Extensible Wickstretchers and HALFMAX

Wickstretcher 1  Hartmut Holzwart  22 April 2005 Hartmut Holzwart and Jason Summers have successfully tamed a extended family of wickstretchers, beginning with the one at right -- a p4 wickstretcher with two central lines and a p8 tail, constructed by Holzwart on 22 April 2005.

Wickstretcher 2  Hartmut Holzwart  22 April 2005 Wickstretcher 3  Hartmut Holzwart and Karel Suhajda  22 April 2005 This was followed by several related results. To the right is an alternate form of the wickstretcher, created by Holzwart, with the right side replaced by a pure p4 tail section. On the far right is another phase of the above wickstretcher, with the tail replaced by a p6 fencepost constructed by Karel Suhajda on the same day.

smaller c/2 p80 puffer  Jason Summers  24 April 2005 Starting from a related p80 puffer ship, Jason Summers produced a new smaller p80 puffer -- 8 cells wider than the known p4 ships in Paul Tooke's collection, but about 20 cells shorter. As with the old ships, there's also an alternate, much less prolific p80 orbit -- as well as a p20 "bread-and-honey" orbit (loaves are created, then converted to beehives a few generations later.)

Wickstretcher 4  Hartmut Holzwart  3 May 2005 Wickstretcher 5  Hartmut Holzwart  25 April 2005 Holzwart also produced a four-central-line wickstretcher, and later a smaller version of the original minimal wickstretcher as well (with no central lines in the wick) -- both completed by a p4 c/2 tail rather than a fencepost.

Wickstretcher 6  Hartmut Holzwart  3 May 2005 Wickstretcher 7  Hartmut Holzwart  4 May 2005 Based on a "double fencepost" pattern of Holzwart's (not shown) Summers found a way to provide an independent fencepost for each of the two active edges of a wick -- allowing any number of stable lines to be added in the middle (the example at right shows a wick with a 14-line "sandwich".) Other possible modifications include changing the phase of the two edges relative to each other, as in the asymmetrical wickstretcher and fencepost at the far right -- or simply shifting one section of the wick by two cells relative to an adjacent section, as shown by the "spacers" (four-line-thick oblongs) toward the center of the pattern below.

Half-plane-filler (HALFMAX)  Jason Summers  4 May 2005
Finally, Summers succeeded in using the new wick and fencepost technology to produce this semi-spacefilling pattern, which expands in three directions at half the speed of light -- producing a triangular region that grows to fill half the plane. [Previous spacefillers have all been diamond-shaped, expanding at c/2 in all four cardinal directions to fill the entire plane.]

Update: 9 May 2005 07:22

HALFMAX2  6 May 2005 minimal wickstretcher  6 May 2005 On May 6, Hartmut Holzwart produced smaller versions of both the original basic wickstretcher and of Jason Summers' HALFMAX pattern (far right).

Update: 26 May 2005 06:45

3-line wickstretcher  Jason Summers  21 May 2005 smaller 4-line wickstretcher  Jason Summers  21 May 2005 On May 21, Jason Summers produced sample patterns that allow the construction of wickstretchers with any number of central lines, by adding the appropriate number of four-line "spacers" to one of the four extensible base patterns. He observed: "For each number of lines, there are eight possible wicks, made by changing the relative position and phase of the two sides of the wick (except for zero lines, where there are only two)."

HALFMAX3  Jason Summers  15 May 2005 5-line wickstretcher  Jason Summers  21 May 2005 Wickstretchers with 3, 4, and 5 central lines are shown here. On the far right is Summers' latest HALFMAX optimization, backed up by one generation to reduce the population to 903 cells.

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