Spaceships in Conway's Life (Part 3b)
David I. Bell
The following shows a weaving wicktrailer tagalong that looks reminiscent
of the wicktrailer for period 2 spaceships. It can be said to have a
period of 34. The three apparently different cycles are actually the
same pattern, just in the 3 different phases.
[Period 3 spaceship with wicktrailer (speed c/3)]
..O................O.....................OO..........O...............
.O.......O.O......OO.........OOO....................OO...............
OO..O.O..O......OOOOO.......O..........OO..O......OOOOO.OOO.......O.O
....OO.OO......O......O...OO....O.....O..........O........O.O...O..O.
OO.O..OOO.....O..O..OO....OOO...O.O..OO....OOO...O.O..OO....O.O.O..OO
OOOO...OO...O..O.O...O..........O......O...OO....O.....O..OOO........
OOOO...OO...O.........OO..O......OOOOO.......O..........O............
OO.O..OOO..........................OO.........OOO....................
....OO.OO...............OO..........O................................
OO..O.O..O...........................................................
.O.......O.O.........................................................
..O..................................................................
The wicktrailer can be attached to some other spaceships if it is slightly
modified at the front. Here is a wicktrailer attached to Dean's second
long spaceship, along with another related tagalong. Compare the top
tagalong with the spaceship above to see the slight modification required.
[Period 3 spaceship with two independent tagalongs (speed c/3)]
.........O........O..................
........O.O......OO..................
........O......OOOOO.OOO.............
.OOO....O...O.O........O.O...........
.OO..O....O.O.O.O..OO....O.O.O..OO...
...OOO.OO.OO...O....O..OOO...O..O....
.O..O.O.OOO..........O.........O.O...
O....O.....O.........................
O....O.....O.........................
.O..O.O.OOO..........O...O.O.........
...OOO.OO.OO...O....O.O.OO.O.........
.OO..O....O.O.O.O..OO................
.OOO....O...O.O......OOOOOO.O.....O..
........O......OOOOO...O........O.O.O
........O.O......OO......O..O.O.O.OO.
.........O........O......O...........
..........................OO.........
Only one cycle of the wicktrailer is shown above because there is no room
for more cycles without removing the bottom tagalong. The bottom tagalong
does not appear to be extensible.
Sometimes a tagalong is not really a tagalong, but becomes a required part
of a spaceship. An example of this is shown below. Here there is a large
tagalong for the turtle spaceship, with what appears to be two copies of
the wicktrailer attached to the back of the tagalong. But if either of
these wicktrailers is removed, then the tagalong will self destruct. So
this is really a single large tagalong.
[Period 3 spaceship with a tagalong with required wicktrailers (speed c/3)]
...............................O...............
..................O...........OO...............
..O..............O..........OOOOO.OOO..........
.O.O......OO....OO..O.OO...O........O.O........
.O...OO..OOO........OO..O.O..O..OO....O.O.O..OO
.O.O...O..O.....OO.O...O...O.O...O..OOO...O..O.
...O..O..OOO....OOOO....O.........O.........O.O
OO..OOO..OOO.OO..OOO....O......................
OO..OOO..OOO.OO..OOO....O......................
...O..O..OOO....OOOO....O.........O.........O.O
.O.O...O..O.....OO.O...O...O.O...O..OOO...O..O.
.O...OO..OOO........OO..O.O..O..OO....O.O.O..OO
.O.O......OO....OO..O.OO...O........O.O........
..O..............O..........OOOOO.OOO..........
..................O...........OO...............
...............................O...............
There are many more tagalongs for Dean's two symmetrical spaceships.
Here is a small selection of them. You can see several components used
repeatedly. Also of interest is that the front and back parts of the
turtle ship appear in various widths.
[Several period 3 spaceships with tagalongs (speed c/3)]
.....................OO.....
.....................OOO.O..
...................O....OOO.
.................OOOOOOO.OO.
.OOO.......O....O........OO.
.OO..O.OO.OO....O.OO.OO.OO..
...OOO....O....O..OO..OO...O
.O..O.O...O....OOO.O.OO...O.
O....O....O..O...O..OO......
O....O....O..O...O..OO......
.O..O.O...O....OOO.O.OO...O.
...OOO....O....O..OO..OO...O
.OO..O.OO.OO....O.OO.OO.OO..
.OOO.......O....O........OO.
.................OOOOOOO.OO.
...................O....OOO.
.....................OOO.O..
.....................OO.....
.................O...........OOO...O...........
................O.O.........O.....O..O.........
