Symmetry breaking is a phenomenon in which critical points decide a system’s future trajectory by determining which branch of a bifurcation is taken. Such transitions usually bring the system from a symmetric but disorderly state into one or more definite states. Such symmetry breaking thus plays a major role in pattern formation as we are now getting differentiation and some form of organization; that is to say that there is now some relationship between these different parts. Symmetry breaking is thought to have played a major part in the early formation of the universe.1 As it cooled down different forces subdivided (weak, strong, electromagnetic etc.), creating a broken symmetry between these four fundamental forces that were once thought to be one. Likewise, within physics, most simple phases of matter and phase transitions, like crystals, magnets, and conventional superconductors can be understood from the viewpoint of spontaneous symmetry breaking.
Bifurcation Symmetry Breaking
Within complex systems, symmetry breaking can be understood with reference to attractors and bifurcations. When we get a bifurcation within a state space the elements within it now break their symmetry as they move into two or more basins of attraction, thus occupying differentiated asymmetric states where previously they had symmetric states. As an analogical example, we can think about the French Revolution. Prior to this event, we had a single attractor within the political state space to the nation: an absolute monarchy beneath which was all political activity. In relation to the monarch, the Tennis Court Oath was then a bifurcation in the topology as a new attractor formed. Any agent within this state space after the bifurcation is going to have to choose one of the attractors, whereas previously everyone was under the same political regime of the monarch. In other words, while everyone had a symmetric homogeneous state before the event, now that there are two attractors people have to choose one state or another, which is an example of symmetry breaking.