Unpredictable and seemingly random behavior occurring in a non-linear system and governed by deterministic laws. In fact chaos, despite being incorrectly associated with randomness, is fully deterministic. Two hallmarks of chaos are that its behavior never cross the same path twice and that a chaotic system has a sensitive dependence on initial conditions, which means that a very small initial difference can result in an enormous and unpredictable change to the future state of the system (the so-called butterfly effect, first described by Edward N. Lorenz in 1972). For this reason, it has been termed determinism without predictability. Chaotic attractors have fractal dimensions [i.e., a dimension between a line (1) and a surface (2), with a snowflake curve having a fractal dimension of 1.26]. Fractals are irregular shapes or surfaces produced by a process of repeated sub-division, which leads to self-similarity in structure at different levels of organisation.
See Attractor, Bifurcation, Chaos theory, Complex system, Complexity, Determinism, Dynamical systems approaches, Fractals, Levels of organization, Non-linear dynamical systems, Non-linear dynamics, Self-organization, Sensitivity to initial conditions