................O...O.OO..OO....O.O...O........
.OOO.......O....O.O..O....OOO...O...O.....O.OO.
.OO..O.OO.OO......O..OO...OO....O.O.O..OO.O.O.O
...OOO....O....OO..OO.O..........O...O......O..
.O..O.O...O....OO..OOOO........................
O....O....O..O..O..OOOO...O....................
O....O....O..O..O..OOOO...O....................
.O..O.O...O....OO..OOOO........................
...OOO....O....OO..OO.O..........O...O......O..
.OO..O.OO.OO......O..OO...OO....O.O.O..OO.O.O.O
.OOO.......O....O.O..O....OOO...O...O.....O.OO.
................O...O.OO..OO....O.O...O........
................O.O.........O.....O..O.........
.................O...........OOO...O...........
..............................OO..O....
.................O............OO..O.OOO
................O.O..............OO....
................O...O.OO..OOOOOOO...O..
.OOO.......O....O.O..O....O..O....O....
.OO..O.OO.OO......O..OO...OOOO.OOOOO...
...OOO....O....OO..OO.O....OO.OO..OO...
.O..O.O...O....OO..OOOO....O.....OOO...
O....O....O..O..O..OOOO....O.....O.....
O....O....O..O..O..OOOO....O.....O.....
.O..O.O...O....OO..OOOO....O.....OOO...
...OOO....O....OO..OO.O....OO.OO..OO...
.OO..O.OO.OO......O..OO...OOOO.OOOOO...
.OOO.......O....O.O..O....O..O....O....
................O...O.OO..OOOOOOO...O..
................O.O..............OO....
.................O............OO..O.OOO
..............................OO..O....
..............................OO..O...........................O.........
.................O............OO..O..................OO......O.O........
................O.O..............OO.........................O........O.O
................O...O.OO..OOOOOOO......OOO.........OO..O...O..OO.O.O..O.
.OOO.......O....O.O..O....O..O....O....OO..O.OO...O......OOOOO.....O..OO
.OO..O.OO.OO......O..OO...OOOO.OOOOO.....OOOO..O.OO....OO......O........
...OOO....O....OO..OO.O....OO.OO..OO...O..O...OOO..O...OO...OO..........
.O..O.O...O....OO..OOOO....O.....OOOO.O....O..OO.........O..OO..........
O....O....O..O..O..OOOO....O.....O...OO....O..OOO.......................
O....O....O..O..O..OOOO....O.....O...OO....O..OOO.......................
.O..O.O...O....OO..OOOO....O.....OOOO.O....O..OO.........O..OO..........
...OOO....O....OO..OO.O....OO.OO..OO...O..O...OOO..O...OO...OO..........
.OO..O.OO.OO......O..OO...OOOO.OOOOO.....OOOO..O.OO....OO......O........
.OOO.......O....O.O..O....O..O....O....OO..O.OO...O......OOOOO.....O..OO
................O...O.OO..OOOOOOO......OOO.........OO..O...O..OO.O.O..O.
................O.O..............OO.........................O........O.O
.................O............OO..O..................OO......O.O........
..............................OO..O...........................O.........
.....................O..............................O...O.O.O...............
.........O..........OO..OO.........OO...O......OO.OO..OOOO.OO...............
........O.O......O.OO.O.........O.OOO..O.O.....OO.O.O.OO....O.O.............
........O......OOO.OO...O.O....O...O...O.O....O....O......OO..OO.O.......O.O
.OOO....O...O.O.O..OO.....O..O.O..OO...O.....OO..O.O......OOO..O...O....OOOO
.OO..O....O.O.O....O....OOO.O....OOO..OO.O.O..O..OO............OO.OO...OO...
...OOO.OO.OO...OO.OOO...OOO.O.....OO.....O.........O..............OO..O.O...
.O..O.O.OOO........OO.........OOO.OO.O....OO.......O.O..........O.O...O.....
O....O.....O....................O..O.O..........................O...O.O.....
O....O.....O....................O..O.O..........................O...O.O.....
.O..O.O.OOO........OO.........OOO.OO.O....OO.......O.O..........O.O...O.....
...OOO.OO.OO...OO.OOO...OOO.O.....OO.....O.........O..............OO..O.O...
.OO..O....O.O.O....O....OOO.O....OOO..OO.O.O..O..OO............OO.OO...OO...
.OOO....O...O.O.O..OO.....O..O.O..OO...O.....OO..O.O......OOO..O...O....OOOO
........O......OOO.OO...O.O....O...O...O.O....O....O......OO..OO.O.......O.O
........O.O......O.OO.O.........O.OOO..O.O.....OO.O.O.OO....O.O.............
