BBMCA rule

Fig. 6,12 The BBMCA rules, defined by using the Margolus neighborhood (see section 8,1.3.3). The complete set of rules may be obtained by writing down all rotations of the rules defined explicitly above.

Fig. 6.13 Diagonal motion of a single particle (represented by solid dot) as induced by successively applying BBMCA rule (b) (see figure 6.12) to even (i.e. thicJc-lined) and odd (i.e. thin-lined) partitions of the lattice.

Mirrors BBMCA rule (e), and its rotated equivalents, allows groups of particles to be built up to form stable configurations. Such configurations can then be used as mirrors to reflect balls, and thereby to act as signal routers. Figure 6.15, for example, shows the smallest possible fixed configuration consisting of four particles. Since adjacent squares remain uncoupled from one another, mirrors of arbitrary size can be built up from this basic four-particle mirror. 

BBMCA rule (c) in figure 6.12 allows for ball-mirror collisions to mimic their classical incarnations. Figure 6.16, for example, shows a collision between a (two-particle) ball and an 8-particle mirror. Notice that, just as for the ball-ball collision shown earlier in figure 6.14, a slight time-delay is again introduced. 

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