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Sensitivity to Initial Conditions
In some systems the faintest difference at the start becomes an enormous difference later.
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Chaos: Order That Looks Like Randomness
A system can be entirely deterministic yet utterly unpredictable.
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Homeostasis: Systems That Hold Themselves Steady
A living body keeps its temperature, its chemistry, its balance within narrow bounds against a changing world.
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Feedback: The Loop That Stabilizes and Destabilizes
Let a system's output influence its input and something new arises: it can correct itself or spiral out of control.
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Cellular Automata: Complexity From Simple Rules
A grid of cells, each following a trivial local rule, can generate patterns of endless intricacy.
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Universality: One Machine to Run Them All
A single machine, given the description of any other, can imitate it exactly.
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P Versus NP: The Boundary of the Feasible
Is finding a solution as easy as checking one? For a vast class of problems we can verify an answer quickly but know no fast way to discover it.
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Kolmogorov Complexity: The Length of the Shortest Description
The complexity of an object is the length of the shortest program that produces it.
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Minimum Description Length
The best theory is the one that, together with the data it explains, can be stated most briefly.