.........O..........OO..OO.........OO...O......OO.OO..OOOO.OO...............
.....................O..............................O...O.O.O...............
Here are more period 3 spaceships found by the exhaustive search. The
first two are rather small, whereas the right one is much larger. I call
the one the left the "dart", and the middle one the "brain" because of
their appearances.
[Three more period 3 spaceships (speed c/3)]
........O. .OO........ ........O.O......................
.......O.O O..O.....OO ........O...OOO..................
......OO.. OOO...OOO.. ......OO.....OO..................
.........O O..O.OOOO.. ......OO...O......O........OO....
.....O...O .OOO...O... .........O.OO..OO.O.......OOO....
..O..O.... .O..OOO.... .....O...O......O..OO.O.O..O.....
.O.O..OOOO ...O....OO. ..O..O......O...OOOO...OO..OO...O
O..O...... ...OOOOO.O. .O.O..OOOOOO........O..O..OO..OOO
.O.O..OOOO ........... O..O..................O...OO..O..
..O..O.... ...OOOOO.O. .O.O..OOOOOO........O..O..OO..OOO
.....O...O ...O....OO. ..O..O......O...OOOO...OO..OO...O
.........O .O..OOO.... .....O...O......O..OO.O.O..O.....
......OO.. .OOO...O... .........O.OO..OO.O.......OOO....
.......O.O O..O.OOOO.. ......OO...O......O........OO....
........O. OOO...OOO.. ......OO.....OO..................
O..O.....OO ........O...OOO..................
.OO........ ........O.O......................
The large spaceship on the right is important for the following reason:
Whenever a spaceship is found which appears to be composed of components
which are only loosely interacting (as in the above spaceship), then a good
thing to try is to remove the components from the back end, and see what
happens to the spaceship. In almost all cases, the ship will be destroyed.
However, occasionally this doesn't occur, and something interesting will
happen. (The best result is that a puffer engine might be found). In the
case of the above spaceship, removing the tail component creates a period 9
spaceship, as shown below.
[Period 9 spaceship (speed c/3)]
........O.O..................
........O...OOO..............
......OO.....OO..............
......OO...O......O........OO
.........O.OO..OO.O.......OOO
.....O...O......O..OO.O.O..O.
..O..O......O...OOOO...OO..OO
.O.O..OOOOOO........O..O..OO.
O..O..................O...OO.
.O.O..OOOOOO........O..O..OO.
..O..O......O...OOOO...OO..OO
.....O...O......O..OO.O.O..O.
.........O.OO..OO.O.......OOO
......OO...O......O........OO
......OO.....OO..............
........O...OOO..............
........O.O..................
The spaceship creates a blinker at the back which unfortunately reacts with
the tail again, and gets eaten. Along with some tagalongs which have the
same tail end as this ship, this is the only method known to make a period
9 spaceship.
Following are two other small tagalongs which turn the period 9 ship back
into a period 3 spaceship. Here the rightmost 3 columns from the spaceship
above have been extracted, with the new tagalongs appended.
[Alternative small tagalongs to make the period 9 spaceship into period 3]
.......O. ........O.
......O.O .......O.O
.OO..OO.. .OO....O..
OOO...O.. OOO...O..O
.O....OO. .O....OOO.
.OO..O.O. .OO..O....
OO..OOO.. OO..OOO...
OO..O.... OO..O.....
OO..OOO.. OO..OOO...
.OO..O.O. .OO..O....
.O....OO. .O....OOO.
OOO...O.. OOO...O..O
.OO..OO.. .OO....O..
......O.O .......O.O
.......O. ........O.
The large spark in the period 9 spaceship is useful. Running a LWSS into
it can produce various debris. One of these reactions produces a loaf.
When the loaf is properly hit with other LWSSs, it can be pulled backwards.
This mechanism was found by Dean Hickerson, and is shown below.
[Period 9 spaceship turns LWSS into a loaf which is then pulled backwards]
........OO...O............................................................
.......OOO....O...........................................................
......O...OOO.............................................................
.....OO.O.OO.O...O.........O..............................................
......O.O......OOO........OO..............................................
.....OOO..O....O..OO.O.OO.O...............................................
..O.OO.O........O...OOO...O..............OO............................OO.
OO....OOOOOO....O..OO.....O.............OOOO...........OO.............OOOO
OO..................OO....O............OO.OO..........OO.OO..........OO.OO
OO....OOOOOO....O..OO.....O.............OO......O..O...OOOO...........OO..
