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Cook's D-gliders, forward velocity c/5

It has been asserted that there are only two D-gliders, running right two every ten generations, and that they are the only right-running gliders besides the family of A's, which run two cells right in three generations, making them about a third as fast as the A's. Note that listing the velocity as c/5 is a reduction to lowest terms of the actual relation, which is to advance two cells in ten generations. The only configuration which meets the one-in-five requirement is the alpha phase of the T2's, as seen in Figure 1.9.

Defining the width of a glider has its interesting points. Lind apparently took the cycle-14, period-7 character of the ether for granted, exhibiting an appropriate interlude to define the members of his list. That works well enough except for the E, where 00000 doesn't make a clean insertion. In all the other cases there is varying amounts of slack which often gets taken up by additional ether tiles (taking as ether the 4x4 T3 with a notch cut from the lower right corner). But if you don't do it his way, you can run into phase relationships which have to be explained.

Just gathering up the minimal unit which repeats, supposing that all the ether continuations are implicitly and uniquely defined, The two D-tiles differ quite subtly, the principal difference being where to position the T1 at the upper left of the first tile. As Cook remarks, there is a discrepancy of two or three little dots now and then distinguishing the two gliders.

From diagram experience, these tiles come from loops (several, in fact, if the lines of successive generations are not cyclic permutations of one another) and the ether tile is lurking in there somewhere, either as a loop or in the linkage between the other loops. Well, tile juggling shows that the D1's and D2's can be juxtaposed in any combination at will and separable when desired minimally by an ether strand which can be interpreted as a jittering (D1 to D1) or intermittent (D2 to D2) glider! Or, of course, something even thicker.

Which goes to confirm that the definition of a glider is rather subjective; it depends on which of several tiles is in the minority, generally a strong minority, with respect to the others.

Figure 2.25: T4 based D gliders, which move slowly right. The one on the left is D2, on the right is a D1.
\put(30,0){\epsfxsize = 120pt \...
...put(120,0){\epsfxsize = 120pt \epsffile{singleD2.eps}}

Figure 2.26: There are two kinds of D gliders, each slightly different.
\put(0,0){\epsfxsize = 350pt \epsffile{multipleD.eps}}

next up previous contents
Next: Cook's E-gliders, velocity -4c/15 Up: The Gliders Previous: de Bruijn approach   Contents
Jose Manuel Gomez Soto 2002-01-31