Day & Night - An Interesting Variant of Life (part 5/5)

[David Bell]

PUFFER TRAINS
-------------

Puffer trains are easy to create in Day & Night. Because the diamond-like
engine at the front of the rocket and other small spaceships is so vigorous,
the back of those ships can be modified in many cases without destroying
the engine. Alternatively, several of the engines can be placed adjacent
to each other so that their outputs merge. In both of these cases, puffers
can result.

An example of the ease of creating puffers was shown earlier for the
"mothership". A slight modification of that ship will produce a
wickstretcher, which is a puffer whose output is a connected object which
grows longer. A simple case of the same spaceship which produces a stable
wick is shown below.

...O.................
.OOOO.OO.O...OOO..OO.
O.OO..OOOOO.OOOOOOOO.
OOO...OOOOOOOOOOOOOOO
OO..O..OOOOOOOOOOOOOO
...O..OOOOOOOOOOOOOO.
OO..O..OOOOOOOOOOOOOO
OOO...OOOOOOOOOOOOOOO
O.OO..OOOOO.OOOOOOOO.
.OOOO.OO.O...OOO..OO.
...O.................

[Figure 89. A period 8 wickstretcher with a stable wick]

The following object can be made arbitrarily wide by adding more engines
at the front, and produces a very wide trail of ON cells. For interest,
an inverted rocket is embedded inside the puffer.

....OO.OO..............................
...OOOOOO......O.............O.OOOO....
..O.OOOO.O...OOOOO.....O...OO.O....O...
.OOOOOOOO..OOOOOOO...OOOO...OOOOOOOOOO.
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
.OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
...O.OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
.....OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
......OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
.....OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
...O.OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
..OOOOOOOOOOOOOO..OOOOOOOOOOOOOOOOOOOO.
.OOOOOOOOOOOOOO.O..OOOOOOOOOOOOOOOOOOO.
OOOOOOOOOOOOOOO........OOOOOOOOOOOOOOOO
.OOOOOOOOOOOOOO.O..OOOOOOOOOOOOOOOOOOO.
..OOOOOOOOOOOOOO..OOOOOOOOOOOOOOOOOOOO.
...O.OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
.....OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
......OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
.....OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
...O.OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
.OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
.OOOOOOOO..OOOOOOO...OOOO...OOOOOOOOOO.
..O.OOOO.O...OOOOO.....O...OO.O....O...
...OOOOOO......O.............O.OOOO....
....OO.OO..............................

[Figure 90. A wide wickstretcher with an embedded rocket]

Wickstretchers generate lots of output, but they are not very useful.
Better puffers would create individual objects which could be used
to create other things. Fortunately, such puffers exist.

Perhaps the simplest puffer known is the following period 20 puffer
based on the period 20 spaceship, which creates blocks. It was found
by Mark D. Niemiec.

....OO.OO...........
...OOOOOO......O....
..O.OOOO.O...OOOOO..
.OOOOOOOO..OOOOOOO.O
OOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOO
.OOOOOOOO..OOOOOOO.O
..O.OOOO.O...OOOOO..
...OOOOOO......O....
....OO.OO...........

[Figure 91. A period 20 block puffer (MN)]

Puffers can also be created by perturbing the tail of a rocket with the
sides of other rockets or the period 20 spaceships. It turns out that
the sides of these spaceships can interact with other objects without
necessarily destroying the ship. The following shows a period 40 puffer
which produces eaters.

...........................................O..............
..........................................O.O.OO..........
........................................O.OOOOOO......O...
.......................................OOOOOOOO.O...OOOOOO
......................................OOOOOOOOOO..OOOOOO.O
.....................................OOOOOOOOOOOOOOOOOOOO.
.....................................OOOOOOOOOOOOOOOOOOOO.
......................................OOOOOOOOOO..OOOOOO.O
.......................................OOOOOOOO.O...OOOOOO
........................................O.OOOOOO......O...
..........................................O.O.OO..........
.....OOOO..................................O..............
....OOOO..OO..............................................
..OOOOOOOOO.O..................OO.........................
.O.OOOOOOOOO....OO.OOO...OOO.OOOOOO.......................
O.OOOOOOOOOO..OOOOOOOO....OOOOOOOOO...........O...........
OOOOOOOOOOOOOOOOOOOOO..OOOOOOOOOOO...........OOO..........
O.OOOOOOOOOO..OOOOOOOO....OOOOOOOOO...........O...........
.O.OOOOOOOOO....OO.OOO...OOO.OOOOOO.......................
..OOOOOOOOO.O..................OO.........................
....OOOO..OO..............................................
.....OOOO..................................O..............
..........................................O.O.OO..........
........................................O.OOOOOO......O...
.......................................OOOOOOOO.O...OOOOOO
......................................OOOOOOOOOO..OOOOOO.O
.....................................OOOOOOOOOOOOOOOOOOOO.
.....................................OOOOOOOOOOOOOOOOOOOO.
......................................OOOOOOOOOO..OOOOOO.O
.......................................OOOOOOOO.O...OOOOOO
........................................O.OOOOOO......O...
..........................................O.O.OO..........
...........................................O..............

[Figure 92. A period 40 puffer which produces eaters]

As another example of a spaceship perturbing the tail of a rocket,
here is a period 40 puffer which produces period 16 oscillators.
In this case, the perturbation by the rocket-like spaceship keeps
the perturbing spaceship from ever recovering its normal shape.
If the front rocket was removed, the unsymmetrical spaceship would
eventually revert back to a normal rocket.

...............................................OO...............
................................................O...............
............................................O...O...OO..........
...........................................OO.OOOOOOOO........O.
..........................................OOOOOOOOOOO.O...OO.OO.
.........................................OOOOOOOOOOOOO..OOOOOOOO
........................................OOOOOOOOOOOOOOOOOOOOO.O.
.........................................OOOOOOOOOOOOOOOOOOOOOO.
..........................................OOOOOOOOOOOOOOOOO.O...
...........................................OO.OOOOOOOOO.OO.OO...
............................................O...O...OO.O........
................................................O...............
...............................................OO...............
................................................................
.....O..........................................................
....O.O.OO...........................OO................OO.......
....OOOOOO......O.......O.....O.O....O.................OO.......
..O.OOOOO.O...OOOOOO...OO......O.OO..O.OO...............O.......
.OOOOOOOOO..OOOOOOO...OOOO..O.O.O.O...OOO.......................
OOOOOOOOOOOOOOOOOOO...OO.....OO.OOOO.OOOOO......................
.OOOOOOOOO..OOOOOOO...OOOO..O.O.O.O...OOO.......................
..O.OOOOO.O...OOOOOO...OO......O.OO..O.OO.......................
....OOOOOO......O.......O.....O.O....O..........................
....O.O.OO...........................OO.........................
.....O..........................................................

[Figure 93. A period 40 puffer which produces period 16 oscillators]

In the above, a rocket is deformed by each impact, but will revert to a
normal rocket again if the series of impacts ceases. But it is possible
for a rocket to be permanently changed from a single impact. In the
following reaction in which a rocket impacts into a period 16 oscillator,
the rocket is changed into a puffer which (after settling down after about
500 generations) generates four of the period 16 oscillators every 260
generations. It whips back and forth while it does so, and so is called
the "sidewinder". The reaction shown here is crucial to the creation of
breeders in Day & Night.

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

[Figure 94. A rocket hits a p16 oscillator to form the
period 260 "sidewinder" puffer]

A related puffer based on the period 20 spaceship produces more varied
output with the much larger period of 1100.

