It is remarkable, the extent to which the Cyclic Tag System depends on nothing more than interactions between C gliders, especially the C2, and EBar gliders. There are solitonic relations between all the different C's and both EBar and F gliders. Due to the differing velocities of the EBar and F, it is hardly surprising that one or the other would prevail; that it was EBar is a definitive disclosure from the book. Equally interesting is the relegation of C1 and C3 to secondary roles, particularly through the coupling of a pair of C1's to a C3.
Before enumerating the C - EBar collisions, it is worth noting that the EBar has a boundary consisting of six ether tiles running in a northeasterly direction, followed by a two tile jog, after which the unit cell repeats. Due to the periodicity of the C gliders, there is only one distinct northeasterly line of approach for the EBar, which is also the direction of approach for B gliders, likewise for BBar's, G's, and even F's.
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Figure 4 shows a C unit cell (which of the three, C1, C2, C3, doesn't matter because they differ along their left margins far from the site of the collision) positioned along the EBar margin. Due to the jog and resultant overhang, separation by a single ether tile is excluded because the collision would have already taken place. Separation by six tiles is redundant, because the collision delays, and corresponds to a displacement of two tiles when it finally occurs.
Not only do we want to examine the collisions between the three C gliders and EBars, there is a fourth set which is important. Namely, they are the collisions with the C1 pair, which are spaced so closely that the encounters are not separable into individual collisions taking place one at a time in sequence.
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