By D.E. Johnson, etc.
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In attempting to put some restrictions on the choice, one may suggest that movement will be such that the Ε value of the subsequent pattern will always increase or, at least, remain the same. In some sense this requirement is implied by the experimental results: configurations of maximum Ε do not change into submaximal configurations with time. As far as elementary permutations are concerned, this restriction may be interpreted to mean that the requirement is global: that is, the Ε of the overall pattern must increase even if some moves are locally energetically unfavorable.
In general, for r types of cells, (in cluding medium), there are ^r(r + 1) different kinds of edges (hence X's) and there are r conservation relations. Thus the number of effective A's, that is, number of //'s = ^r(r + I) - r = ^r(r - 1). (12) We may now list the possible patterns of absolute stability involving two cell types. (1) "ONION" PATTERN: For μ^> 0, from Eqs. (9) the absolutely stable pattern is the one for which N^,^, and N^^, are maximum and N^,^ is minimum, that is, the patterns in which one type of cells are closely packed and sur rounded by cells of other types.
2) N o PREFERRED PATTERN: F o r //j = 0, ^ is constant and, therefore, all structures are equally stable. Note that this result is more general than the trivial one in which all the A's are equal to each other. (3) CHECKERBOARD PATTERN: F o r / / i < 0, from Eqs. (9), the absolutely stable pattern is the one for which iV^b a n d Λ^^^ are minimum a n d iVbw is maximum. Such a pattern involves the minority cell dispersed in the pre dominant cell type; in the case where the minority cells are as close together as possible, the pattern resembles a checkerboard.
A Handbook of Active Filters by D.E. Johnson, etc.