.....O.............................
....O.O.OO....................O....
....OOOOOO......O.........OO.O.O...
..O.OOOOO.O...OOOOOO....OOOOOOOO.O.
.OOOOOOOOO..OOOOOOO...OOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.O
.OOOOOOOOOOOOOO..OOOOOOOOOO.OOOOO.O
..O..OOOOOOOOO.O...OOOOOOOO..O.O...
...O.O.OOOOOOOO......OO.OO.........
.....O....OO.OO..........O.........
..........O........................

[Figure 95. A period 1100 puffer related to the sidewinder]

Allan Wechsler found another puffer similar to the one in figure 94, but it
produces a different set of junk and has the even larger period of 1240.
This puffer is also unusual in that it appeared naturally from a blob.
This is the only example known of a spaceship or puffer with two central
rows appearing naturally.

......OO.....................
.....OOOO.OO.................
...O.OOOOOOO......O...OO.....
..OOOOOOOOO.O...OOOO.OO.O....
.OOOOOOOOOOO..OOOOOO.OOOOOO..
OOOOOOOOOOOOOOOOOOOOOOOOOOO..
OOOOOOOOOOOOOOOOOOOOOOOOOOO..
.OOOOOOOOOOOOOOO..OOOOOOOOO.O
..OO.OOOOOOOOOO.O...OOOOOOO..
....OO..OO...OOO......OO.OO..
.......O..O...OO.............

[Figure 96. A period 1240 puffer related to the sidewinder (AW)]

The interaction of a sidewinder with a rocket results in a period 240
puffer which produces eaters.

.........................OOOO........O.OO...
........................OOOO..OO......O.....
......................OOOOOOOOO.O...O.OOO.O.
.....................O.OOOOOOOOO.....OOOOO..
....................O.OOOOOOOOOO..O..OOOOOO.
....................OOOOOOOOOOOOOOOOOOOOOOOO
....................O.OOOOOOO.OOOOOOOOOOO.O.
.....................O.OOOO..O.OOOOOOOOO..O.
......................OOOO.O.....OOOOOOOO...
.........................OO.........OO......
............................................
............................................
............................................
................O...................O.......
.....OO.........O..................OO.......
..OOOO.O.....OOO.O.......O........O.OO......
.O.OOOO..O.OOOOOO....OO...OO..OO...OOO.O....
O.OOOOOOO.OOOOOOO..OOOOO.OO.OO..O..OOOOO....
OOOOOOOOOOOOOOOOOOOOOOOOOOO.OOOO..OOOOO.....
O.OOOOOOO.OOOOOOO..OOOOO.OO.OO..O..OOOOO....
.O.OOOO..O.OOOOOO....OO...OO..OO...OOO.O....
..OOOO.O.....OOO.O.......O........O.OO......
.....OO.........O..................OO.......
................O...................O.......

[Figure 97. A period 240 puffer which creates eaters]

In the puffers shown so far, only miscellaneous output has been produced.
What is most useful from puffers is to produce spaceships, since then
the spaceships can be collided together to create many other objects.
It is also most useful to produce spaceships which are emitted at right
angles from the path of the puffer since only in this way can multiple
spaceships interact. Fortunately, ways to produce such puffers are known.
Puffers which produce spaceships are called "rakes".

The basic method to produce a rake is to find a blob which grows out so
that it can be perturbed by the spark at the back of a rocket after the
spark has turned symmetrical. The blob itself doesn't start off with any
symmetry. The blob reacts with the spark to form another blob which grows
across the path of the receding rocket. At that point, the blob might
still be unsymmetrical, and would still just die out or turn into junk.
But before then, it is perturbed by the symmetrical spark from another
passing rocket. This creates yet another blob which crosses the path
of that receding rocket. This process continues as long as is necessary.
Eventually, the blob breaks apart and the front part becomes symmetrical
since the original asymmetry doesn't keep up with the influence of the
symmetrical sparks. Once the blob becomes symmetrical, then further sparks
from more rockets keep perturbing it until something useful such as a
spaceship appears. Then the whole convoy of rockets converts the original
blob into that useful object.

Because of the numerous possibilities of perturbations by rockets, almost
any blob which has a point even vaguely like a spaceship (i.e., one cell
adjacent to three cells) can be transformed into a spaceship by using
enough rockets. Once the first one or two rocket perturbations succeed,
the number of possibilities explodes so that some combination of rockets
is almost sure to work.

As an example of the process, the following shows an unsymmetrical blob
being converted into a sideways rocket by the perturbations of four
passing rockets. This reaction is used in the period 120 sideways rocket
rake shown later.

.........................................O..............................
.........................................O..OOO.O.......................
..........................................OOOOOOOO......................
........................................OOOOOOOO.O......................
......................................OOOOOOOOOOO.......................
.......................................O.OOOOOOOO.......................
........................................O..OOOOOOO......................
...........................................O.OOOOOO.....................
............................................OOOOOO......................
...........................................OOOOOO.......................
..........................................OOOOOOOO......................
...........................................OOOOOOO......................
..........................................OOOOOOO.......................
...........................................OOOOOO.......................
............................................OOO.........................
.............................................O..........................
........................................................................
........................................................................
....OO.OO....................................O..........................
...OOOOOO......O............OO..............OOO.........................
..O.OOOO.O...OOOOO.....OO.OOOOOO.............O..........................
.OOOOOOOO..OOOOOOO...OOOOOOOOOOO.............O..........................
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.........................................
.OOOOOOOO..OOOOOOO...OOOOOOOOOOO.............O..........................
..O.OOOO.O...OOOOO.....OO.OOOOOO.............O..........................
...OOOOOO......O............OO..............OOO.........................
....OO.OO....................................O..........................
........................................................................
........................................................................
........................................................................
........................................................................
...............................................O........................
..............OO.OO............................O........................
.............OOOOOO......O.......OOO..OO.O....OO..O.....................
............O.OOOO.O...OOOOO......O.....O.O...O.OOO.....................
...........OOOOOOOO..OOOOOOO...OOOO...O..OO....OOOOO....................
..........OOOOOOOOOOOOOOOOOOOOOOOOO.O..O.O..OOOOOOO.....................
...........OOOOOOOO..OOOOOOO...OOOO...O..OO....OOOOO....................
............O.OOOO.O...OOOOO......O.....O.O...O.OOO.....................
.............OOOOOO......O.......OOO..OO.O....OO..O.....................
..............OO.OO............................O........................
...............................................O........................
........................................................................
........................................................................
........................................................................
........................................................................
........................................................................
.........................O.OO.......O.OO.........................O......
........................OOOOO......O............OO...............OO.....
.......................OOOOOO....OOOOO.O...OO.OOOOOO...........O.O.O....
......................OOOOOOOO.OOOOOOOO..OOOOOOOOOOO..............O.....
.....................OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO..........OOOO.O.O...
......................OOOOOOOO.OOOOOOOO..OOOOOOOOOOO..............O.....
.......................OOOOOO....OOOOO.O...OO.OOOOOO...........O.O.O....
........................OOOOO......O............OO...............OO.....
.........................O.OO.......O.OO.........................O......
........................................................................
........................................................................
........................................................................
........................................................................
........................................................................
........................................................................
........................................................................
..........................................OO............................
...........................................O............................
.......................................O...O...OO.......................
......................................OO.OOOOOOOO........OO.........OO..
.....................................OOOOOOOOOOO.O...OO.OOO.......OOOOOO
....................................OOOOOOOOOOOOO..OOOOOOOO..OOO.OOOOOOO
...................................OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.
....................................OOOOOOOOOOOOO..OOOOOOOO..OOO.OOOOOOO
.....................................OOOOOOOOOOO.O...OO.OOO.......OOOOOO
......................................OO.OOOOOOOO........OO.........OO..
.......................................O...O...OO.......................
...........................................O............................
..........................................OO............................

