The theory of chaos is an extraordinarily broad mathematical topic, and we all have some intuition for what it means when a system is *chaotic*. The ideas of unpredictability, spontaneity, intractability, turbulence, and perhaps randomness, all come to mind. But deterministic chaos is somewhat different than our intuitions would have us believe. If you watch the shape of a flickering flame, the whitewater in a rocky river, or the price of crude oil in North America, you’re definitely seeing behavior which can’t be described without chaos. But you’re also most likely seeing the effects of any number of *random* influences on the system, whether a faltering breeze or some oil speculator’s whimsy. Chaos theory deals with the behavior of *deterministic* systems—that is, systems with no random inputs. All the intricacy and intrigue of chaotic behavior can arise in systems which might seem deceptively uncomplicated, like a pendulum hanging from another pendulum, or three stars orbiting each other.

But if you’ve ever heard of the “butterfly effect” (a term coined by a pioneer of chaos theory, Edward Lorenz), it’s likely your intuition is right about the central feature of deterministic chaos: **chaotic systems have high sensitivity to initial conditions. **

If chaotic systems are so unpredictable and temperamental, how can we possibly make chaos work for us? One answer is encryption. Continue reading Sending Your Secrets Safely with Chaos