New Transcendental Patterns
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".
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