..O.OO.O........O...OOO...O.....OOOO...........O........OO....OOOO........
.....OOO..O....O..OO.O.OO.O.....O...O..........O...O..........O...O.......
......O.O......OOO........OO....O..............OOOO...........O...........
.....OO.O.OO.O...O.........O.....O..O..........................O..O.......
......O...OOO.............................................................
.......OOO....O...........................................................
........OO...O............................................................
Dean used a reaction like the above to construct another sawtooth pattern.
In this sawtooth pattern, salvos of two LWSS are repeatedly shot at the
receding period 9 spaceship. When the first LWSS reaches the period 9
ship, it is turned into a loaf. The loaf is then pulled back by the
"tractor beam" of further LWSS reactions until it reaches the salvo gun
where the loaf is deleted. The cycle is then repeated, but with more
salvos needed since the period 9 spaceship has receded further.
Here are some tagalongs for the period 9 spaceship, most of which turn the
spaceship into period 3. Like the other spaceships, there are many of these
tagalongs and the following is only a selection.
The following shows an unusual two bit spark at the back.
[Period 3 spaceship with tagalong (speed c/3)]
........O.O............................................O........
........O...OOO...................OOO..............O.OO.O.......
......OO.....OO...................OO...O...O...OO.O.OOO.O.......
......OO...O......O........OO.......OOO.O.OO...OO.O.............
.........O.OO..OO.O.......OOO.....O..OO....O.O..OO.OOO...O......
.....O...O......O..OO.O.O..O..........OO.OO..OOOOO..O....O......
..O..O......O...OOOO...OO..OO..OOOO.O..O.........OO..OO..OOO....
.O.O..OOOOOO........O..O..OO..OOO.......OOOOOOOOO.O.O.......O...
O..O..................O...OO..O.....................OOO...OO..OO
.O.O..OOOOOO........O..O..OO..OOO.......OOOOOOOOO.O.O.......O...
..O..O......O...OOOO...OO..OO..OOOO.O..O.........OO..OO..OOO....
.....O...O......O..OO.O.O..O..........OO.OO..OOOOO..O....O......
.........O.OO..OO.O.......OOO.....O..OO....O.O..OO.OOO...O......
......OO...O......O........OO.......OOO.O.OO...OO.O.............
......OO.....OO...................OO...O...O...OO.O.OOO.O.......
........O...OOO...................OOO..............O.OO.O.......
........O.O............................................O........
The two bit spark in the above spaceship can be replaced by a small tagalong
that can be repeatedly attached to itself (in its next phase). But that
small tagalong always needs terminating with the final tagalong shown here.
[Period 3 spaceship with repeatable and terminating tagalongs (speed c/3)]
........O.O............................................O....................
........O...OOO...................OOO..............O.OO.O...................
......OO.....OO...................OO...O...O...OO.O.OOO.O...................
......OO...O......O........OO.......OOO.O.OO...OO.O.........................
.........O.OO..OO.O.......OOO.....O..OO....O.O..OO.OOO...O..............O.O.
.....O...O......O..OO.O.O..O..........OO.OO..OOOOO..O....O.......O.O....OO.O
..O..O......O...OOOO...OO..OO..OOOO.O..O.........OO..OO..OOO....OO.O...O....
.O.O..OOOOOO........O..O..OO..OOO.......OOOOOOOOO.O.O.......O..O.O....OO....
O..O..................O...OO..O.....................OOO...OO..OOO.OO..O.....
.O.O..OOOOOO........O..O..OO..OOO.......OOOOOOOOO.O.O.......O..O.O....OO....
..O..O......O...OOOO...OO..OO..OOOO.O..O.........OO..OO..OOO....OO.O...O....
.....O...O......O..OO.O.O..O..........OO.OO..OOOOO..O....O.......O.O....OO.O
.........O.OO..OO.O.......OOO.....O..OO....O.O..OO.OOO...O..............O.O.
......OO...O......O........OO.......OOO.O.OO...OO.O.........................
......OO.....OO...................OO...O...O...OO.O.OOO.O...................
........O...OOO...................OOO..............O.OO.O...................
........O.O............................................O....................
The following tagalong ends in a tail which has the same shape as the base
ship, and therefore can be repeatedly attached to itself. Because of that
special tail, this becomes a period 9 spaceship.
[Period 3 spaceship with repeatable period 9 tagalong (speed c/3)]
........O.O....................................................
........O...OOO................................................
......OO.....OO...................................O............
