# Chaos Theory

## Table of Contents

Chaos: When the present determines the future, but the approximate present does not approximately determine the future. – Edward Lorenz

## Notation

## Definitions

For systems which are *deterministic*, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved.

Chaotic systems such as these are what we call **deterministic chaos**, meaning that yes, given initial conditions we can deterministically determine what will happen, but if we're ever so slightly off in our initial conditions (e.g. rounding errors in mathematical computation) then we can get widely different results.