We'll accumulate technical references here. No need to worry about formatting for now.
J. M. Baetens and B. De Baets, "On the Topological Sensitivity of Cellular Automata," Chaos, preliminary, 2011.
J. M. Baetens and B. De Baets, "Phenomenological Study of Irregular Cellular Automata Based on Lyapunov Exponents and Jacobians," Chaos, 20, 2010, 033112.
F. Bagnoli, R. Rechtman, and S. Ruffo, "Damage Spreading and Lyapunov Exponents in Cellular Automata," Physics Letters A, 172, 1992, pp. 34–38.
Sandri, M. "Numerical Calculation of Lyapunov Exponents." Mathematica J. 6, 78-84, 1996.
Chirikov, B. V. "A Universal Instability of Many-Dimensional Oscillator Systems." Phys. Rep. 52, 264-379, 1979.
Ramasubramanian, K. and Sriram, M. S. "A Comparative Study of Computation of Lyapunov Spectra with Different Algorithms" 1999.
Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, p. 24, 2004.
fractal
Lyapunov
stochastic
Poincare
bifucation
butterfly effect
attractor
strange attractor
cellular atomaton
logistic equation
turbulence
nonlinear
chaos
Von Koch snowflake
Brownian motion
plasma clouds
self-organization
repellor
strange repellor
Links and demos:
http://demonstrations.wolfram.com/LogisticMapOnsetOfChaos/LogisticMapOnsetOfChaos
http://demonstrations.wolfram.com/LyapunovFractals/