#chaos

Topics tagged "chaos".

• Sensitive Dependence on Initial Conditions

  The hallmark of chaos — infinitesimally close starting points diverge exponentially fast, making long-term prediction impossible.

• Chaos

  Deterministic systems whose long-term behavior is so sensitive to initial conditions that it becomes effectively unpredictable.

• Lorenz System

  Three coupled equations, distilled from a weather model, whose solutions trace the iconic butterfly-shaped strange attractor.

• Three-Body Problem

  Three gravitating masses — the smallest many-body system, and the birthplace of chaos in celestial mechanics.

• Double Pendulum

  Two rods hinged end to end — the simplest everyday mechanical system that exhibits genuine chaos.

• Logistic Map

  A one-line population model, x_{n+1}=r x_n(1-x_n), whose period-doubling cascade is the canonical road from order into chaos.

• Feigenbaum Constant

  The universal ratio δ ≈ 4.6692 by which the gaps between successive period-doubling bifurcations shrink — the same number on the road to chaos in countless unrelated systems.

• Is the Feigenbaum Constant Transcendental?

  δ ≈ 4.6692 has been computed to thousands of digits, yet no one has proved it irrational — let alone transcendental.

• Strange Attractor

  An attractor with fractal structure, onto which chaotic motion settles while never repeating itself.

• Fractal

  A shape that repeats its structure at every scale, with a fractional dimension that measures how intricately it fills space.

• Poincaré Section

  A slice through a continuous flow that turns it into a discrete map, exposing the hidden structure of complicated trajectories.