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The nonlinear three-dimensional map X^. = -(Y+Z) (1) Y^. = X+aY (2) Z^. = b+XZ-cZ (3) whose strange attractor is show above for a=0.2, b=0.2, and c=8.0.

The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a ...

The path of an object through phase space.

A string or word is said to be admissible if that word appears in a given sequence. For example, in the sequence aabaabaabaabaab..., a, aa, baab are all admissible, but bb is ...

A fractal process for which H<1/2, so r<0.

A Z-action or N-action. A cascade and a single map X->X are essentially the same, but the term "cascade" is preferred by many Russian authors.

A theorem that guarantees that the trajectory of Langton's ant is unbounded.

The largest n such that |z_n|<4 in a Mandelbrot set. Points of different count are often assigned different colors.

A word or string which is not admissible.

Quantifies deviation from translational invariance by describing the distribution of gaps within a set at multiple scales. The more lacunar a set, the more heterogeneous the ...