[Figure 98. Four passing rockets turn a "blob" into a sideways rocket]

Now the trick of producing rakes depends on finding blobs which can be
perturbed by the first passing rocket. This turns out to be a slightly
difficult problem. Either the output from puffers lies near to the line
containing the puffer itself thus leaving no room for the perturbing
rocket, or else a lot of junk besides the blob is also produced which
cannot be cleaned up to form a clean rake. Only a few solutions to the
problem have been found.

One such blob producing puffer is shown below, which has a period of 120.
The blob barely sticks out far enough, and an extra period 16 oscillator
is produced. But this is good enough, since the blob CAN be reached,
and the period 16 oscillator CAN be deleted.

.....................................O...................................
..............................O.O.O....OO.........O......................
...............................OOO.OOOOO.O........O.........OO...........
...........................OO.O.OOOOOOOOO....OO..O.O..O....OOOOO.........
..........................O.OOOOOOOOOOOOO..OOOOOOOO..O.O..OOOOOO.........
..........................OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO..........
..........................O.OOOOOOOOOOOOO..OOOOOOOO..O.O..OOOOOO.........
...........................OO.O.OOOOOOOOO....OO..O.O..O....OOOOO.........
...............................OOO.OOOOO.O........O.........OO...........
..............................O.O.O....OO.........O......................
.....................................O...................................
.........................................................................
.............................................OOOO......................O.
............................................OOOO..OO...................OO
..........................................OOOOOOOOO.O.....O.........OOOO.
.........................................O.OOOOOOOOO....OOOOO.........OOO
........................................O.OOOOOOOOOO..OOOOOO......OOO.OOO
........................................OOOOOOOOOOOOOOOOOOOOOO...OO..OOOO
........................................O.OOOOOOOOOO..OOOOOOO.O..OOO.O.O.
.........................................O.OOOOOOOOO....OOOOOO....OOOO...
..........................................OOOOOOOOO.O......O.O...........
............................................OOOO..OO......OOO......O.....
.............................................OOOO........................
.........................................................................
...............O.........................................................
.....O.........OO........................................................
...OOOO....O.OOOO.........OO...............O.............................
..OOOOOO...O.OOO.O...OO.OOOOOO............OOO............................
.OOOOOOOOOOOOOOOO..OOOOOOOOOOO..........OOOOO............................
OOOOOOOOOOOOOOOOOOOOOOOOOOOOO..........O.OOOO............................
.OOOOOOOOOOOOOOOO..OOOOOOOOOOO..........OOOOO............................
..OOOOOO...O.OOO.O...OO.OOOOOO............OOO............................
...OOOO....O.OOOO.........OO...............O.............................
.....O.........OO........................................................
...............O.........................................................

[Figure 99. A period 120 puffer which is the basis of many period 120 rakes]

Combining the above two results results in a complete period 120 sideways
rocket rake made up of eight spaceships.

x = 219, y = 119, rule = B3678/S34678
32boo$33bo$29bo3bo3boo$28boob8o8boo9boo14b3o$27b11obo3boob3o7b6o$26b
13obb8obb3ob7o12bobo$25b36o125boboo7boboo$26b13obb8obb3ob7o12bobo108b
5o6bo7bobo$27b11obo3boob3o7b6o122b6o4b5obo7bo$28boob8o8boo9boo14b3o77b
obobboo22b8ob8obb5obo$29bo3bo3boo51bobbobo56b3ob4obo20b25obo$33bo51boo
b7obo59b5o21b25obo$32boo51bob9obo58b4o23b8ob8obb5obo$45bo38bob11o58b4o
25b6o4b5obo7bo$44boboboo16b3o17b10o60b3o26b5o6bo7bobo$42bob6o6bo9bobo
14b13o62b5o23boboo7boboo$41b8obo3b6o3bobboo16b11o61boobbo$40b10obb7obb
7o17b11o61bo$39b13ob16o11bobob3obb5obo56bo$40b10obbobb12obo10boo3b3o5b
3o46bo7bobob4o$41b8obo3b3ob9o13bob3o7b3o45b3o10b3oboo$42bob6o6bobbobb
5o13boobbo55bo7bobbobbob3o$44boboboo13boobbo14boo$45bo21bo83bob5o$153b
4o$11bo142b4o$4bobobo4boo77b3oboo35b3o$5b3ob5obo8boo16bo49b5obo5bobo
10boo13b5o$boobob9o4boob6o14bo46b9o4b5o5boob6o12bobo$ob13obb11o10bobbo
bo44bob8obb7o3b11o13bo$27o12b4o45b18obobob9o$ob13obb11o10bobbobo44bob
8obb7o3b11o13bo$boobob9o4boob6o14bo46b9o4b5o5boob6o12bobo$5b3ob5obo8b
oo16bo49b5obo5bobo10boo13b5o$4bobobo4boo77b3oboo35b3o$11bo141bo$154bo$
153b3o$153b3o$$102b3oboo$102b5obo5bobo4bo7bobobboobo$99b9o4b5o3bo6b3ob
o5boo13boobo$98bob8obb7o3boo6boboobbob3o15boo$98b18oboboboo3bob6ob5o
14b3o$98bob8obb7o3boo6boboobbob3o14boo$99b9o4b5o3bo6b3obo5boo15bo$102b
5obo5bobo4bo7bobobboobo16bo$102b3oboo45b3o$151b7o$152b5o$152bobobo$
153b3o3$112b3oboo35b3o$112b5obo5bo12boo14b3o$110b8o4b5o5boob6o13bo$
109bob7obb7obob11o$109b19ob11o$109bob7obb7obob11o$110b8o4b5o5boob6o13b
o$112b5obo5bo12boo14b3o$112b3oboo35b3o9$134bo$127bobobo4boo9bo$128b3ob
5obo8bo9boo$124boobob9o4boobbobobbo4b5o$123bob13obb8obbobobb6o$123b37o
$123bob13obb8obbobobb6o$124boobob9o4boobbobobbo4b5o$128b3ob5obo8bo9boo
$127bobobo4boo9bo$134bo10$211booboboo$211b7o$210b9o$211b7o$211b7o$212b
5o$212b5o$213b3o$213b3o$214bo$212bobobo$210boob3oboo$210b9o$211b7o$
212b5o$212b5o$210bob5obo$211b7o$211b7o$210bob5obo$212b5o$211b7o$211bob
3obo$212b5o$212b5o$213b3o$214bo!

[Figure 100. A period 120 sideways rocket rake]

A different perturbation of the blob results in the following period 120
sideways p32 spaceship rake.

