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four left in six generations

There are two more glider situations in the sixth generation. Both are based on the T5 triangle as a base piece, but since its use with the two gliders are diagonal reflections of one another, there probably isn't a clear coexistence situation in which one can overtake the other and produce nice simple collisions. That's something that still has to be tried, however.

In the first combination, there is a shift of four cells after six generations. The two different tiles needed to make up two species are are:

Figure 2.5: One species moves 4 left every six generations against a background generated by the other.
\begin{figure}\centering\begin{picture}(80,40)
\put(0,-10){\epsfxsize = 80pt \epsffile{tm4in6a.eps}}
\end{picture}\end{figure}

To tile the plane and thus construct an evolution, make diagonals from either tile:

Figure 2.6: The second species is the glider, moving against a background established by the first.
\begin{figure}\centering\begin{picture}(200,100)
\put(0,0){\epsfxsize = 200pt \epsffile{tm4in6b.eps}}
\end{picture}\end{figure}

Figure 2.7: The first species is the glider, moving against a background established by the second.
\begin{figure}\centering\begin{picture}(200,100)
\put(0,0){\epsfxsize = 200pt \epsffile{tm4in6c.eps}}
\end{picture}\end{figure}

Figure 2.8: The de Bruijn diagram for shifting four cells left in six generations shows the ways in which one of the species can move within a background generated by the other, and all the combinations in between. The diagram has three connected components, one of which is the field of zeroes, meaning that designs belonging to one of them cannot mix with designs belonging to the other. On the other hand, the large component contains several cycles, transitions between which will result in intermingling their patterns.
\begin{figure}\centering\begin{picture}(340,380)
\put(0,-20){\epsfxsize = 340pt \epsffile{dbm4in6.eps}}
\end{picture}\end{figure}


next up previous contents
Next: one left in six Up: Gliders not using the Previous: two right in five   Contents
Jose Manuel Gomez Soto 2002-01-31