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+----- Thread: The Chaos Textbook [Elert] (/showthread.php?tid=323)
The Chaos Textbook [Elert] - mklabgr - 06-13-2026
The Chaos Textbook: Mathematics in the age of the computer
Glenn Elert
Summary The "Experiments" chapter of The Chaos Hypertextbook explores how chaos emerges from simple feedback loops called one-dimensional iterated maps, where a function's output is continuously reused as its next input. As the system's control parameters are adjusted, its behavior transitions from a stable steady-state to alternating periodic cycles through a splitting process known as bifurcation. This period-doubling accelerates until the system breaks down into unpredictable chaos; however, this transition is governed by a universal constant (Feigenbaum's number), proving that the path to chaos follows strict, predictable mathematical laws regardless of the equation used.
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