This page is a transcript of Volume 10 of the Lifeline newsletter
This article may contain spelling mistakes and/or errors that will not be corrected -- it is preserved in this way for history's sake
A QUARTERLY NEWSLETTER FOR ENTHUSIASTS OF JOHN CONWAY'S GAME OF LIFE
O OOOOO OOOOO OOOOO O OOOOO O O OOOOO
O O O O O O OO O O
O O OOO OOO O O O O O OOO
O O O O O O O OO O
OOOOO OOOOO O OOOOO OOOOO OOOOO O O OOOOO
Since publishing the last issue of LIFELINE, I received a unique letter
which I am including in this issue in its entirety and without any
editing. This reply is not only laid out in newsletter fashion but
also includes a kaleidoscope of new and interesting discoveries. I
certainly welcome any and all letters of this nature no matter how long
or short!
As usual, I will present a cross-section of the new and more recent
discoveries reported by all the readers who have taken the time and
effort to reply.
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o$b2o$2o3$b3o$3bo3bo$2bo3bo$6b3o4$6bobo$6b2o$7bo3$9b2o$9bobo$9bo!
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o$b2o$2o$20bo$10bo7b2o$9bo9b2o$9b3o4$14bo$9b2o2b2o$10b2obobo$9bo4$4b3o
$6bo$5bo6b2o$11b2o$13bo2$17bo$16b2o$16bobo!
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2bo$obo$b2o$9bo$8bo$3o5b3o$2bo$bo$6b2o$5b2o$7bo!
The glider arrangements shown on this cover page of LIFELINE Number Ten
are described in the previously mentioned letter sent in by Douglas G.
Petrie of Lake Oswego, Ore. These patterns discovered by Petrie
produce respectively in a varying number of generations, the pentedecathlon(!),
Conway's heavyweight spaceship(!!), and Corderman's Switch Engine(!!!).
Details of these reactions and other newsworthy events
are described in Petrie's letter which begins on page three. Is there
pattern beside Gardens of Eden that can not be constructed with gliders?
Lifequote submitted by Mark Linimon of Houston, Tx:
'Life is too important a matter to be taken seriously.'
Class E, Evolutionaries, Exercises, Events, Et. cetera . . .
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bo$2bo$3o2$5b2o$b2o2b2o$b2o!
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2o2b2o$b2ob2o$o$6bo$6b2o$5bobo!
In keeping up with the new and exciting series of
glider(s) and block(s) collisions reported last
issue, Dave Filpus of East Lansing, Mi. submits
the following reaction of a single glider and two
blocks which in 113 generations yields a glider
(reflected 180 degrees) and three blocks!
Additionally, Peter Raynham of Sarnia, Ontario,
Canada submits the following collision of a block
and two gliders which in 47 generations results
in two gliders (reflected 90 degrees) and three
beehives!
The fates of the two unknown nonominoes introduced last issue were
first discovered and sent in by Robert Bison of Hopewell Jct., N.Y.
and then later by Bryan Drake of Lansing, Mi. and Harvey Lerman of
Maitland, Fla. Incidentally, Drake supplied some very nice Polaroid
photographs of these final populations that were left on the screen
of the IMLAC device described last issue. A summary of these results
as submitted by Bison follows:
Additionally, Bison notes that the Filpus-Karplus glider-blocks collision
described last issue (p.2) goes to 3360 generations after
spawning 15 gliders (!) for a Final population of 457 (max was 769
@2931). During its history it expanded to 160x200 (@2592) before
settling down to within 150x180.
A spaceship collision resulting in an unusual still life has been reported by D. R. Mc Entee of St. Louis, Mo. Shown below are two lightweight spaceships colliding to form a 14-bit stable object.
I was glad to receive copies of all the newer LIFELINEs in the mail recently.
Some general comments: I notice that the newsletter is now being held to a limit
of eight pages, and when rereading the "Coming Events" notices I get the impression
thar a number of interesting items are, because of this limitation, being withheld.
If the reason for the limit is cost rather than some other factor (taking too much
of your time?), I for one would be willing to kick in more money for a subscription.
