From: dbell@pdact.pd.necisa.oz.au (David I. Bell)
Subject: Spaceships in Conway's Life (Part 5b)
Organization: NEC Information Systems Australia, Canberra
Date: Fri, 09 Oct 1992 03:17:38 GMT
Keywords: life

----------------- [Continued from previous mail article] --------------------

Here are a series of spaceships with a different front part.  The front
part of these consists of two almost-spaceships and a HWSS.  The HWSS
serves no purpose except to support the almost-spaceships.  Several of
these spaceships have the capacity of having the back end sizes changed
in the same way as the standard spaceships.

[Period 4 tagalongs for convoy of HWSS and almost-spaceships (speed c/2)]
 .O......................
 O.....O..OOOO.O.........
 O.....O.O..............O
 OOOOO.O...........OO...O
 .........OO.OOO...OOO...
 ....OO.....O..O.....OO.O
 ..O....O......OO..O.OO..
 .O...........O.O.O...OO.
 .O.....O....OO..OOO.O...
 .OOOOOO......OO...O.O...
 ..............O.OO......
 ...........O....O.OOO.OO
 .O..O.....O....O..OO..OO
 O....O.O.OO...OO....O.O.
 O...OO.OO...OO..........
 OOOO.....O...O..........
 ..........O.O...........


 .O..........................
 O.....O................OO...
 O.....O..............OO.....
 OOOOO.O..OO..O...OO..O......
 ..........OOOOO.OO.OO.OO.O..
 ....OO.......OO.O...O....O.O
 ..O....O...O.O..O...O....O..
 .O.........O.O...O.......OOO
 .O.....O..O........OO.......
 .OOOOOO....O.....O.OOO...OOO
 ...........OO...OOO.OO...O..
 ..........OOO.......OOO.O...
 .O..O.......O....O...OO.OOO.
 O....O.O.OO.O...OOOOO....O..
 O...OO.O..........OO..O..O..
 OOOO..................O.O...


 .O...........OO.O.O.........
 O.....O......OOOO.O.........
 O.....O..O..O...............
 OOOOO.O..OO..OO.O.O....OO.O.
 ..........O..OO.O.O...O...O.
 ....OO...........OOO......O.
 ..O....O.........OOO.O.O....
 .O..........OO..............
 .O.....O...OO.OOO...O.......
 .OOOOOO.....OOOOOOO..O......
 .............OOO............
 ................OOO.OOO.....
 .O..O.....O..OOO.......OOO.O
 O....O.O.....O.O.........O.O
 O...OO.O.OO..O..O...........
 OOOO........OOO.OOO.........


 .O...........OO.O.O..........
 O.....O......OOOO.O..........
 O.....O..O..O................
 OOOOO.O..OO..OO.O.O....OOOOO.
 ..........O..OO.O.O...O.....O
 ....OO...........OOO.........
 ..O....O.........OOO.O.O....O
 .O..........OO...............
 .O.....O...OO.OOO...O........
 .OOOOOO.....OOOOOOO..O.......
 .............OOO.............
 ................OOO.OOO.OOOO.
 .O..O.....O..OOO.......O....O
 O....O.O.....O.O.............
 O...OO.O.OO..O..O.......O...O
 OOOO........OOO.OOO.......O..


 .O...........OO.O.O....
 O.....O......OOOO.O....
 O.....O..O..O..........
 OOOOO.O..OO..OO.O.O....
 ..........O..OO.O.O....
 ....OO...........OOO...
 ..O....O.........O.O..O
 .O..........OO....OOO.O
 .O.....O...OO.OOO....O.
 .OOOOOO.....OOOOOO..OOO
 .............OOO......O
 ................OOO....
 .O..O.....O..OOO.......
 O....O.O.....O.O.......
 O...OO.O.OO..O..O......
 OOOO........OOO.OOO....


 .O....................OO.OO.
 O.....O......OOO.....OOOOOOO
 O.....O....O.....OO....OOOOO
 OOOOO.O...O.O...OOO...O.....
 .........OO..O.O.....O......
 ....OO....OO.OO....O........
 ..O....O....O.OO.O..........
 .O..........OOOO............
 .O.....O....O.O...O.........
 .OOOOOO.....OO..OO..........
 .............O..OOO.........
 ..........OO................
 .O..O....O...O..O..O....OOO.
 O....O.O.OOO.......OO..OOOOO
 O...OO.O...OOO.OO.O...O.OOOO
 OOOO.........O.......OOO....


