The Edge of Chaos

 

 

These images show histories of the spatial and temporal behaviour of one-dimensional cellular automata, a type of complex system. The state of the system is represented by a single horizontal line of pixels. At each time step, the state of the system is updated according to a fixed rule which operates on each pixel and its immediate neighbours. The images are made by plotting the line of pixels from top to bottom over time.

According to the nature of the update rule, a spectrum of behaviour can be found. At one extreme, the system settles into a stable, frozen state (top); at the other, the system displays incoherent, random behaviour in space and time (bottom). In between these regimes, however, is the edge of chaos where the system never settles, but displays complex, structured behaviour with periods of relative stability interrupted by bursts of activity.

Behaviour at the edge of chaos can exhibit fractal characteristics in both space and time and has been shown to have the ability to compute. Within this regime, the mutual information, or shared coherence, between cells is maximised relative to the entropy of a cell, or its degree of disorder. That is, the trade-off between transmission of information, which requires disorder, and storage, which requires the opposite, is balanced to give the system the ability to compute. Chris Langton considers that this is congruent to the behaviour of living systems where "the dynamics of information has gained control over the dynamics of energy".

 

 

Living systems can perhaps be characterized as systems that dynarnically avoid attractors. The periodic regime is characterized by limit-cycle or fixed-point attractors, while the chaotic regime is characterized by strange attractors, typically of very high dimension. Living systems need to avoid either of these ultimate outcomes, and must have learned to steer a delicate course between too much order and too much chaos - the Scylla and Charybdis of dynamical systems.

They apparently have done so by learning to maintain themselves on extended transients - i.e., by learning to maintain themselves near a "critical" transition. Once such systems emerged near a critical transition, evolution seems to have discovered the natural information-processing capacity inherent in near-critical dynamics, and to have taken advantage of it to further the ability of such systems to maintain themselves on essentially open-ended transients.

from Life at the Edge of Chaos, Chris Langton, 1991