As far as the articles printed went, most were quite interesting (but, please, don't
go overboard on the occult symbology). I strongly hope that the next issue will
include something about glider logic circuitry. Everett Boyer ought to be keeping
you informed of the rather extensive work he and I have done in that field, but I
would also Like to see what others might have done -- I can't believe we are the
only ones working on computer design.
Following are some recent discoveries of mine, of varying importance:
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bo11b2o$obo4bo6bo$7bo4bo$2bo2bo3bo2bo$2b2o6bo$3bo!
The ordinary-looking object at right has a very un-ordinary history:
its final population is infinite! This (along with a
few relatives of similar structure) is the smallest single object
known to achieve infinite growth. You may recognize it
as a cousin of the switch engine puffer shown in #4 p.1.
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#C [[ COLOR 2 Darkgray ]]
#C [[ COLOR GRID 229 229 229 ]]
#C [[ LABEL 15 18 8 "gen. 14" ]]
#C [[ LABELT 0 0 0 ]]
#C [[ LABEL 11 5 8 "gen. 0" ]]
x = 22, y = 20, rule = immigration
6.3A6.2B$.3B2.A7.B.B$B2.B3.A8.B3.A$3.B15.2A$3.B15.A.A$B.B5$5.2A8.2B$
4.A2.A8.B$4.A.A9.B.A$2.2B.A3.A7.2A$.B2.B3.A.A$.B.B3.A2.A$2.B3.B.2A$5.
B.B$4.B2.B$5.2B!
hybrid objects
Following a suggestion by Parrello and Tetenbaum (#7
p.7) I have used "Immigration" rules on about 20 previously
known collisions in order to determine the
exact parentage of the resultant patterns; in only
two cases did the final census include both types of
live bits. These are illustrated at the right. In
view of their rarity, any further examples of mixed
populations that people might discover would be of
interest, and in particular, any reaction that results
in an allied glider, (such as glider-toad, #9 p.5)
would be noteworthy. There are two 2-g1ider collisions
whose result is a single glider each; in both cases
the new glider is shown to be produced by a 180°
reflection of one of the original gliders.
Addendum: Boyer has just informed me that three glider-blinker collisions result
in a hybrid ship, a hybrid loaf, and a hybrid pond, respectively. EN: any others?
Enclosed with this letter is a list of 121 12-bit Class I objects which was compiled
jointly by Boyer and myself. There may still be some missing, but not many.
It is noteworthy that out of the entire list only one object (the half-fleet) has
yet been reported to result from a "naturally-occurring" reaction.
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2bo$obo9b2o$b2o9bobo$4bo10bo$3bo12bo$5b3o7b2o$5bo$6bo!
ERRATA: The "race against time" scenario (#3 p.14) will not
work as shown; the correct form is pictured here. Also, in
the table of 3x3 patterns (#9 p.4) note that A10=D11, E11=H10,
so the number of unique arrangements is actually 102.
EN: thanks, I missed that.
By using eaters instead of blocks for shuttle-stabilizers (#3 p.5) it is possible to
stack glider guns as close as 20 spaces apart, rather than 24 as reported in #9 p.5.
EN: I would still be satisfied to see a period 48 NEWBREEDER!
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3bo13bo4bo$b2ob2o12bo$6bo12b3o$o20bo!
Now that Boyer's procrastination quotient has appeared, readers
might be interested in trying to find the most procrastinating
ancestor of each of the common terminal forms. For the blinker
and the beehive the objects reported by Thompson (#8 p.5) will
surely hold the record. Presented here as further candidates are (A) an interchange
ancestor (21 gens., PQP=.167), and (B) a traffic lights ancestor (28 gens., PQP=.333).
As a number of readers probably know, in
the multitude of glider collisions can be
found methods for constructing almost all
of the familiar Class I&II objects. Two
unusual examples are illustrated at the
left. In Class III, ways of making light
or medium spaceships have long been known,
but as yet no one has reported any method
to build the heavy spaceship. This hole has
now been filled. Shown at the right is a complex
reaction between three gliders, a ship,
and an eater which produces a heavy spaceship
in ten generations. Shown also is one of many three-glider collisions
which results in a ship. Since two gliders react to form an eater,
making a heavy spaceship therefore requires a total of eight gliders.
