The Theory
Rules, uncertainty and sensitive dependence
The science behind the metaphor. Complexity and randomness are not proof of mathematical chaos.
Deterministic systems
A deterministic system evolves according to rules. Exactly the same initial state produces the same trajectory. Some nonlinear deterministic systems are chaotic: nearby starting states can diverge dramatically over time.
Sensitivity to initial conditions
Measurements have finite precision. In a chaotic system, a small uncertainty in the initial state can grow until a long-term forecast becomes unreliable. The rules remain deterministic even when practical prediction becomes difficult.
The butterfly effect
The butterfly effect is a metaphor for sensitive dependence on initial conditions, not a promise that every small disturbance creates a large event. The Lorenz attractor illustrates how a small set of deterministic equations can produce intricate, aperiodic motion.
CHAOS uses this lens for its identity. Its market index does not establish that markets satisfy the mathematical definition of chaos.