# Chaos

A property of some non-linear dynamic systems which exhibit sensitive dependence on initial conditions.

This means that there are initial states which evolve within some finite time to states whose separation in one or more dimensions of state space depends, in an average sense, exponentially on their initial separation.

Such systems may still be completely deterministic in that any future state of the system depends only on the initial conditions and the equations describing the change of the system with time.

It may, however, require arbitrarily high precision to actually calculate a future state to within some finite precision.

["On defining chaos", R. Glynn Holt <rgholt@voyager.jpl.nasa.gov> and D. Lynn Holt <lholt@seraph1.sewanee.edu>. (ftp://mrcnext.cso.uiuc.edu/pub/etext/ippe/preprints/Phil_of_Science/Holt_and_Holt.On_Defining_Chaos)]

Fixed precision floating-point arithmetic, as used by most computers, may actually introduce chaotic dependence on initial conditions due to the accumulation of rounding errors (which constitutes a non-linear system).

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