The last spaceship above has a very nice spark at the back corner.  The
spark is probably about as far away from the generating ship as is possible
for period 4.

The following ship is another one whose front part has period 4, but which
changes to period 2 at the back.  As seen in a previous article, the back
of this can support a repeatable period 2 tagalong.  The back end can also
support the period 3 tagalong from that article, making the final spaceship
have a total period of 12.

[Period 4 spaceship with period 2 back end (speed c/2)]
 .O...........OO.O.O..........
 O.....O......OOOO.O..........
 O.....O..O..O................
 OOOOO.O..OO..OO.O.O....O.O...
 ..........O..OO.O.O...O..O.OO
 ....OO...........OOO.OO......
 ..O....O.........O.O.O...O...
 .O..........OO....OOO.OO.O...
 .O.....O...OO.OOO..........OO
 .OOOOOO.....OOOOOO..OOOO.O...
 .............OOO.........O...
 ................OOO..OO......
 .O..O.....O..OOO.....OO..O.OO
 O....O.O.....O.O.......O.O...
 O...OO.O.OO..O..O............
 OOOO........OOO.OOO..........


In this final spaceship with the same front end, the HWSS does have a
role other than supporting the almost-spaceships.  The back end of the
HWSS is used to keep some cells OFF that would otherwise be turned ON.

[Period 4 spaceship with tagalong (speed c/2)]
 .O...........O.O......
 O.....O....OOO.OO.....
 O.....O...O......OO...
 OOOOO.O..OO..OOOOO....
 ..........O.O.....O...
 ....OO....OO...OO.OO.O
 ..O....O..O.O..OOO....
 .O.......O..O..O.O....
 .O.....O.O.....OO.....
 .OOOOOO..O.....O......
 .........O...O.OO..O..
 ..........OO.O.O...OO.
 .O..O........O...OOOO.
 O....O.O.OOOOOOOO.OOO.
 O...OO.O.OO...........
 OOOO.......OOOO.O.O...
 ..............O.O.O...


The following two spaceships have a front end which is an OWSS.  In these
spaceships, the OWSS is mutually supported by the rest of the spaceship,
and so these are not really tagalongs.  The first ship shown seems to have
the same variable-sized back end as other spaceships.  But only the HWSS-
like back end shown here will work.

[OWSS featuring in period 4 spaceship (speed c/2)]
 .......OOO.O.O.........
 ......OOOO.O.OO...OO...
 .....OO.......O..OOO...
 ......OOOOO.O..O.OO.O..
 ...OO....O...OOOOO.....
 .O...........O...O.....
 O.............OO.OO....
 O......O.....O.....OOOO
 OOOOOOO......OO..OOOOOO
 ................OOOOOO.
 .......OO..OOOOO.......
 ......OOO........O.....
 .....OO.O...OO.OOO.....
 ......OO...O.....O.....
 .........OO...OO.......


The following spaceship is another one with a period 4 front part which
has a period 2 back end.

[Period 4 spaceship with period 2 back end (speed c/2)]
 .......OOO.O.O.............
 ......OOOO.O.OO...OO.......
 .....OO.......O..OOO....O.O
 ......OOOOO.O..O.OO....O..O
 ...OO....O...OOOOOO...OO...
 .O...........O...OO..O....O
 O.............OO.OO.OOOOO.O
 O......O.....O.............
 OOOOOOO......OO..OOOOOOOO.O
 ................OOO.......O
 .......OO..OOOOO......OO...
 ......OOO........O.....O..O
 .....OO.O...OO.OOO......O.O
 ......OO...O.....O.........
 .........OO...OO...........


The following cute spaceships were found by Hartmut.  In the first one, a
pre-beehive is pulled and pushed along by four LWSSs.  In the second one,
a piece of "trash" is pulled and pushed along.

[Four LWSSs escort a pre-beehive (speed c/2)]
 OOOO.....O..O
 O...O...O....
 O.......O...O
 .O..O...OOOO.
 .............
 .....OO......
 .....OO......
 .....OO......
 .............
 .O..O...OOOO.
 O.......O...O
 O...O...O....
 OOOO.....O..O


[Four LWSSs escort a piece of "trash" (speed c/2)]
 .........O...O
 ..OO....O.....
 .OOOO...O....O
 OO.OO...OOOOO.
 .OO...........
 ..............
 ......OO......
 .......O.O....
 ..OO....OOOO..
 .OOOO....O...O
 OO.OO...O.....
 .OO.....O....O
 ........OOOOO.