......OO...O......O........OO................OOO.O.O..O.......O
.........O.OO..OO.O.......OOO..........O.O.O...O..OOO.O......OO
.....O...O......O..OO.O.O..O...OO.....OOOO.OO.....OO.O.OO.OO.O.
..O..O......O...OOOO...OO..OO...O....OO......O..O.OO..O.OO...O.
.O.O..OOOOOO........O..O..OO.O....O..OO......O.O....O.OO.....O.
O..O..................O...OO.O...O..O...................O....O.
.O.O..OOOOOO........O..O..OO.O....O..OO......O.O....O.OO.....O.
..O..O......O...OOOO...OO..OO...O....OO......O..O.OO..O.OO...O.
.....O...O......O..OO.O.O..O...OO.....OOOO.OO.....OO.O.OO.OO.O.
.........O.OO..OO.O.......OOO..........O.O.O...O..OOO.O......OO
......OO...O......O........OO................OOO.O.O..O.......O
......OO.....OO...................................O............
........O...OOO................................................
........O.O....................................................
Note that this tagalong uses two previously known small tagalongs in order
to make the connection to the base ship. The connection between the second
of those tagalongs and the new one is tenuous, and is similar to several
other ships and tagalongs. But the spacing between the two points of contact
makes it difficult to connect the tagalong to them. The following is the
best that has been found. Here two turtle ships plus wicktrailers are used
to pull the tagalong.
[Alternate attachment of period 9 tagalong to period 3 spaceships (speed c/3)]
...................O................................
.................OO.................................
.OOO.......O.....OO.........O.O.....................
.OO..O.OO.OO.......O.......OOOO.....................
...OOO....O......O...O....OO........................
.O..O.O...O...O.O...OOOO..OO........................
O....O....O..O.OO...O.O..O..........................
O....O....O..O.OO...O.O..O..........................
.O..O.O...O...O.O...OOOO..OO...........O............
...OOO....O......O...O....OO......OOO.O.O..O.......O
.OO..O.OO.OO.......O.......OOOO.O...O..OOO.O......OO
.OOO.......O.....OO.........O.O.OO.....OO.O.OO.OO.O.
.................OO...............O..O.OO..O.OO...O.
...................O..............O.O....O.OO.....O.
.............................................O....O.
...................O..............O.O....O.OO.....O.
.................OO...............O..O.OO..O.OO...O.
.OOO.......O.....OO.........O.O.OO.....OO.O.OO.OO.O.
.OO..O.OO.OO.......O.......OOOO.O...O..OOO.O......OO
...OOO....O......O...O....OO......OOO.O.O..O.......O
.O..O.O...O...O.O...OOOO..OO...........O............
O....O....O..O.OO...O.O..O..........................
O....O....O..O.OO...O.O..O..........................
.O..O.O...O...O.O...OOOO..OO........................
...OOO....O......O...O....OO........................
.OO..O.OO.OO.......O.......OOOO.....................
.OOO.......O.....OO.........O.O.....................
.................OO.................................
...................O................................
The above construction can be widened by repeatedly adding another turtle
ship, wicktrailer, and tagalong in a similar manner. This gives a spaceship
with multiple period 9 sparks at the back which are closer together than can
be accomplished using multiple copies of the original period 9 spaceship.
The following shows two more tagalongs of the period 9 spaceship. (The
second one begins at the large gap near the end of the ship, and is 10
columns long.) Without the final tagalong, a single spark is produced at
the center of the back. With the final tagalong, that spark is suppressed.
The final tagalong shares a property with one of the period 2 tagalongs in
my previous article, in that cells are turned OFF by the rest of the
spaceship, instead of cells being turned ON. The final tagalong also has
a spectacular set of parallel sparks.
[Period 3 spaceship with two tagalongs (speed c/3)]
........O.O...............................................................
........O...OOO...................OOO.............OOOO..O.O.......O.......
......OO.....OO...................OO...O...O...OO...O..OO.O.OO..OO........
......OO...O......O........OO.......OOO.O.OO...OO.O.............OO..O.....
.........O.OO..OO.O.......OOO.....O..OO....O.O..OO.OOOOOOOO.........O...OO
.....O...O......O..OO.O.O..O..........OO.OO..OOOOO..O...O....O..O.O.O.O.O.
..O..O......O...OOOO...OO..OO..OOOO.O..O.........OO..OO...OO....O......OO.
.O.O..OOOOOO........O..O..OO..OOO.......OOOOOOOOO.O.O.....OO....OOOOOOO.O.
