(Received 4 January 1994; revised manuscript received 18 April 1994; accepted for publication 1 July 1994)

Ref: J. C. Sprott, Physics Letters A **192**,
355-360 (1994)

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Fig. 1. The average correlation dimension of 6080 chaotic attractors
scales approximately as the square root of the dimension of the system
for low-order polynomial maps (O) and flows (X). The error bars
represent
the spread in dimensions, not an uncertainty in the average values.

Fig. 2. The correlation dimension has a high probability of a value
about 0.81 times the square root of the dimension of the system.

Fig. 3. The average Lyapunov exponent of 6080 chaotic attractors
scales
approximately inversely with the dimension of the system for low-order
polynomial maps (O) and flows (X). The error bars represent the spread
in exponents, not an uncertainty in the average values.

Fig. 4. The average value of the largest Lyapunov exponent for
chaotic
maps has a relatively uniform probability when multiplied by the system
dimension.