While looking to stabilize a very large OWSS, I found the following escort.
The following shows the largest OWSS that can be escorted by it.

[Period 4 escorts for OWSS (speed c/2)]
 .....OO.........
 ..OO.OOO........
 .OO..OO.........
 ..OO..OO........
 ...OO.OOO.......
 ......O.O.......
 ............OO..
 .O.............O
 O...............
 O..............O
 OOOOOOOOOOOOOOO.
 ................
 ................
 ....OOO.O.......
 ...OOOO..OO.....
 ..O.O...........
 .OO.............
 ..OOOO.O........
 ...OOO.O........


The OWSS spaceship shown in the above spaceship can be made smaller in
several different sizes.  Besides supporting an OWSS, this escort can also
survive by being "pushed" by a MWSS.  So this could be called a "pushalong"
instead of a tagalong.  One MWSS can push two of these along if desired.

[MWSS escorting a period 4 "pushalong" (speed c/2)]
 ....OO.O....
 .OOO...O....
 .O..........
 .O......O...
 ..OOO...O...
 .....OO.....
 ............
 ............
 .......OO...
 ......OO.OOO
 .......OOOOO
 ........OOO.


That ends the survey of results which make use of standard spaceships.
Now I will survey the results for the spaceships which do not use standard
spaceships.

I found the first c/2 period 4 spaceship which does not use any standard
spaceship at the beginning of May, 1992.  The front of this spaceship has
period 2, but then a period 4 change appears within a few columns.  The
spaceship has a nice two-bit spark at the back.

[Period 4 spaceship (speed c/2)]
 .........O.............
 ......OO.O.............
 ......O...O....OO..OO..
 ...O.O..OO....OOO..OOOO
 ..OOOOO...O.O.OOO.O..OO
 .OO.....OO.OO..........
 OO....O......O.O..OO...
 .OO....OOOOOOOO........
 ......O.........O..O...
 .OO....OOOOOOOOO.......
 OO....O........OOO.....
 .OO.....OOOO.OO.OO..O..
 ..OOOOO.........OO..O..
 ...O.O..OOO..OOO.O.OO..
 ......O................
 ......OO.O.O...........
 .........O.............


Hartmut Holzwart later found two tagalongs for the above spaceship.
These are shown below.

[Period 4 spaceships with tagalongs (speed c/2)]
 .........O......................
 ......OO.O......................
 ......O...O....OO..OO......O....
 ...O.O..OO....OOO..OOOO..OOO....
 ..OOOOO...O.O.OOO.O..OOOO...O...
 .OO.....OO.OO.............OOOO.O
 OO....O......O.O..OO.......OO.O.
 .OO....OOOOOOOO.........OO..O...
 ......O.........O..O.....OO.O..O
 .OO....OOOOOOOOO.........OO..O.O
 OO....O........OOO......O.OO..O.
 .OO.....OOOO.OO.OO..O..OO.O...OO
 ..OOOOO.........OO..O..O.....OO.
 ...O.O..OOO..OOO.O.OO...OOOOOO..
 ......O...................O.OO..
 ......OO.O.O....................
 .........O......................


 .........O.....................O.O.
 ......OO.O....................O...O
 ......O...O....OO..OO......O..O...O
 ...O.O..OO....OOO..OOOO..OOO...O...
 ..OOOOO...O.O.OOO.O..OOOO...O...O..
 .OO.....OO.OO.............OOOO.O..O
 OO....O......O.O..OO.......OO.OOOOO
 .OO....OOOOOOOO.........OO..O...O..
 ......O.........O..O.....OO.O..OO..
 .OO....OOOOOOOOO.........OO..O.OO..
 OO....O........OOO......O.OO..O....
 .OO.....OOOO.OO.OO..O..OO.O...O...O
 ..OOOOO.........OO..O..O.....OOOOO.
 ...O.O..OOO..OOO.O.OO...OOOOOO.....
 ......O...................O.OOO....
 ......OO.O.O...................OOO.
 .........O.........................


As previously described, one way to find spaceships which do not use any
of the standard spaceships is to just perform the search, but then manually
backtrack over the results whenever a standard spaceship turns up.  This is
time-consuming and error prone.