O..O..................O...OO..O.....................OOO....O............OO
.O.O..OOOOOO........O..O..OO..OOO.......OOOOOOOOO.O.O.....OO....OOOOOOO.O.
..O..O......O...OOOO...OO..OO..OOOO.O..O.........OO..OO...OO....O......OO.
.....O...O......O..OO.O.O..O..........OO.OO..OOOOO..O...O....O..O.O.O.O.O.
.........O.OO..OO.O.......OOO.....O..OO....O.O..OO.OOOOOOOO.........O...OO
......OO...O......O........OO.......OOO.O.OO...OO.O.............OO..O.....
......OO.....OO...................OO...O...O...OO...O..OO.O.OO..OO........
........O...OOO...................OOO.............OOOO..O.O.......O.......
........O.O...............................................................
Finally I shall give a few results from the search that are really large
spaceships on their own. This is because they were found from a slightly
modified period 9 spaceship.
The following spaceship has an interesting "square" shaped component near
the back with a cavity in the back. This cavity must be filled with something
or the ship will not work. In this case, it is filled with a copy of the
dart spaceship. This is an example of a "pushalong" instead of a tagalong.
That is, an object that has to have a following spaceship instead of a
leading spaceship. The following spaceship's purpose here is simply to
prevent some cells from being turned ON.
[Large period 3 spaceship with embedded "dart" spaceship (speed c/3)]
........O.O.............................................
........O...OOO.....................O..OO..O.O.O......O.
......OO.....OO..........OOO......OO...OO..O.OOOO....O.O
......OO...O......O......OO.......OO......OO...OO...O..O
.........O.OO..OO.O........O..O.....OOOOOO...........O..
.....O...O......O..OO.O.OO.O...O..O....O...O........OOOO
..O..O......O...OOOO...OO..OOO.....OO...OOOO.....O.OO.O.
.O.O..OOOOOO........O..O..OOO.OOO..O.......O...OO....OOO
O..O..................O...OO......O........O...OO.......
.O.O..OOOOOO........O..O..OOO.OOO..O.......O...OO....OOO
..O..O......O...OOOO...OO..OOO.....OO...OOOO.....O.OO.O.
.....O...O......O..OO.O.OO.O...O..O....O...O........OOOO
.........O.OO..OO.O........O..O.....OOOOOO...........O..
......OO...O......O......OO.......OO......OO...OO...O..O
......OO.....OO..........OOO......OO...OO..O.OOOO....O.O
........O...OOO.....................O..OO..O.O.O......O.
........O.O.............................................
The following shows the void in the square component being filled with a
non-spaceship, and reacting with it more substantially. This ends in the
period 9 tail.
[Very large period 9 spaceship (speed c/3)]
........O.O...........................................................
........O...OOO.....................O..OO..O.O........................
......OO.....OO..........OOO......OO...OO..O.OOOO.....O...OOO.........
......OO...O......O......OO.......OO......OO.........OO...OOO........O
.........O.OO..OO.O........O..O.....OOOOOO......O..OO.......OO......OO
.....O...O......O..OO.O.OO.O...O..O....O...O....O..OOO....O..OOO.OO.O.
..O..O......O...OOOO...OO..OOO.....OO...OOOO...O..O...OOO......OO...O.
.O.O..OOOOOO........O..O..OOO.OOO..O.......O..OOO..OOO....OO.OO.....O.
O..O..................O...OO......O........O..O...............OO....O.
.O.O..OOOOOO........O..O..OOO.OOO..O.......O..OOO..OOO....OO.OO.....O.
..O..O......O...OOOO...OO..OOO.....OO...OOOO...O..O...OOO......OO...O.
.....O...O......O..OO.O.OO.O...O..O....O...O....O..OOO....O..OOO.OO.O.
.........O.OO..OO.O........O..O.....OOOOOO......O..OO.......OO......OO
......OO...O......O......OO.......OO......OO.........OO...OOO........O
......OO.....OO..........OOO......OO...OO..O.OOOO.....O...OOO.........
........O...OOO.....................O..OO..O.O........................
........O.O...........................................................
The following shows yet another way to fill the void. This ends in the
same two bit spark that was found in one of the previously shown ships.
[Period 3 spaceship (speed c/3)]
........O.O.....................................................OO......
........O...OOO.....................O..OO..O.O.O.............O....O.....
......OO.....OO..........OOO......OO...OO..O.OOOO........OO.O.O.O.......
......OO...O......O......OO.......OO......OO...OO.......O...O...O.......
.........O.OO..OO.O........O..O.....OOOOOO.............O.....OOO........