x = 253, y = 138, rule = B3678/S34678
40bo$30bo9boo$28b4o4bob4o9boo15bo$27b6o3bob3obo3boob6o12b3o$26b16obb
11o10b5o118bo$25b29o10bob4o117boboboo$26b16obb11o10b5o60bo54bob6o6bo$
27b6o3bob3obo3boob6o12b3o57boo55b8obo3b6o$28b4o4bob4o9boo15bo57bobb4o
50b10obb6obo$30bo9boo81b9o50b20o$40bo80bobb8o50b20o$46boo73bob8o52b10o
bb6obo$47bo73b3ob7o52b8obo3b6o$43bo3bo3boo6b3o3boo55boob6o54bob6o6bo$
42boob8o7boobb4obo55b5o57boboboo$41b11obo3b4obobobob3o4b3o47b6o57bo$
40b13obb7obboobb3o3b4o47b3oboo$39b23obbobb3o4b6o47b4obo41bo$40b24o4b3o
bob4obo32b3o14b3o41boo$41b23obb3obobbobooboo33boo58b3o$42boob9obb4ob8o
b3obo38bo$43bo3bo3boobob4obboobbobboboo3bo$47bo8b3obob3obboo$46boo8boo
bobb3o29boo$37bo20boobobo30boo$3booboo27boo55bob3obboo$bbob3obo5bo3bo
4boobobbo5bob3o50boobb6obo8boo12bo$bob5o4b5o5b3obooboo5b4o49bob10o4boo
b6o9bo3bo$ob6obb8obb5o4b3obobb5o47bob11obb11o10b5o$25o3booboobb5o48b
25o7b9o$ob6obb8obb5o4b3obobb5o47bob11obb11o10b5o$bob5o4b5o5b3obooboo5b
4o49bob10o4boob6o9bo3bo$bbob3obo5bo3bo4boobobbo5bob3o50boobb6obo8boo
12bo65bo$3booboo27boo55bob3obboo88boo$37bo56boo93bo$94boo93bo4$104b4o
39bo$103b4obboo34booboo$101b9obo18boo15bo$100bob9o4boob3o3b3ob6o11bo3b
o$99bob10obb8o4b9o$99b21obb11o13b3o$99bob10obb8o4b9o53bo$100bob9o4boob
3o3b3ob6o11bo3bo35booboo$101b9obo18boo15bo39bo$103b4obboo34booboo36b3o
$104b4o39bo39bo$184b7o$185b5o$184b7o$183bob5obo52bobo$184b7o54bobo$
185b5o57b3o$185b5o53b3oboo$185b5o54b3oboo$184b7o52bobo3bo$184b7o53b3ob
o$185b5o52b3obbo$184b7o53b5o$184b7o54b5o$185b5o55b5o$184b7o53b7o$185b
5o55b5o$183bob5obo52b7o$183b9o52b7o$182b11o50b9o$184b7o51bob7obo$184b
7o52b9o$185b5o53b9o$184b7o54b5o$183bob5obo54bobo$184b7o$185b5o$185b5o$
186b3o$185booboo$$185bo3bo7$170bo19bo$159boo9bo18boo$156b4obo5b3obo7bo
8boboo$155bob4obbob6o4boo3boobboo3b3obo$154bob7ob7obb5obooboobbobb5o$
154b27ob4obb5o$154bob7ob7obb5obooboobbobb5o$155bob4obbob6o4boo3boobboo
3b3obo$156b4obo5b3obo7bo8boboo$159boo9bo18boo$170bo19bo26$247bo$247bo$
247bo5$246bobo$246b3o$247bo$247bo$246b3o$245b5o$245bobobo$246b3o!

[Figure 101. A period 120 sideways p32 spaceship rake]

Another perturbation of the blob results in the following period 120
sideways snail rake.

x = 305, y = 170, rule = B3678/S34678
30b4oboo$28b3ob4obo5bobo12b3o5bo$27bob8o4b3obob3o8b3obo4boo$26bob9obb
11o8b6obo128bo$26b19obobb4o4b7ob4o118bobobo4boo$26bob9obb11o8b6obo122b
3ob5obo7bo$27bob8o4b3obob3o8b3obo4boo51bo3bo59boobob9o4booboo$28b3ob4o
bo5bobo12b3o5bo51bobbooboo57bob13obb8o$30b4oboo76boobo3bob3obo56b25obo
$113boobb11o55b25obo$116b10o57bob13obb8o$117b11o56boobob9o4booboo$43b
ooboo28bo42b8o61b3ob5obo7bo$42bob3obo5bo3bo16bobo41boo3b3o60bobobo4boo
$41bob5o4b5o6boo9bobo38bobooboo72bo$40bob6obb8obbob3o5bo4boo40bo$40b
26obbobobo5bo$40bob21obb5o5boobo30boo57b3o$41bob14ob5obob7obobo30b3o
57boo$42bob12oboboo4b3oboobbo$43booboo3boboo10bo8bo108boo$51boo131boo$
7boo173b3o$5boobo115bo59bo$6b4oboo36bo42boboo7boboo17boo$3bob8o8bo5bo
4boo14b3o40b5o6bo12bo8b4o$bb10obo3boobobo4boob6o12b3o39b6o4b5obo3b4ob
4o4bob3o$b12obb9obb10o11b5o37b8ob8obb4o4boobo4b5o$22obobb9o13bobo37b
27obob10o$b12obb9obb10o12b3o38b8ob8obb4o4boobo4b5o$bb10obo3boobobo4boo
b6o54b6o4b5obo3b4ob4o4bob3o$3bob8o8bo5bo4boo13bo3bo39b5o6bo12bo8b4o$6b
4oboo35bobo41boboo7boboo17boo$5boobo39bobo73bo$7boo4$102boboo7boboo25b
o$101b5o6bo12boo15boo$100b6o4b5obo3boob6o11bobobo$99b8ob8obb11o14bo$
98b30o10b4obobo$99b8ob8obb11o14bo$100b6o4b5obo3boob6o11bobobo$101b5o6b
o12boo15boo$102boboo7boboo25bo6$124bo$114bo9boo18b3o$112b4o4bob4o8boo
8boo$111b6o3bob3obo3boobobo7bob4o$110b16obb5obbobb4obb5o$109b27ob5ob5o
$110b16obb5obbobb4obb5o$111b6o3bob3obo3boobobo7bob4o$112b4o4bob4o8boo
8boo$114bo9boo18b3o$124bo6$180b5o$130boo48b5o$128boobo49b3o$129b4oboo
44b5o$126bob8o9boo13bo20bobo$125b10obo3boob3obo11boo20bobo$124b12obb
11o7bob6o16booboo$123b24obbo6b7obo16b3o$124b12obb11o7bob6o17b3o$125b
10obo3boob3obo11boo18boo3boo$126bob8o9boo13bo20b3o$129b4oboo45b3o$128b
oobo49b3o$130boo48b5o$180bobobo$181b3o25$240booboo$240b5o$239b7o$239b
7o$240b5o$240b5o$241b3o$239bob3obo$241b3o$241bobo$242bo$242bo$240b5o$
240bobobo$240b5o$240b5o$241b3o$240b5o$240b5o$241b3o$241b3o$239bob3obo$
241b3o$242bo$242bo$241b3o$242bo$242bo$241bobo$190b3oboo15bo12boo14bobo
bo$190b5obo5bo8bo5bo5boo15booboo$188b8o4b5o5bo4bobobo3boobo13booboo$
187bob7obb7oboboboo4bob3o3b5o$187b19ob4o3boobbobobb5o$187bob7obb7obobo
boo4bob3o3b5o$188b8o4b5o5bo4bobobo3boobo$190b5obo5bo8bo5bo5boo$190b3ob
oo15bo12boo9$301b3o$301bobo$300b5o$301b3o$300b5o$301b3o$301b3o$230b3ob
oo$230b5obo5bobo4bo7bobobboobo$227b9o4b5o3bo6b3obo5boo$226bob8obb7o3b
oo6boboobbob3o$226b18oboboboo3bob6ob5o$226bob8obb7o3boo6boboobbob3o$
227b9o4b5o3bo6b3obo5boo$230b5obo5bobo4bo7bobobboobo$230b3oboo!