Hartmut Holzwart thought of and implemented a new search feature which
avoids this problem completely.  He made the observation that for all of
the standard spaceships, there is a generation in which some cell has seven
ON neighbors (the "eye" of the spaceships).  By changing the program to
suppress results in which any cell has more than six ON neighbors, all
results which make use of standard spaceships are also suppressed.  This
makes it much easier to find these new spaceships (but at the cost of missing
some possible spaceships).

Hartmut found the following series of spaceships using this new search
feature.

[Period 4 spaceship (speed c/2)]
 ....OO.........................
 .OO.......................OO.O.
 OO..O.O................OOOO...O
 .OO.O.O......OO......OO........
 ..O...OO....OOOO.....OO..OO...O
 ...OO.OOO.....O...O.O....O..OO.
 ....OO.......OOO..OO.O..O......
 ......O.OO.O.O.................
 ....OOO.....O...O.O...O.OO.....
 ....OOO.OO...OO..O...OO....O...
 ......O..OO.OO.O...O.O..OO.O...
 ..OO.OO.O...OOO.....OO.OOO.O...
 .O.OO.................O.....O..
 OO.....................OOO..O..
 .OOOO....................O..O..
 ..OOO..........................


The back of the above spaceship can be slightly modified to attach to two
different larger back ends.

[Period 4 spaceships with larger back ends (speed c/2)]
 ....OO...............................
 .OO.......................OO.O.......
 OO..O.O................OOOO...O......
 .OO.O.O......OO......OO..............
 ..O...OO....OOOO.....OO..OO...O......
 ...OO.OOO.....O...O.O....O......OO..O
 ....OO.......OOO..OO.O..O......O.OO..
 ......O.OO.O.O...............O...OOOO
 ....OOO.....O...O.O...O.OO...OO.O....
 ....OOO.OO...OO..O...OO....O...OO.OOO
 ......O..OO.OO.O...O.O..OO.O.....OO..
 ..OO.OO.O...OOO.....OO.OOO.O.....OO..
 .O.OO.................O.....O........
 OO.....................OOO..O........
 .OOOO....................O..O........
 ..OOO................................


 ....OO.........................................
 .OO.......................OO.O.................
 OO..O.O................OOOO...O...........O....
 .OO.O.O......OO......OO.............O...OO.O...
 ..O...OO....OOOO.....OO..OO...O....O....O...O..
 ...OO.OOO.....O...O.O....O....O...OO.....O.O...
 ....OO.......OOO..OO.O..O......OO.OOO...OO.O.OO
 ......O.OO.O.O...............O.OO..O.OOO.O.O...
 ....OOO.....O...O.O...O.OO...OO..O........O.O..
 ....OOO.OO...OO..O...OO....O.........OO.O.O.O..
 ......O..OO.OO.O...O.O..OO.O......OOOOOOO.O.O..
 ..OO.OO.O...OOO.....OO.OOO.O.......OO....O.....
 .O.OO.................O.....O.......O....O...O.
 OO.....................OOO..O............O..O..
 .OOOO....................O..O..................
 ..OOO..........................................


The following spaceships are nice because they have a new spark at the edge.

[Period 4 spaceships with new edge spark (speed c/2)]
 ................................O...
 ..............................O..O..
 ....OO..............................
 .OO.........................OO.OO...
 OO..O.O......................O.OO...
 .OO.O.O......OO..........OOO.O.OOO..
 ..O...OO....OOOO........OO.O.O.O.OO.
 ...OO.OOO.....O...O........O.O...O..
 ....OO.......OOO..OO...OOO.O.OO...O.
 ......O.OO.O.O......OOO.OO.O........
 ....OOO.....O...O.O......O..O..O....
 ....OOO.OO...OO..O......OO..O...O...
 ......O..OO.OO.O...O..O.O.O.O.O.OOO.
 ..OO.OO.O...OOO.........O.O.O.O..O.O
 .O.OO....................O..O.O.....
 OO........................OOO.O.....
 .OOOO.......................O....O..
 ..OOO........................OO..O..
 ...............................OO...