.....O...O......O..OO.O.OO.O...O..O....O...O..........OOOO......O.OO....
..O..O......O...OOOO...OO..OOO.....OO...OOOO...O.....O......O.OO...OOO..
.O.O..OOOOOO........O..O..OOO.OOO..O.......O..O.O..O.OOOOOO.O.O....O..O.
O..O..................O...OO......O........O..O...OO..........O......OOO
.O.O..OOOOOO........O..O..OOO.OOO..O.......O..O.O..O.OOOOOO.O.O....O..O.
..O..O......O...OOOO...OO..OOO.....OO...OOOO...O.....O......O.OO...OOO..
.....O...O......O..OO.O.OO.O...O..O....O...O..........OOOO......O.OO....
.........O.OO..OO.O........O..O.....OOOOOO.............O.....OOO........
......OO...O......O......OO.......OO......OO...OO.......O...O...O.......
......OO.....OO..........OOO......OO...OO..O.OOOO........OO.O.O.O.......
........O...OOO.....................O..OO..O.O.O.............O....O.....
........O.O.....................................................OO......
Finally, here is a slightly different spaceship with a tagalong. Without
the tagalong, the same two bit spark is produced as in the previous ship.
This tagalong has yet another size of a back end similar to the turtle
spaceship.
[Period 3 spaceship with tagalong (speed c/3)]
........O.O...................................O..................O.........
........O...OOO...........................O.OO..................O.O.....O.O
......OO.....OO..........OOO..........O.OO..O.O.................OO......O..
......OO...O......O......OO..........OO.OO...O............OO....O...O.OO...
.........O.OO..OO.O........O..O....O..O...OOOOO..........O.O.....OOO..OO...
.....O...O......O..OO.O.OO.O...O...OOO.......O.OO.......OO.OO...O....OO.O..
..O..O......O...OOOO...OO..OOO.........OO..OO.....O.....OOO.OO....OOOOO.O.O
.O.O..OOOOOO........O..O..OOO.OOOOOOOOO.O..O....O....O..OO..O.OOO...O......
O..O..................O...OO...............OO....OO..OO...........OOO......
.O.O..OOOOOO........O..O..OOO.OOOOOOOOO.O..O....O....O..OO..O.OOO...O......
..O..O......O...OOOO...OO..OOO.........OO..OO.....O.....OOO.OO....OOOOO.O.O
.....O...O......O..OO.O.OO.O...O...OOO.......O.OO.......OO.OO...O....OO.O..
.........O.OO..OO.O........O..O....O..O...OOOOO..........O.O.....OOO..OO...
......OO...O......O......OO..........OO.OO...O............OO....O...O.OO...
......OO.....OO..........OOO..........O.OO..O.O.................OO......O..
........O...OOO...........................O.OO..................O.O.....O.O
........O.O...................................O..................O.........
No method has been found to make a puffer train from period 3 spaceships.
But the next best thing is something which I call a pseudo-puffer. A
pseudo-puffer creates debris from a period 3 spaceship, but not by itself.
It must be "fed" some input in the form of a c/2 spaceship stream. It can
then turn that input into debris which can be manipulated by sparks from
other period 3 spaceships.
The following is a pseudo-rake. (A rake is a puffer which produces a wave
of gliders). In this construction, the reaction that converts a glider
into a LWSS was found by Bill Gosper, and the reaction that converts 3
gliders into a LWSS was found by David Buckingham.
This picture is compressed to prevent lines which are too long. Here each
dollar sign should be replaced by 10 periods to reconstruct the full picture.
[Pseudo-rake producing gliders from spaceship stream (speed c/3)]
$$$$$$$$$$$.....O.O..OO$$
$$$$$$$$$$$....O...O.OOO....OO$...
......O$$$$$$$$$$........O......OO...OO$...
....OO$$$$$$$$..O...OO$$..OOOOO.O$.........
....OO$$$$$$$....OO....OO.O.OOO$$.....OOO$$
......O$$$$$$$...OO....O....OOO$$$$........
....O$$$$$$$$.O...O$$........OOO$$
....O.O$$$$$$$$OOO$$......OOOOO.O$.....OO..
....O.O$$$$$$$$$$........O......OO$....OO..
.....O$$$$$$$$.OOO$$....O...O.OOO$.........
...OO$$$.....OO$$$$....O...O$$....O.O..OO$$
....O$$.....OO.......O.O$$$........OO....O....OOO$.....O$$$..
