GlossaryThe words
Every term on this site, in one place, in plain language. 19 of them.
- Attractor
- The shape a system is drawn onto and then stays on, whatever start you pick. A resting point, a loop, or —
- Bifurcation
- A fork: a place where turning the knob a hair splits one steady behaviour into two. Stack enough forks close together and you reach chaos.
- Chaos
- A system that follows a fixed rule with no randomness in it, yet cannot be forecast far ahead, because starts too close to tell apart pull rapidly apart.
- Deterministic
- Set by a rule, with no dice. Run it twice from the same start and you get the same answer. Chaotic systems are deterministic — that is what makes them surprising.
- Diversification
- Spreading a stake across many uncorrelated bets so the swing shrinks without the return shrinking. The law of large numbers, used on purpose.
- Feigenbaum constant
- 4.669… — the fixed ratio by which those forks crowd together, the same for a whole class of systems that share nothing else.
- Invariant distribution
- The fixed shape the values of a chaotic map settle into over the long run, even though each single value is unforecastable. Chaos in the one, law in the many.
- Law of large numbers
- As you pile up independent trials, their average closes on the true mean and its wobble shrinks as one over the square root of the count. The first tool for living with chaos.
- Logistic map
- The rule x → r·x·(1−x). A herd that breeds and runs short of grass. The simplest thing that goes chaotic, and the workhorse of this site.
- Lorenz system
- Three equations Edward Lorenz reduced weather to in 1963; the first clear example of chaos in a physical model.
- Lyapunov exponent
- The single number λ that says how fast nearby paths separate. Positive means chaos; bigger means less warning. Its reciprocal is roughly how far ahead you can see.
- Negative feedback
- Measuring your error and pushing back a share of it, every step. The move that keeps a system near its centre without anyone forecasting the shocks.
- Period doubling
- The particular road the logistic map takes into chaos — one beat, two, four, eight — each fork closer than the last.
- Redundancy
- Spare parts that can each do the job, so the whole survives any one failing — worth exactly as much as the parts' independence.
- Resilience
- How large a shock a system can take and still recover its shape — as distinct from how fast it bounces back. The second tool.
- Sensitive dependence on initial conditions
- The plain name for the above: a tiny change in where you start becomes a large change in where you end. The “butterfly effect”.
- Strange attractor
- — an attractor that never repeats and has structure at every scale, like the Lorenz butterfly. The signature of chaos in a flow.
- Stretch and fold
- The two motions under every chaotic map: pull neighbours apart, then fold the whole thing back to stay in bounds. Taffy on a hook.
- Tipping point
- The knob setting where a system flips from one world to another — steady to chaotic, lake to swamp. Resilience is margin to this edge.