 ................................O...........
 ..............................O..O..........
 ....OO....................................O.
 .OO.........................OO.OO......OOOO.
 OO..O.O......................O.OO......O....
 .OO.O.O......OO..........OOO.O.OOO..OO..O...
 ..O...OO....OOOO........OO.O.O.O.OOO.O.OO...
 ...OO.OOO.....O...O........O.O...O.O.O...O..
 ....OO.......OOO..OO...OOO.O.OO....O......O.
 ......O.OO.O.O......OOO.OO.O.......O..O...O.
 ....OOO.....O...O.O......O..O..O...OO..OO...
 ....OOO.OO...OO..O......OO..O...O.O.OO..O..O
 ......O..OO.OO.O...O..O.O.O.O.O.OO..O..O....
 ..OO.OO.O...OOO.........O.O.O.O..O..O.O.....
 .O.OO....................O..O.O.....O.O...O.
 OO........................OOO.O......OOO....
 .OOOO.......................O....O.....O...O
 ..OOO........................OO..O......OO.O
 ...............................OO...........


Here are two more spaceships which only differ in the last few columns.
Note the curious pattern of vertical rows of ON cells in these.  Possibly
there may be a way to make this extensible to continue the pattern, but
this isn't known.

[Two very similar period 4 spaceships (speed c/2)]
 ..............................OOO.......O.......
 ....OO.........................OO.OO...OO.......
 .OO.........................OO.O.OOO..O.........
 OO..O.O......................O.O.O.O..O..OO.O.O.
 .OO.O.O......OO..........OOO.O.O.....OO...OO...O
 ..O...OO....OOOO........OO.O.O.O...........O.O..
 ...OO.OOO.....O...O........O.O..O..O...O.O......
 ....OO.......OOO..OO...OOO.O.OO...O.....O.......
 ......O.OO.O.O......OOO.OO.O...OO.O.OO..........
 ....OOO.....O...O.O......O..O....O....O.........
 ....OOO.OO...OO..O......OO..O....O.O.O..........
 ......O..OO.OO.O...O..O.O.O.O.O...O.....O.......
 ..OO.OO.O...OOO.........O.O.O.O.OO....OOO....OO.
 .O.OO....................O..O.O.O....O...OO.OOO.
 OO........................OOO.O.O...OO.....O....
 .OOOO.......................O.O..O.O.O.O...O....
 ..OOO........................OO.OO.....O........
 ...............................OOO......OO......
 ................................OO..............


 ..............................OOO.......O......
 ....OO.........................OO.OO...OO......
 .OO.........................OO.O.OOO..O........
 OO..O.O......................O.O.O.O..O..OO.O..
 .OO.O.O......OO..........OOO.O.O.....OO...OO..O
 ..O...OO....OOOO........OO.O.O.O...........O..O
 ...OO.OOO.....O...O........O.O..O..O...O.O.....
 ....OO.......OOO..OO...OOO.O.OO...O.....O......
 ......O.OO.O.O......OOO.OO.O...OO.O.OO.........
 ....OOO.....O...O.O......O..O....O....O........
 ....OOO.OO...OO..O......OO..O....O.O.O.........
 ......O..OO.OO.O...O..O.O.O.O.O...O.....O......
 ..OO.OO.O...OOO.........O.O.O.O.OO....OOO....O.
 .O.OO....................O..O.O.O....O...OO.OO.
 OO........................OOO.O.O...OO.....O...
 .OOOO.......................O.O..O.O.O.O...O...
 ..OOO........................OO.OO.....O.......
 ...............................OOO......OO.....
 ................................OO.............


The following two spaceships have a totally different front end.
They are identical, except that first first spaceship has a large hole
in it, and the second spaceship has a tagalong inside that hole.

[Large period 4 spaceships without and with internal tagalong (speed c/2)]
 ............................O.OO..............
 ..........................OOOOOO..............
 .........................O.....OOOO.O.........
 .........................O..OO..O....O........
 .......OOO...............OO.O.OOOO.O.....O....
 ..OOOOOO...................OO.......OOOO.O....
 ..O...OO...OO..OO.OO........OO.......O........
 ..O...O.......OOOO..O..OO...OO.........OO.....
 ...OO.O..OO..........O..OO.O...OO.....O.......
 ....OOOO..O....OO.O.O..O..O............O......
 ........O...O..OO.O..OO.OOO............O...O..
 ..OO....OO..OOOO...O.O..O...............OOOOOO
 OO.....O.OOO.O.....O.O.OO...................OO
 O..O..OOO..O.O............O.................OO
 O......OO.............O...O..............O..O.
 .OO.....O...OO....OOOOO.....................O.
 .........OOOOO.....O..OOO..............OO.O...
 ...O...O.O...O..O..O....OO...O.........O......
 ...O.O.O.O.....O.OO....O..O...O.......O..O....
 ..OO.OO...OOO.OOO.O....OOOO.O.O........OO.....
 ..O..O............O..O...OOO..O......O........
 ..O....O..................OO...O..O..O.OO.....
 ...O..OOOO...............O...O....O.O...O.....
 .....O..OO...............O..OOOOO.OO..........
 .........................OO...O....O..........
 ...........................OOO...O............
 .............................O................