[Figure 102. A period 120 sideways snail rake]

The following period 120 puffer is in two parts. The first part is the
normal blob producing spaceships and perturbing spaceships which turn the
blob into a nova. The second part is a period 120 eater puffer.
The expanding novas react with the eaters to form forwards snails.
Therefore, this is a period 120 forwards snail rake. This puffer is
the first puffer found in any Life universe which produces spaceships
which travel in the same direction as the puffer and which travel slower
than the puffer. Adjusting the placement of the eater puffer can change
this puffer to one which generates backwards snails instead.

x = 241, y = 151, rule = B3678/S34678
106boo$104boobo87booboo$105b4oboo82b6o6bo$102bob8o9boo13bo56bob4obo3b
5o$101b10obo3boob3obo11boo55b8obb7o3bobob3o$100b12obb11o7bob6o51b23obo
4bo$99b24obbo6b7obo50b23obo4bo$32bobbo3boo59b12obb11o7bob6o52b8obb7o3b
obob3o$29boobboo3b3o8b3o7b3o39b10obo3boob3obo11boo56bob4obo3b5o$27boob
10obo3boobbo8bob4o38bob8o9boo13bo57b6o6bo$26b15obb8obb3o3b5o41b4oboo
83booboo$25b38o41boobo110boboo7boboo$26b15obb8obb3o3b5o42boo109b5o6bo
7bobo$27boob10obo3boobbo8bob4o152b6o4b5obo7bo$29boobboo3b3o8b3o7b3o
153b8ob8obb5obo$32bobbo3boo51bobbo61booboo52b25obo$88bob9o56b6obo51b
25obo$46boo39b12o56b8o52b8ob8obb5obo$44boobo21bo16bob11o55b8o54b6o4b5o
bo7bo$45b4oboo16bobo17b10o57b8o54b5o6bo7bobo$42bob9o6bo6bobb3o15b11o
57b8o55boboo7boboo$41b12o4bobo5b6o14bob10o60b3oboo$40b12o4bobbo3b4obb
oo14b4ob8o62bo$39b14o6boob6obbo11boo5bobobb6o57bo45bo$40b12o5bob11o11b
3obbo7b5o42boo12bo46boo$41b10obo6b10obo9b3o13boo44boo14bo44boo$42bob8o
7boobooboobo17bo55bo12bo3bo$45b4oboo8bob3obobo86bo3boo$44boobo106boo3b
o$46boo108b5o$16bo76b4o39bo17boboobbo$5boo9bo75b4obboo34booboo15b3obo$
bb4obo5b3obo8boo14b3o45b9obo18boo15bo19bo$bob4obbob6o4boob6o13boo44bob
9o4boob3o3b3ob6o11bo3bo$ob7ob7obb11o10boboobo42bob10obb8o4b9o33bo$29o
11b4obo42b21obb11o13b3o17bobo$ob7ob7obb11o10boboobo42bob10obb8o4b9o31b
obobo$bob4obbob6o4boob6o13boo44bob9o4boob3o3b3ob6o11bo3bo16bobo$bb4obo
5b3obo8boo14b3o45b9obo18boo15bo19bo$5boo9bo75b4obboo34booboo$16bo76b4o
39bo$$103boo$103boo$101bob3obboo$99boobb6obo8boo12bo$98bob10o4boob6o9b
o3bo$97bob11obb11o10b5o13boobo$97b25o7b9o14bobboo$97bob11obb11o10b5o
15b3oboo$98bob10o4boob6o9bo3bo15b6obo$99boobb6obo8boo12bo17bob8o$101bo
b3obboo41b3o4bo$103boo47b3o3boo$103boo50bobboo$152b3obo$114boo36boob3o
bo$109bobobboboboo32b5obo$108bobb5oboobo6b3o9boo12boob3o$107bob11o4boo
bbobobbobb7o10b5o$106bob12obb8obbobobb6o11bobobo$106b36o13b3o$106bob
12obb8obbobobb6o13bo$107bob11o4boobbobobbobb7o11b5o$108bobb5oboobo6b3o
9boo15bo$109bobobboboboo36bo$114boo13$132boo3b3o9bo9bo$127b3o8bobo8bo
8b3o$125boob7ob4o4boo3boobbo4b5o$124bob14obb7o3bobo3b5o$124b32ob5o$
124bob14obb7o3bobo3b5o$125boob7ob4o4boo3boobbo4b5o$127b3o8bobo8bo8b3o$
132boo3b3o9bo9bo19$166bo$159bobobo4boo$160b3ob5obo8boo16bo$156boobob9o
4boob6o14bo$155bob13obb11o10bobbobo$155b27o12b4o$155bob13obb11o10bobbo
bo17bo$156boobob9o4boob6o14bo16b5o$160b3ob5obo8boo16bo16bobobo$159bobo
bo4boo44booboo$110bobbo3boo47bo49bo$107boobboo3b3o9boo85b3o$105boob10o
bo3boob6o13b3o67b3o$104b15obb11o11bobo68b5o$103b28o11b4obo65b7o$104b
15obb11o11bobo69b3o$105boob10obo3boob6o13b3o66b5o$107boobboo3b3o9boo
84bobobo$110bobbo3boo96b3o$$189bo$188boo$147b4oboo9bo23b6o$145b3ob4obo
7boob4o18bob4o34bo$144bob8o7b8o8b4o7b8o30bobo$143bob9o4b11o8boboo6bob
6o30bobobo$143b13obb11obboo5b3o3bo3b8o30bobo$143bob9obbob5ob8o4bobobbo
bbobb7obo31bo$144bob8o4b3obb4obo7b4obboobobb7obo$145b3ob4obo5boo13boo
bbob4obb10o$147b4oboo24bo4boobboob5obo$189bobb3o$192boobo$191boboo$
156bo35bo$124boboo7boboo17boo33bo$123b5o6bo12bo8b4o$122b6o4b5obo3b4ob
4o4bob3o$121b8ob8obb4o4boobo4b5o$120b27obob10o$121b8ob8obb4o4boobo4b5o
$122b6o4b5obo3b4ob4o4bob3o$123b5o6bo12bo8b4o$124boboo7boboo17boo$156bo!

[Figure 103. A period 120 forwards snail rake]

A breeder has been found for Day & Night. A breeder is a pattern whose
population grows quadratically with time. In the following period 120
breeder, sideways rockets run into period 16 oscillators to form sidewinders.
Since each sidewinder produces a growing row of p16 oscillators, and the
puffer keeps producing new sidewinders, the number of p16 oscillators
grows quadratically to form a triangular region.

