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less orderly lattices


Table: Besides the columnar and diagonal forms of T4 lattices, there is enough flexibility in packing the smaller triangles that many ofhter lattices are possible. Among these are the ones involving D gliders.
  10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10
1 . D2 . . . . . . . . . . . . . . . . . . .
2 . . . . . . . . . . . . . . . . . . . 37 .
3 . D1 . 74 . 37 . . . . . . . . . . . . . . .
4 . 25 . . . . . . . . . . . . . . . . . . .
5 . . . . . . . . . . . . . . 37 . . . . . .
6 37 . . . . . . . . . . . . . . . . . . . .
7 17 . . . . . . . . . . . . . . . . 17 . . .
8 . D2 . . . . . . . 37 . . . . . . 74 25 . . .
9 161 . . . . . . . . . . . . . . . . . . . .
10 . . . . . . . . . . . . D . f . . . 37 . .


Figure: Diagonally slanting lines of T4's can be separated by T3's and some additional packing. However the packing does not quite make an ether string. The left lattice has a cycle of 25, with shifts ``left 9 in 4'' and 11right 7 in 8.'' The right lattice has a cycle of 17, corresponding to ``left 10 in 7'' and to ``right 7 in 7,'' which is just light velocity.
\begin{figure}\centering\begin{picture}(300,150)
\put(0,10){\epsfxsize =150pt \e...
...}
\put(160,0){\epsfxsize =150pt \epsffile{t4cy17.eps}}
\end{picture}\end{figure}

Figure: Somewhat shallower diagonal strings of T4's. The left lattice has a small unit cell containing 38 cells, and a cycle length of 37. It appears 6 times in the de Bruijn map, at ``right 4 in 5,'' ``right 8 in 10,'' ``right 9 in 2,'' ``left 1 in 8,'' ``left 5 in 8,'' and ``left 10 in 6.''
\begin{figure}\centering\begin{picture}(300,130)
\put(0,5){\epsfxsize =150pt \ep...
...}
\put(160,0){\epsfxsize =150pt \epsffile{t4cy37.eps}}
\end{picture}\end{figure}

Figure: T4's can make diagonals in both directions. This example is very close to the format of the D gliders, but fails to develop an ether interface. The unit cellhhas 151 cellular automaton cells, with a cycle length of 161. It sits in the de Bruijn map at ``left 10 in 9.''
\begin{figure}\centering\begin{picture}(150,100)
\put(0,0){\epsfxsize =150pt \epsffile{t4cy161.eps}}
\end{picture}\end{figure}


next up previous contents
Next: dominant D glider component Up: periodic lattice component Previous: columnar lattices   Contents
Jose Manuel Gomez Soto 2002-05-15