06-13-2026, 10:35 AM
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.
BOOK PAGE
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.
BOOK PAGE
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