x = 222, y = 145, rule = B3678/S34678
37bo$30bobobo4boo9bo$31b3ob5obo8bo9boo$27boobob9o4boobbobobbo4b5o$26bo
b13obb8obbobobb6o$26b37o123b3oboo$26bob13obb8obbobobb6o122b5obo5bo$27b
oobob9o4boobbobobbo4b5o120b8o4b5o8bo$31b3ob5obo8bo9boo99boo20bob7obb7o
bobobbo$30bobobo4boo9bo41bobbo62b6o19b19oboobbobobo$37bo49boob8o62boo
21b19oboobbobobo$87bob10o59b5o20bob7obb7obobobbo$45b4o39b11o57b8o20b8o
4b5o8bo$44b4obboo16b3o15b12o59b5oboo21b5obo5bo$42b9obo3boboo8b3o16b11o
59b3ob4o21b3oboo$41bob10o3bobobo4b4obo15b11o60boobboo$40bob10o5b3o3b3o
3bo15b12obo59boo$40b13o3bob10obbo13boboo3bobb5o43bo13boo$40bob10o7b12o
10b3obbo7b3obo43bo11b4oboo$41bob9o6boboob5o13boo3boo8boo44boo10bobb5o$
42b9obo6boob8o11bobo59bo10bobboboo$44b4obboo9bo4bo18bo72bobo$45b4o17bo
88b3obo$153boboboboo$15bo78boo58boobobo$5bo9boo76b4oboo35b3o17b3o$3b4o
4bob4o9boo15bo47bob7o14bo4boo13b5o$bb6o3bob3obo3boob6o12b3o45b9obo3boo
boo4bobob6o13bo$b16obb11o10b5o44b11obb6oboobb10o12bobo$29o10bob4o43b
22obb10o14bo$b16obb11o10b5o44b11obb6oboobb10o12bobo$bb6o3bob3obo3boob
6o12b3o45b9obo3booboo4bobob6o13bo$3b4o4bob4o9boo15bo47bob7o14bo4boo13b
5o$5bo9boo76b4oboo35b3o$15bo78boo60bo$155boboo$154bob3o$155boboo$104b
oo50bo$103b4oboo22bo$101bob7o9bobo9boboo5bo$100b9obo3boob4obo7bob5obbo
$99b11obb6o3bobbo6b6o$98b24obo6b6ob3o$99b11obb6o3bobbo6b6o19boo$100b9o
bo3boob4obo7bob5obbo17bo$101bob7o9bobo9boboo5bo14boo$103b4oboo22bo$
104boo49b3o$155b3o$154b5o$155b3o$156bo$115bo39b3o$114boboboo35b3o$112b
ob6o6bo12boo13bobobo$111b8obo3b6o4boob6o11b5o$110b10obb6obobbob9o$109b
20o3b10o$110b10obb6obobbob9o$111b8obo3b6o4boob6o11b5o$112bob6o6bo12boo
13bobobo$114boboboo34booboo$115bo40bo8$138bo$128bo9boo18b3o$126b4o4bob
4o8boo8boo$125b6o3bob3obo3boobobo7bob4o$124b16obb5obbobb4obb5o$123b27o
b5ob5o$124b16obb5obbobb4obb5o$125b6o3bob3obo3boobobo7bob4o$126b4o4bob
4o8boo8boo$128bo9boo18b3o$138bo10$213booboboo$213b7o$212b9o$213b7o$
213b7o$214b5o$214b5o$215b3o$215b3o$216bo$213bobbobbo$211boob5oboo$213b
7o$213b7o$213b7o$214b5o$214b5o$215b3o$214bobobo$103bo111b3o$96bobobo4b
oo9bo96bob3obo$97b3ob5obo8bo9boo84bob5obo$93boobob9o4boobbobobbo4b5o
82b9o$92bob13obb8obbobobb6o83b7o$92b37o84b7o$92bob13obb8obbobobb6o83bo
b3obo$93boobob9o4boobbobobbo4b5o84bobobo$97b3ob5obo8bo9boo87b3o$96bobo
bo4boo9bo41bobbo$103bo49boob8o$153bob10o$111b4o39b11o$110b4obboo16b3o
15b12o$108b9obo3boboo8b3o16b11o$107bob10o3bobobo4b4obo15b11o$106bob10o
5b3o3b3o3bo15b12obo$106b13o3bob10obbo13boboo3bobb5o43bo$106bob10o7b12o
10b3obbo7b3obo43bo$107bob9o6boboob5o13boo3boo8boo44boo$108b9obo6boob8o
11bobo59bo$110b4obboo9bo4bo18bo$111b4o17bo$$81bo$71bo9boo$69b4o4bob4o
9boo15bo$68b6o3bob3obo3boob6o12b3o$67b16obb11o10b5o$66b29o10bob4o$67b
16obb11o10b5o$68b6o3bob3obo3boob6o12b3o$69b4o4bob4o9boo15bo$71bo9boo$
81bo!

[Figure 104. A period 120 breeder formed by a puffer which emits sidewinders]

Moving up from period 120 results, rakes have been found based on the
period 260 sidewinder. These are rather ugly, and the only spaceships
produced so far by these rakes are backwards ones, and so are not as useful
as sideways rakes. Their spaceship production method is to impact two
blobs symmetrically to create a blob which then reacts with an eater to
form the spaceship. The reaction which creates the blobs is shown below.
The blob moves at right angles to the path of the rocket.

................O.............
.........O.O.O....OO..........
..........OOO.OOOOO.O.........
......OO.O.OOOOOOOOO....OO.OOO
.....O.OOOOOOOOOOOOO..OOOOOOOO
.....OOOOOOOOOOOOOOOOOOOOOOOO.
.....O.OOOOOOOOOOOOO..OOOOOOOO
......OO.O.OOOOOOOOO....OO.OOO
..........OOO.OOOOO.O.........
.........O.O.O....OO..........
................O.............
.O............................
.OO...........................
OO............................

[Figure 105. A period 16 oscillator is impacted by a rocket
to form a sideways blob]

The following period 260 rake based on the method described above shows
the only known period 4 ship which is produced by a puffer. This puffer
also shows an application of the asymmetrical period 4 spaceship with its
spark being used to produce the eaters.

x = 478, y = 65, rule = B3678/S34678
268boo$266boobo$267b4oboo$264bob8o36bo$263b10obo3booboo22bo4booboo$
262b12obb9o18bobob8o$261b23obo16bobb9obo3boob3o$261b23obo15b14obb7o25b
o$262b12obb9o15b27o15bobobo4boo9bo34b3oboo35b3o$263b10obo3booboo17b27o
16b3ob5obo8bo9boo23b5obo5bo12boo14b3o$264bob8o27b14obb7o15boobob9o4boo
bbobobbo4b5o19b8o4b5o5boob6o13bo$267b4oboo28bobb9obo3boob3o13bob13obb
8obbobobb6o18bob7obb7obob11o26b3oboo$266boobo33bobob8o23b37o19b19ob11o
27b5obo5bo$180boo72b3o11boo35bo4booboo23bob13obb8obbobobb6o18bob7obb7o
bob11o24b8o4b5o5boob3o$179bobobo50boo4bobo10bobo54bo28boobob9o4boobbob
obbo4b5o19b8o4b5o5boob6o13bo9bob7obb7obob8o$179b3obo25booboo20boo6bo
11b5o84b3ob5obo8bo9boo23b5obo5bo12boo14b3o8b19ob8o$179boo27b6o6bo8bobb
4obboboobo6boobb3o85bobobo4boo9bo34b3oboo35b3o8bob7obb7obob8o$179b3o
25bob4obo3b5o4b3obb6oboobboo3boboobbo94bo100b8o4b5o5boob3o$180bo25b8o
bb7o3b11obboobobboobobboo199b5obo5bo$63boo113boobo23b23ob9obo3bo3b3obb
o47bo151b3oboo$64bo113b3o25b13obb7obbobb4obobo6b5o48boo$60bo3bo3boo
111bo25b11obo3b5o3bob3oboboo4boboobobbo45boo$59boob8o109bo28boob8o6bo
8b3o9boobobo67bo130boo$58b11obo3boob3o99boo28bo3bo3boo15b4o12b3o65b3o
128boo$57b13obb8o99bo33bo22bo83bo129bo$56b26o97bo32boo$56b26o99bo$57b
13obb8o98b6o$58b11obo3boob3o98b4obo$59boob8o109bobbo$60bo3bo3boo110boo
$64bo238bobo127bobo$63boo239bo129bo$5bo297bobo127bobo$4boboboo7boboobo
$4b6o6bob3obo29bo$bbob5obo3b9obo26boo$b9obb11obo27boo$25o148b6o$b14obb
o3bob3o145b5oboo33boo$bbobb9obo3booboboo108b3oboo31b4oboboo33bo22bo83b
o129bo$3bobob8o119b5obo5bo9bo12bobobb7o28bo3bo3boo15b4o12b3o65b3o128b
oo$5bo4booboo117b8o4b5o5boboo11bo6b4obo26boob8o6bo8b3o9boobobo67bo130b
oo$10bo90bo29bob7obb7oboboobo12bo10bo27b11obo3b5o3bob3oboboo4boboobobb
o45boo$100boboboo25b19obob4o11boo8boo26b13obb7obbobb4obobo6b5o48boo$
98bob6o6bo18bob7obb7obob4o12boo8boobo23b23ob9obo3bo3b3obbo47bo151b3ob
oo$60booboo32b8obo3b6o16b8o4b5o6boo49b8obb7o3b11obboobobboobobboo199b
5obo5bo$59b6o6bo24b10obb6obo18b5obo5bo7bo26bo25bob4obo3b5o4b3obb6oboo
bboo3boboobbo94bo100b8o4b5o5boob3o$58bob4obo3b5o21b20o19b3oboo68b6o6bo
8bobb4obboboobo6boobb3o85bobobo4boo9bo34b3oboo35b3o8bob7obb7obob8o$57b
8obb7o3bobob3o11b20o94booboo20boo6bo11b5o84b3ob5obo8bo9boo23b5obo5bo
12boo14b3o8b19ob8o$56b23obo4bo10b10obb6obo118boo4bobo10bobo54bo28boobo
b9o4boobbobobbo4b5o19b8o4b5o5boob6o13bo9bob7obb7obob8o$56b23obo4bo11b
8obo3b6o138b3o11boo35bo4booboo23bob13obb8obbobobb6o18bob7obb7obob11o
24b8o4b5o5boob3o$57b8obb7o3bobob3o14bob6o6bo153boobo33bobob8o23b37o19b
19ob11o27b5obo5bo$58bob4obo3b5o26boboboo161b4oboo28bobb9obo3boob3o13bo
b13obb8obbobobb6o18bob7obb7obob11o26b3oboo$59b6o6bo29bo162bob8o27b14o
bb7o15boobob9o4boobbobobbo4b5o19b8o4b5o5boob6o13bo$60booboo198b10obo3b
ooboo17b27o16b3ob5obo8bo9boo23b5obo5bo12boo14b3o$262b12obb9o15b27o15bo
bobo4boo9bo34b3oboo35b3o$261b23obo15b14obb7o25bo$261b23obo16bobb9obo3b
oob3o$262b12obb9o18bobob8o$263b10obo3booboo22bo4booboo$264bob8o36bo$
267b4oboo$266boobo$268boo!