....OOO$$...OO......OO.O$$$........OO....OO.O.OOO$......OO$$$
.....O$$$...OO$$......OO$.........O...OO$.....OO$$$.
.......O$$$..O$$......O.O.......OO$$$$$$...
.....OO$$$$$$..O.......OO$$$$$$...
.....OO$$$...O$$......OOO$$$$$$$..
$$$.........OO$$$$$$$$$$.
..OOO$$.....OO......OO.O$$$$$$$$$$
..OO..OO$$..OO.......O.O$$$$$$$$$$
....O$$$.....OO.......O.O$.....OOO$$$$$$$..
...OO$$$$....OO$........O.......OO$$$$$..OO.....OO..
...OO$$$$.....O$......O.O.......OO$$$$$.O..O...O..O.
...O..O$$$$$$OO$$$$$.O.O$OO.OO....
.......O$$$$$$$$$$$...OO.........O.O.O.O...
....OOOOO$$$$$$$$$$$..O$O.O.O.O...
........OO$$$$$$$$$$$$O.........O.
........OO$$$$$$$$.O..O$$$....O$.O
.....OOOO$$$$$........OOOO$.........O$$..OOOO$$.....
....O...O$$$$$........O...O$........O...O$........O...O$.....OO.OO....
....OOO$$$$$$O$$..OOOO$.........O$.......O..O.O..O..
....O..O$$$$$$O..O$$$$..O..O$...OOO...OOO..
.....O$$$$$$$$$$$$$......
.....O.O$$$$$$$$$$$$$....
......O$$$$......OOO$$$$$$$$..OO..
$$$$$...O$$$$$$$$....OO..
$$$$$....O$$$$$$$$.......
$$$$$$$$$$$$$$..
$$$.........OOO$$$$$$$$$$
$$$$.O$$$$$$$$$$
$$$$O$$$$$$$$$$.
$$$$$$$$$$$$$$..
$$$$$$$$$$$$$$..
$$$$$$$$$$$$$$..
$$$$$$$$$$$$$$..
$$$$$$.....OO$$$$$$$.....
$$$$$$.....O.O$$$$$$$....
$$$$$$.....O$........OO$$$$$......
$OO$$$$$$$.O$$$$$........
OO.......O.O$......OO$$$$$..O..OO$OO$$$$...
OO......OO.O$.....O.O$$$....O$.......O..O$.OO$$$$...
.........OO$........O.......OO$$...O..O$......O.O$$$$$.......
$O$$.....OO.OO......OO.OO$OOOOO$......OO$$$$$.......
$$$.......O..O......OO.OO$OOO.OO$$$$$$$....
$O$$......O..O$$..OO.O$......OO$$$$$.......
.........OO$$.......OO$$....OO$......O.O$$$$$.......
OO......OO.O$$$$$$$O..O$.OO$$$$...
OO.......O.O$$......OO$$....OO$......O..OO$OO$$$$...
$OO$$.....O..O$$..OO.O$......O$$$$$........
$$$.......O..O......OO.OO$OOO.OO$......OO$$$$$......
$$$......OO.OO......OO.OO$OOOOO$$$$$$$.....
$$$.......OO$$...O..O$$$$$$$......
$$$$$$....O$$$$$$$.......
Gliders from several of these pseudo-rakes can be collided to produce some
desired puffer output. In addition, a glider or the result of a collision
can be perturbed by using some of the period 3 spaceships. For example,
the following shows the brain spaceship perturbing a glider to produce a
honey farm. This can be added to the pseudo-rake above to form a row of
honey farms.
[Period 3 spaceship perturbing a glider to make a honey farm]
.............O.
............O..
............OOO
...............
...............
..OO...........
.O..O.....OO...
.OOO...OOO.....
.O..O.OOOO.....
..OOO...O......
..O..OOO.......
....O....OO....
....OOOOO.O....
...............
....OOOOO.O....
....O....OO....
..O..OOO.......
..OOO...O......
.O..O.OOOO.....
.OOO...OOO.....
.O..O.....OO...
..OO...........
No period 3 spaceship with really good accessible sparks has been found.
For perturbing purposes, such sparks should be on the edge of the spaceship
so that debris can be perturbed as the spaceship passes by. But it appears
that period 3 isn't large enough for such sparks to be far enough away from
the ship to be useful for many things. Most perturbations end up destroying
the spaceship. Compare this with the MWSS and HWSS, which are much more
effective at perturbing things successfully.
The next article in this series will deal with two classes of the period 4
spaceships, in particular the c/4 orthogonal and diagonal period 4 spaceships.
That article should appear in about two weeks.