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5.3. EFFICIENCY OF THE ND-SYSTEMS APPROACH 67<br />

(a)<br />

(b)<br />

Figure 5.5: (a) The initial state w 0,0,0 (b) The initial state and the full recursions <strong>to</strong><br />

compute y 2,0,0 , y 0,2,0 , y 0,0,2<br />

Figure 5.6: A stable pattern (green) for shifts in all three directions<br />

repeated, yielding points with <strong>to</strong>tal time n(m − 1) + 2, etc., showing the pattern of<br />

points in N <strong>to</strong> yield a stable pattern.<br />

□<br />

However, for n>2 the stable pattern N in the above proposition is not minimal.<br />

To investigate minimality of stable patterns it is helpful <strong>to</strong> study the relationship

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