[Figure 106. A period 260 backwards period 4 rake]

A similar period 260 rake which produces backwards p32 ships is shown
below. A small adjustment of the collision of the back blobs with the
eaters can create a backwards rocket rake instead.

x = 460, y = 61, rule = B3678/S34678
251booboo$250b6o6bo29bo$249bob4obo3b5o26boboboo$248b8obb7o3bobob3o14bo
b6o6bo$247b23obo4bo11b8obo3b6o$247b23obo4bo10b10obb6obo63bobo18bo$248b
8obb7o3bobob3o11b20o22b4oboo35bobo11bobobo4boo$249bob4obo3b5o21b20o20b
3ob4obo5bobo10boo12b3ob3o10b3ob5obo8boo16bo$172bobo75b6o6bo24b10obb6ob
o18bob8o4b3obo4b3ob6o12b3o8boobob9o4boob6o14bo23bo$171b3o77booboo32b8o
bo3b6o17bob9obb8o3b10o12b3o7bob13obb11o10bobbobo15bobobo4boo$170b4o
115bob6o6bo20b19obob11o23b27o12b4o17b3ob5obo$71bo98bobobo62bo53boboboo
27bob9obb8o3b10o12b3o7bob13obb11o10bobbobo12boobob9o4boob3o$61bo9boo
98bobo27bo32bobobobo51bo32bob8o4b3obo4b3ob6o12b3o8boobob9o4boob6o14bo
12bob13obb8o$59b4o4bob4o97bo25bo4booboo21bo4boob5ob3o82b3ob4obo5bobo
10boo12b3ob3o10b3ob5obo8boo16bo12b24o$58b6o3bob3obo3b3obo88bo23bobob8o
6boobbo5boo3bo4b10obo84b4oboo35bobo11bobobo4boo40bob13obb8o$57b16obb4o
bboo87b4o19bobb9obo3b5obo4b3oboboo3b14o124bobo18bo44boobob9o4boob3o$
56b25o89bo21b14obb15oboobboo3b9oboo195b3ob5obo$56b25o110b27ob3o4b5obob
obb3o199bobobo4boo$57b16obb4obboo87b3o19b9obb7obbob4obb4obo3b3obb3o46b
oo161bo$58b6o3bob3obo3b3obo88boo21bob5obo3b5o3bob3obobobo4boobo50boo
17bo129bo$59b4o4bob4o99bo22b6o6bo9bobbo62bo17b3o127boo$61bo9boo97bo3bo
20boboboo17bo83bo127boo$71bo98boboo22bo$7boo161b4o$5boobo161b4o$6b4ob
oo10bo6bo$3bob8o6booboboo3boo104bo$bb10obo3b8obb6o101boo$b12obb18oboo
98b3o$32obboo33bo191b4o126b4o$b8ob8obb12obbo34b3o64b4o121b4o126b4o$bb
6o4b5obo3b5ob5o37bo64b4obboo118b4o126b4o$3b5o6bo9boobobo103b9obo$4bob
oo7boboo10b3o70boo28bob9o4boob3o3b3ob3o$29bo73bo27bob10obb8o4b6o$99bo
3bo3boo22b21obb8o$62boo34boob8o22bob10obb8o4b6o$61b4oboo29b11obo3boob
3o13bob9o4boob3o3b3ob3o$59bob7o28b13obb8o14b9obo52bo$58b9obo3booboo18b
26o14b4obboo52boboboo17bo83bo127boo$57b11obb6obo17b26o15b4o55b6o6bo9bo
bbo62bo17b3o127boo$56b23o17b13obb8o74bob5obo3b5o3bob3obobobo4boobo50b
oo17bo129bo$56b23o18b11obo3boob3o73b9obb7obbob4obb4obo3b3obb3o46boo
161bo$57b11obb6obo20boob8o82b27ob3o4b5obobobb3o199bobobo4boo$58b9obo3b
ooboo22bo3bo3boo83b14obb15oboobboo3b9oboo195b3ob5obo$59bob7o35bo89bobb
9obo3b5obo4b3oboboo3b14o124bobo18bo44boobob9o4boob3o$61b4oboo34boo90bo
bob8o6boobbo5boo3bo4b10obo84b4oboo35bobo11bobobo4boo40bob13obb8o$62boo
132bo4booboo21bo4boob5ob3o82b3ob4obo5bobo10boo12b3ob3o10b3ob5obo8boo
16bo12b24o$201bo32bobobobo51bo32bob8o4b3obo4b3ob6o12b3o8boobob9o4boob
6o14bo12bob13obb8o$237bo53boboboo27bob9obb8o3b10o12b3o7bob13obb11o10bo
bbobo12boobob9o4boob3o$289bob6o6bo20b19obob11o23b27o12b4o17b3ob5obo$
251booboo32b8obo3b6o17bob9obb8o3b10o12b3o7bob13obb11o10bobbobo15bobobo
4boo$250b6o6bo24b10obb6obo18bob8o4b3obo4b3ob6o12b3o8boobob9o4boob6o14b
o23bo$249bob4obo3b5o21b20o20b3ob4obo5bobo10boo12b3ob3o10b3ob5obo8boo
16bo$248b8obb7o3bobob3o11b20o22b4oboo35bobo11bobobo4boo$247b23obo4bo
10b10obb6obo63bobo18bo$247b23obo4bo11b8obo3b6o$248b8obb7o3bobob3o14bob
6o6bo$249bob4obo3b5o26boboboo$250b6o6bo29bo$251booboo!

