Notes

(1) This sampling and many other investigations reported in this paper were performed using the C language computer program [4].

(2) The terms ``set'' and ``measure'' entropy, together with ``set'' and ``measure'' dimension, are introduced here to rationalize nomenclature.

(3) Such as the set formed from the end points of the intervals at each stage in the geometrical construction of the classic Cantor set. This set has zero Hausdorff dimension, but Kolmogorov dimension [9].

(4) They are thus of direct significance for digital image processing.

(5) Each site in this cellular automaton can take on one of two possible values; the time evolution rule involves nine site (type II) neighbourhoods. If the values of less than 2 or more than 3 of the eight neighbours of a particular site are nonzero then the site takes on value 0 at the next time step; if 2 neighbouring sites are nonzero the site takes the same value as on the previous time steps; if exactly 3 neighbouring sites are nonzero, the site takes on value 1.

(6) This feature allows practical simulation of such cellular automata to be made more efficient by storing information on the evolution of the specific sequences of sites which occur with larger probabilities (cf. [23]).

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