Euclidean Geometry

Fractal Geometry

Linear Dynamics—unpredictable behavior only comes from random events (high-dimensional system).

Nonlinear Dynamics: unpredictable behavior can result from internal deterministic interactions of low-dimensional system.

Statistics: high-dimensional systems can be characterized by an average (“ergodic”), eg temperature.

Self-organization: high-dimensional systems can have emergent phenomena, eg fractal structures, adaptive behaviors, and evolution. Non-ergodic.