Complex Systems

Brownian Motion is the random movement of particles suspended in a fluid, demonstrating stochastic processes in physics and mathematics.

The Cascade Model is a framework for understanding how changes in one system can lead to effects in interconnected systems.

Emergent behavior refers to complex patterns that arise from simple rules in systems, often seen in AI and nature.

Emergent capability refers to unexpected skills or behaviors that arise from complex systems.

Euler's Formula connects complex exponentials to trigonometric functions, expressed as e^(ix) = cos(x) + i*sin(x).

A navigable small world is a network structure that allows efficient connectivity and minimal path lengths between nodes.

Non-linear dynamics studies systems where outputs are not directly proportional to inputs, leading to complex behaviors and chaos.