 ............................O.OO..............
 ..........................OOOOOO..............
 .........................O.....OOOO.O.........
 .........................O..OO..O....O........
 .......OOO...............OO.O.OOOO.O.....O....
 ..OOOOOO...................OO.......OOOO.O....
 ..O...OO...OO..OO.OO........OO.......O........
 ..O...O.......OOOO..O..OO...OO.........OO.....
 ...OO.O..OO..........O..OO.O...OO.....O.......
 ....OOOO..O....OO.O.O..O..O.......OO...O......
 ........O...O..OO.O..OO.OOO......O.....O...O..
 ..OO....OO..OOOO...O.O..O.......O.......OOOOOO
 OO.....O.OOO.O.....O.O.OO......O....O.......OO
 O..O..OOO..O.O............O....O...O........OO
 O......OO.............O...O....O..O......O..O.
 .OO.....O...OO....OOOOO.........OO..........O.
 .........OOOOO.....O..OOO..........O...OO.O...
 ...O...O.O...O..O..O....OO...O...O.O...O......
 ...O.O.O.O.....O.OO....O..O...O...O...O..O....
 ..OO.OO...OOO.OOO.O....OOOO.O.O........OO.....
 ..O..O............O..O...OOO..O......O........
 ..O....O..................OO...O..O..O.OO.....
 ...O..OOOO...............O...O....O.O...O.....
 .....O..OO...............O..OOOOO.OO..........
 .........................OO...O....O..........
 ...........................OOO...O............
 .............................O................


The tagalong inside the above spaceship is only connected by a pair of
two-bit sparks from the base ship.  But no other spaceship is known which
produces that same spark such that the tagalong can be pulled by it.

Two more spaceships found by Hartmut with another different front end are
shown below.  (The second spaceship actually uses a pair of LWSS to stabilize
the back end, but I am including it here with the other one anyway.)

[Two related period 4 spaceships (speed c/2)]
 ....O..O...............
 ..OOO....OO............
 .O......OOOO...........
 OO.OO.O.O..O...........
 .OO....O..OO.O.O.......
 ..O...O....OOO.O...OO..
 ...OOO......O..O.O.....
 .....O.......O...O...O.
 ....O..O....O..O.O....O
 ........O...O.....OOO..
 ..OO.......OOO.O.......
 .O.OO...O.O....O.......
 OO...OO..OO............
 .OO.....OO.............
 ..OOOOO................
 .....O.................


 ....O..O.................
 ..OOO....OO.......OOOO...
 .O......OOOO......O...O..
 OO.OO.O.O..O......O......
 .OO....O..OO.O.O...O...O.
 ..O...O....OOO.O.........
 ...OOO......O..O.O...OO..
 .....O.......O...OOOOO...
 ....O..O....O..O.OO..O.OO
 ........O...O......O.OOOO
 ..OO.......OOO.O......OO.
 .O.OO...O.O....O.........
 OO...OO..OO.......OOOO...
 .OO.....OO........O...O..
 ..OOOOO...........O......
 .....O.............O..O..


The following is another reasonably small spaceship found by Hartmut.
This one is interesting because each of the front two quarters of the
spaceship is the same as the "pushalong" that I had previously described
above.  Here two copies of the pushalong are stabilized by the back half
of the spaceship, instead of by a MWSS.

[Period 4 spaceship (speed c/2)]
 ................OO
 ..OOO.O........O..
 .OOOO.O...OOOO.OOO
 OO......O.O...OO..
 .O.O....O......O..
 ..OOOO....OO...OO.
 ...OOO.OO....O.OO.
 ..........OOOO.O..
 .........OO.....O.
 ......O..O.OOOO...
 .....O......O.OO..
 ..OO.OO.OOO.......
 .OO..OO....OOO....
 OO..OO...O....O...
 .OO.OOO..OO.......
 ....OO.........OO.
 ................O.


