Bill Gosper has been doing some fascinating original research on patterns with 'simple' initial states but complex long-term behavior, using the new cross-platform hashlife-capable Game of Life simulator,
Golly.
The following are Gosper's detailed notes on the "Gotts-puzzle" pattern shown at right:
...[O]bserve that the bursts forming the bottom-left corners are acute Vees (inset) flying backwards! In fact, the inset shows two backwards mirror image Vees flying apart. This is seriously weird by the following argument.
Experiments on this scale nearly always take on a characteristic expanding star shape, with typically eight or fewer "limit" points, each receding with the velocity vector of a hypothetical glider or spaceship launched from the Origin by a Big Bang. (Any finite initial configuration (Origin) is infinitesimal compared with with these billions-wide star diagrams.) The diagrams are often crisscrossed by numerous linear features at many different angles, e.g., the patterns on Nick Gotts' weblog or the pattern shown below.
Golly screen shot of 'nick-gotts-g' around generation 2,000,000
The above screenshot shows the complex long-term behavior of the 'nick-gotts-g' pattern shown at right, which consists of two interacting rakes. Here is a
larger screenshot of the same pattern at 4.9e8 ticks.
The components of each line have equal velocity vectors, easily determined by which of the star-points radiates the extended line. The Origin is a ninth point which radiates all lines of immobile objects. (The production of particles with a nonstandard velocity would create an additional star-point.) Lines joining two star-points are guns or puffers. Thus the little tick designated by the red arrow in gottspuzz.png can only be a wave of a million or so spaceships (MWSS in fact) pointing toward the N spaceship limit, which unfortunately is graphically inapparent because no spaceships are actually escaping. (They can't be heading S because there was a single pixel NW-SE jog in that tick that my screenshot was too slow to catch.)
Thus when several rays emanate from the vertex of an internal wave crossing, it is easy to see the chain of causality, i.e. which lines are inputs and which are collision products, because components along a ray are older toward its star-point.
In other words, Vees fly frontwards.
And one of the two arms (apparently the sparser) of these backwards Vees heads at an "inexplicable" angle, i.e., not through a star-point!
