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The Western Badlands

After working out possible data and program representations, there remains the job of verifying that transmission across a program is feasible, and that the information which has been sent can be stopped. With transmission and the decision to use C2 and EBar gliders, there is only one possibility, consisting in the solitonic relation between the two. For convenience it is repeated in the right drawing of Figure 22, where it is seen that the spacing between EBars and C2's must lead to an encounter at Bresenham index 3.

Additional increments of integral EBar lengths are possible. Having a unique arrangement is fortunate, because all C2's are displaced equally by the passage of solitons, leaving their relative spacings intact. The only problems arise in guaranteeing that they are eventually stopped at the correct places.

Figure 22: EBar interactions for which there are no alternative forms.
\begin{figure}\centering\begin{picture}(310,260)
\put(0,0){\epsfxsize =130pt \ep...
...ut(180,10){\epsfxsize =130pt \epsffile{C2EBarolo.eps}}
\end{picture}\end{figure}

Interpreting the predicate creates spurious EBar gliders, leaving the two possibilities of ignoring them or destroying them. The latter is problematic; parity implies leaving residues. For A tetramers the fortunate alternatives exist, of letting EBars pass which arrive with Bresenham index 1, or of stopping those with indices 2, 3, or 6. Passage is shown in the left drawing of Figure 22.

Deciding which combinations are to be used is part of designing the Cyclic Tag System, and are not further discussed here. Just as accomodating the EBar packets arriving from the far right so that they can either be erased or transmitted (albeit with filtering) requires a synchronizing independent of the inner structure of the packets, so the stopping choices at the left require an invariance. The collision at Bresenham indes 2 is especially prompt.

Figure 23: Three alternatives by which an A tetramer can stop an EBar and convert it into a C2.
\begin{figure}\centering\begin{picture}(430,260)
\put(0,70){\epsfxsize =130pt \e...
...ut(300,40){\epsfxsize =130pt \epsffile{A4EBar(6).eps}}
\end{picture}\end{figure}

Beyond checking the synchronization of the activities at the left and far right of the Cyclic Tag System, the verification that it is actually a computer is important. Presumably this verification exists in the literature, and in any event could be carried out symbolically without any drawings of the evolution of Rule 110.

Once that was done, it would still be entertaining to watch some simple calculations, such as the operation of a binary counter, or even of simple monary arithmetic with addition, subtraction, multiplication and division.


next up previous contents
Next: Bibliography Up: ``Rule 110 is Universal!'' Previous: Shimming Succeeding EBar Packs   Contents
Harold V. McIntosh 2002-07-11