On July 10, 1992 Hartmut Holzwart found the following very important period 4
c/2 spaceship.  This spaceship is small and simple enough that it might have
been found manually or naturally.  Unlike almost all of the new spaceships,
there is hope that this spaceship can be constructed from gliders, and thus
have a spaceship gun made for it.  It has a nice set of sparks at the back.
This spaceship is symmetric but is not glide-reflective.

[Small period 4 spaceship (speed c/2)]
 ..O.......
 .OOOOO....
 OO...OO.O.
 .O.......O
 ..OO..O.O.
 ..........
 ..OO..O.O.
 .O.......O
 OO...OO.O.
 .OOOOO....
 ..O.......


The two halves of the spaceship interact in only one place in one generation,
and therefore one half of the spaceship can be supported by a standard
spaceship if that single reaction is preserved.  This is shown below.

[Half of small period 4 spaceship supported by HWSS (speed c/2)]
 ...O......
 .OO.......
 .O..OOO..O
 .O....OOO.
 ..OOO..OO.
 ..........
 ....OO....
 ..O....O..
 .O........
 .O.....O..
 .OOOOOO...


The following shows the two halves of the ship split apart with an OWSS
between them, so that the new and old ships support each other.

[Small period 4 spaceship halves and OWSS supporting each other (speed c/2)]
 ......O.......
 ....OO........
 ....O..OOO..O.
 ....O....OOO..
 .....OOO..OO..
 ..............
 ...OOOOO......
 ..OOOOOOO.....
 .OO.OOOOO.....
 ..OO..........
 ..............
 ..............
 ......O.......
 ....OO...OO.OO
 ....O..O.OO...
 ....O..OOOO...
 .....OO.O.....


Several other sizes of OWSS can also be supported by the halves of this new
spaceship.  Following is the largest OWSS that is known to be supported.

[Halves of small period 4 spaceship and large OWSS supporting each other
(speed c/2)]
 .....O.........
 ....OOOOO......
 ...OO...OO.O...
 ....O.......O..
 .....OO..O.O...
 ...............
 ..O...........O
 .O.............
 .O............O
 .OOOOOOOOOOOOO.
 ...............
 ...............
 .....O.........
 ....OOO.OOOO...
 ...OO.OO.......
 ....O.....O....
 .....OO.O......


After Hartmut found this new small spaceship, I tried looking for tagalongs
for it.  During this search, I stumbled across an almost-tagalong which
attempted to produce blinkers as puffer output, but which self-destructed.
Searching specially to make this partial result work, I found the following
two related puffers.

[Two related period 8 blinker puffers (speed c/2)]
 .............OOO.         .............OOOO.
 ............OOOOO         .............O...O
 ...........OO.OOO         .............O....
 ............OO...         ..............O..O
 .................         .................O
 .................         ...............O.O
 .........O.O.....         .............OO...
 ..O.....O..O.....         .............O..O.
 .OOOOO...O.O.....         .........O.OOO.OOO
 OO...OO.OO.......         ..O.....O..O......
 .O.......O.......         .OOOOO...O.O......
 ..OO..O..O.......         OO...OO.OO........
 ..........O......         .O.......O........
 ..OO..O..O.......         ..OO..O..O........
 .O.......O.......         ..........O.......
 OO...OO.OO.......         ..OO..O..O........
 .OOOOO...O.O.....         .O.......O........
 ..O.....O..O.....         OO...OO.OO........
 .........O.O.....         .OOOOO...O.O......
 .................         ..O.....O..O......
 .................         .........O.OOO.OOO
 ............OO...         .............O..O.
 ...........OO.OOO         .............OO...
 ............OOOOO         ...............O.O
 .............OOO.         .................O
                           ..............O..O
                           .............O....
                           .............O...O
                           .............OOOO.


These puffers produce a row of blinkers, with one blinker every 8 generations.
The puffer output is the same as Robert Wainwright's blinker puffer.  However,
unlike the previous puffer, the engine is period 4, and only the puffer
output is period 8.  The blinker puffers will be used in my next Life article.

The next and last article in this series will deal with the only known
period 5 spaceship, and with the methods for making spaceships which have
an arbitrarily large period.

That article should appear in about two weeks.
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