[Figure 107. A period 260 backwards p32 ship rake]

There are also rakes with period 520, also based on the sidewinder and the
same blob reaction used above. The following shows the general method,
which creates a nova and then perturbs that nova into a sideways rocket.
Other perturbations of the nova can produce other ships, or the rocket
itself can be perturbed to produce other ships.

x = 418, y = 135, rule = B3678/S34678
363bo$362boboboo27boo$362b6o6bo7bo5bobo4bo$360bob5obo3b6o3boo6boboobbo
boo$359b9obb7o3b4obbobobobo3b3o$358b19o3boo5boob4ob5o$359b9obb7o3b4obb
obobobo3b3o$360bob5obo3b6o3boo6boboobboboo$362b6o6bo7bo5bobo4bo$362bob
oboo27boo$363bo29$301boo$301boo$299bob3obboo$297boobb6obo8boo12bo$296b
ob10o4boob6o9bo3bo$295bob11obb11o10b5o$295b25o7b9o$295bob11obb11o10b5o
$296bob10o4boob6o9bo3bo78bobo$297boobb6obo8boo12bo39b4oboo35bobo$299bo
b3obboo61b3ob4obo5bobo10boo12b3ob3o$301boo65bob8o4b3obo4b3ob6o12b3o$
301boo64bob9obb8o3b10o12b3o$367b19obob11o$367bob9obb8o3b10o12b3o$297bo
19bo50bob8o4b3obo4b3ob6o12b3o$286boo9bo18boo51b3ob4obo5bobo10boo12b3ob
3o$283b4obo5b3obo7bo8boboo52b4oboo35bobo$282bob4obbob6o4boo3boobboo3b
3obo92bobo$281bob7ob7obb5obooboobbobb5o$281b27ob4obb5o$281bob7ob7obb5o
booboobbobb5o$282bob4obbob6o4boo3boobboo3b3obo$283b4obo5b3obo7bo8boboo
$286boo9bo18boo$297bo19bo6$273booboo37bo$272bob3obo5bo3bo8boo15boo$
271bob5o4b5o5boob6o12boo$270bob6obb8obb11o14bo$270b30o$270bob6obb8obb
11o14bo$271bob5o4b5o5boob6o12boo$272bob3obo5bo3bo8boo15boo$273booboo
37bo4$277bo19bo$266boo9bo18boo$263b4obo5b3obo7bo8boboo$262bob4obbob6o
4boo3boobboo3b3obo$261bob7ob7obb5obooboobbobb5o$261b27ob4obb5o$261bob
7ob7obb5obooboobbobb5o$262bob4obbob6o4boo3boobboo3b3obo$263b4obo5b3obo
7bo8boboo$266boo9bo18boo$277bo19bo6$253booboo37bo$252bob3obo5bo3bo8boo
15boo$251bob5o4b5o5boob6o12boo$250bob6obb8obb11o14bo$250b30o$250bob6o
bb8obb11o14bo$251bob5o4b5o5boob6o12boo$252bob3obo5bo3bo8boo15boo$253b
ooboo37bo6$3booboo7bo3bo108boo$bbob3obo5b4obbo24bobo80boo$bob5o4b9o6bo
15bobbo62b3o17bo120boo$ob6obb9obo21boboo63boo127bobo10bo9boo$19o7boboo
12boboobo199bo3bo3boboboob5o$ob10obb4obo7bo17b5o145boo40bo8boob8ob11o$
bob12obboo6b4o15bob4o87bo58bo48b19ob3o$bboobb6obobb3o6bobbo16bob3o86bo
boboo27boo21bo3bo3boo35b3o4b21oboboo$4bob3obboo13boo19boo87b6o6bo7bo5b
obo4bo21boob8o8boo9boo14b3o3b21o3b5o$6boo39boo85bob5obo3b6o3boo6boboo
bboboo17b11obo3boob3o7b6o19b13obb4obbobooboo$6boo90b3oboo29b9obb7o3b4o
bbobobobo3b3o16b13obb8obb3ob7o12bobo5b11obo3boo5booboo$72bo25b5obo5bo
21b19o3boo5boob4ob5o14b36o22boob8o12b3o$61boo9bo23b8o4b5o8bo11b9obb7o
3b4obbobobobo3b3o16b13obb8obb3ob7o12bobo7bo3bo3boo$58b4obo5b3obo4bo16b
ob7obb7obobobbo14bob5obo3b6o3boo6boboobboboo17b11obo3boob3o7b6o26bo$
57bob4obbob6o4boobobo12b19oboobbobobo12b6o6bo7bo5bobo4bo21boob8o8boo9b
oo14b3o10boo$56bob7ob7obb5obo13b19oboobbobobo12boboboo27boo21bo3bo3boo
$56b25o14bob7obb7obobobbo17bo58bo$56b25o15b8o4b5o8bo73boo$56bob7ob7obb
5obo16b5obo5bo$57bob4obbob6o4boobobo15b3oboo$58b4obo5b3obo4bo$61boo9bo
$72bo!

[Figure 108. A period 520 sideways rocket rake based on sidewinders and novas]

LOGIC GATES
-----------

Collisions between spaceships can be used to build "logic" gates.
A logic gate is a reaction in which one or more input "signals" are
combined to form one or more output "signals". A signal is a boolean
value indicated by the presence or absence of a spaceship at a particular
place at a particular time. The paths taken by the spaceships are like
wires carrying the signals from place to another. You can build NOT gates,
AND gates, and OR gates using collisions between the spaceships. These
can be combined to create larger "circuits" which can calculate arithmetic
values.

There are other types of logic gates which act as switches. I will show two
examples of this. In the first example, two p32 ships collide to form an
eater. The eater is placed correctly so as to destroy any further p32 ships
arriving from the right (if they are a multiple of 4 generations apart).
But when another p32 ship arrives from below, the eater is cleanly destroyed.
This can be used to toggle a p32 ship stream on and off. Furthermore, the
p32 ship which creates the eater escapes, allowing multiple copies of this
reaction to be cascaded in order to form a counter.

........................O....
......................OOO....
.....................O.OOO.O.
.....................OOOOO.OO
....O................O.OOO.O.
...OOO................OOO....
..OOOOO.................O....
.OOOOOOO.....................
OOOOOOOOO....................
..OOOOO......................
...OOO.......................
....O........................
...OOO.......................
...OOO.......................
...OOO.......................

[Figure 109. Two p32 ships create an eater which turns a p32 ship stream off]

In the second example, two p32 ships again collide to form an eater.
But in this case, the eater is formed off of the path of the upwards
moving p32 ship. This allows further p32 ships to travel upwards without
harm. This implements an OFF switch for a p32 ship stream. Other ships
traveling on a parallel path can be used to delete the eater and so turn
the p32 stream back on. Once again the upwards moving p32 ship escapes,
and so it can be used to turn off multiple p32 ship streams.

...............OOO........
..............O.O.........
.............O.OOOO..OOO.O
.............OOOOOOOO..OO.
..OOO........O.OOOO..OOO.O
.O.O.O........O.O.........
.OOOOO.........OOO........
OOOOOOO...................
..OOO.....................
..........................
..OOO.....................
...O......................

[Figure 110. Two p32 ships create an eater which turns a p32 ship stream off]

OPEN QUESTIONS
--------------

Here are a few questions about Day & Night whose answers are not yet known.

Are there oscillators of all periods? The 1-D XOR oscillators show that
all even periods occur. The smallest unknown odd period is 19.

Can a signal along an edge of slope 1/2 be made to turn a corner?
If so, this might answer the previous question. It would at least imply
that all nonmultiples of 3 occur as periods.

Can we characterize the periods of the spark oscillators?

Is there a quadratic growth pattern in which a single blob grows to fill
the entire universe?

Is there a single blob which is a natural rocket gun?

Is there a simple reaction which creates the butterfly spaceship?

CONCLUSION
----------

I would like to thank Allan Wechsler and Dean Hickerson for reviewing this
article to make it better. (The part of the article dealing with the 1-D
XOR automaton is essentially Dean's.) I especially would like to thank
Dean for his discoveries in this universe, and Nathan Thompson for
introducing me to this interesting Life universe.

I hope you agree with me that the Day & Night universe is a very nice
Life variant and and contains many interesting objects. My favorite
objects in this universe are the rocket, the snail, the spark oscillators,
the nova, and the period 128 rocket gun. There are probably many more
interesting things remaining to be found in this universe. If you find
anything, please send them to me and I will collect them and give you
credit for them.