- The Geometry -

Sonoran Desert. These Hohokam Indian petroglyphs can be found in Arizona's Saguaro National Park atop of Signal Hill. United States.

    Transcription excerpt: Isolated systems tend to evolve towards a single equilibrium, a special state that has been the focus of many-body research for centuries. But when we look around us we don't see simple periodic patterns everywhere, the world is a bit more complex than this and behind this complexity is the fact that the dynamics of a system maybe the product of multiple different interacting forces, have multiple attractor states and be able to change between different attractors over time. Before we get into the theory lets take a few examples to try and illustrate the nature of nonlinear dynamic systems. A classical example given of this is a double pendulum; a simple pendulum with out a joint will follow the periodic and deterministic motion characteristic of linear systems with a single equilibrium that we discussed in the previous section. Now if we take this pendulum and put a joint in the middle of its arm so that it has two limbs instead of one, now the dynamica