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Renormalization: Seeing Across Scales
To understand a system one need not track every detail.
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Phase Transitions: Matter Changing Kind
Cool water and at a precise point it becomes ice, its character transformed.
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Percolation: The Sudden Onset of Connection
Add links to a scattered set of nodes and for a long while little changes.
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Scale-Free Networks
In many real networks, most nodes have few connections while a handful have enormous numbers.
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Power Laws: The Signature of Scale
Most things cluster around an average, but some do not.
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Criticality: Poised Between Order and Chaos
At the knife's edge between rigid order and formless chaos lies a special state where systems become exquisitely responsive.
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Self-Organization: Order Without a Designer
Order can arise from within, unbidden and unplanned.
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Attractors: Where Dynamics Settle
Left to run, a system tends toward certain states and shuns others.
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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.