs of oscillators (pink) and their averages (black) against each other. This simulation used low levels of noise on the motion of the microstates and the log-rate constants that disperse the speeds of each oscillator. The initial states were randomised by sampling from a Gaussian distribution with a standard deviation of eight.
