An Introduction to Fractals and Chaos

Abstract

Fractals and chaos have gained immense popularity in the last few years. Fractal objects and chaotic dynamics are being postulated and observed in diverse areas of science. This report gives a mathematical introduction to fractals and chaos, including some necessary background for the technical definitions. Partial Contents: Fractal -- Observations and representations; Topology and open covers; Topological dimension; Hausdorff dimension (A definition of fractal); Similarity dimension; The Cantor set; Koch snowflakes; Random coastlines; Another approach - IFS (Iterated Function System); and Further examples; Chaos -- The Poincare map; Iterations of continuous functions -- Orbits; Periodic points; Invariant sets/Attractors; Scrambled Sets -- Definitions of chaos; Universality -- The bifurcation diagram; Higher dimensions; Complex dynamics; and Randomness. (EDC)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1989
Accession Number
ADA210257

Entities

People

  • John W. Haussermann

Organizations

  • United States Air Force Academy

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Birds
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Graphics
  • Computer Programming
  • Computer Programs
  • Computers
  • Fluid Dynamics
  • Geometry
  • Nonlinear Dynamics
  • Nonlinear Systems
  • Physical Theories
  • Quantum Mechanics
  • Random Variables
  • Theorems
  • Three Dimensional
  • Two Dimensional

Readers

  • Aerospace Propulsion Engineering.
  • Theoretical Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Space