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.
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.
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.)
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.
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.
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.]
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)."
Dean Hickerson has presented a pair of new transcendental patterns he's created. These consist of puffers and guns, which grow in what appear to be unpredictable ways.
This produces groups of LWSSs headed west, with gaps of fixed size between them. The lengths of the groups form the 'ruler' sequence, 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 ... (Sloane's A001511). The first group of length n is emitted about generation 96*2^n. The pattern uses a Corderman eater puffer found by Paul Tooke (Jan 2004), a p48 glider gun by Noam Elkies (Jun 1997), a p8 glider reflector by Noam Elkies (Sep 1998), and a p24 LWSS puffer (source unknown).
Shown are the starting pattern at Gen 0 and later at Gen 850, after 1-2-1-3-1 as been emitted. (Note: They've been rotated 90° to better fit the page.)
The second object is "Jagged Lines":
Jagged lines of gliders, formed by a drifting collision of two Lightweight Spaceships (LWSS) streams, crash to form an approximately vertical jagged line of pairs of blocks. I don't know if the line stays within a bounded distance of the center line, or extends infinitely far to the left, or to the right, or both.
Shown are the starting pattern at Gen 0 and later at Gen 850, shortly after the second block pair has been created. (Note: They've been rotated 90° to better fit the page.) Hickerson also simulated the placement of the block pairs and presented a plot showing the first 11,426,769 Twin Blocks produced by Gen 4,113,636,213. (The horizontal:vertical scale is 488:1 to emphasize the shifting locations.) The dimensions of the jagged line of Twin Blocks are cells 140,480 wide with a tail 685,605,960 cells long.
Hickerson says that he doesn't think it's a random walk:
There are some large portions of it that are almost symmetric across horizontal lines. Also, the transitions between successive minimal and maximal x-coordinates are rather brief. I.e. it spends a long time far to the left of the center line, then moves quickly to a point far to the right, spends a long time there, etc. I think there's an approximate scale-invariance; if you expand the picture by appropriate factors horizontally and vertically it'll look almost the same. But I don't understand it well enough to say what those factors are.
Gabriel Nivasch points out that if the Pre-Block (shown in red), which is responsible for the asymmetry of the pattern, is removed, then the pattern generated is one generated by a growing sequence which starts out with zero and adds four new items at the end while sequentially reading the digits already laid out. The additions are
0 -> 1 0 1 0
1 -> 1 0 1 1
which gives the initial sequence of "0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1".
Earlier, Nicolay Beluchenko pointed out that only 3 of the 6 possible state combinations for the top cell on the line of bilateral symmetry of a "P5 squirter" type oscillator were known, as shown to the right. The sequences are—