Using this mechanism a P60 heavy spaceship factory can probably be
built, but in the present state of the art such a factory would require about 25 P30
glider guns. Perhaps future collision discoveries will allow simplification.
In #7 p.4 there were presented several examples of objects
which, when attacked by a virus, would reproduce themselves.
Another "friendly" virus has now come to light, one which
stimulates growth rather than reproduction. A spaceship of
any length (including overweight ones) with a virus attached
as shown will immediately turn into a spaceship of the next larger size. This reaction
is more important than might first appear; it is vital to the heavy-spaceship construction
described earlier.
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#C Note that the switch engine an block syntheses are placed
#C incorrectly. They should be one cell further apart. The placement
#C of the switch engine and block in the pattern labeled "gen. 6" is
#C correct.
bo3bo12bobo$2bo2bobo10b2o$3o2b2o12bo$22bo$21b2o$9bo11bobo$8b2o$8bobo$
4b2o$3bobo$5bo!
gen. 0
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13b2o$3o10b2o$bo$bo2bo$bo2bo$2bobo!
gen. 6
With various rather complicated collision scenarios
a number of Class IV patterns can be produced, too.
A new and surprisingly simple construction of this
nature was recently discovered: six gliders colliding
to form a puffer train. Gen. 6 at right is the
same as gen. 2 of the pattern pictured in #4 p.1.
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#C [[ POLYFILL 9.5 13.5 10.5 13.5 10.5 14.5 9.5 14.5 9.5 13.5 64 ]]
#C [[ POLYFILL 11.5 18.5 12.5 18.5 12.5 19.5 11.5 19.5 11.5 18.5 64 ]]
#C Note that the bottom two gliders should be moved northeast by one
#C cell as noted by the gray cells.
2$2bo$3b2o$2b2o3$3b3o$5bo3bo$4bo3bo13bo$8b3o11bo$21bobo$22bo$22bo$22bo
$7bobo12bo$7b2o12bobo$8bo13bo$22bo2$10b2o$10bobo$10bo!
gen. 0
gen. 9
By now ways are known to form from glider collisions
almost all of the "significant" objects or patterns,
including eaters, pentadecathlons, both major types
of shuttle, the three basic orthogonal spaceships,
both glider guns, and two of the three types of puffer
train. (For completeness, the simplest pentadecathlon-forming
collision I know of is shown here.) "Significant"
in this case refers to all objects which might
prove essential to such large-scale constructions as
puffer train factories, a p31 glider gun, glider logic
circuitry, or a pattern capable of self-replication.
Still missing from the list is any method of producing
"Schick's Flying Machine". Why bother with these
collisions at all? For one thing, any pattern able to reproduce itself must entirely
be composed of objects which can be created with glider collisions; we now have a wide
variety of objects which might be used to build such a pattern. For another, it keeps
me off the streets and out of trouble. (Regarding the question (#9 p.2) concerning
the purpose of LIFE, the most practical result I have seen is the prevention of boredom
among computer programmers.)
That's all for now; more to follow later on, including more results obtained in
collaboration with Boyer.
Sincerely yours,
Douglas G. Petrie
Enclosure: 12-bit objects.
Lifequote:
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2$5bo8bo$5b3o5bobo$3b2o3bo3bobobo$4bo2bo4bobobo$4bobo6bobo$5bo8bo4$5b
2o$5bo7bo$6bo6b3o$3b4o9bo$3bo9b2obo$4bo8b2ob2o$3b2o!
'Life is very short
and there's no ti i
i
i
i
i me . . . '
. . . Paul and John
Reader Brief . . .
Philip Cohen of Aliquippa, Pa.: 'I may have mentioned this before,
but - of the 10,000's of possible 8-bit figures consisting of an
R-pentomino and a tromino at a greater or lesser distance, isn't
it likely that at least one grows to infinity? It would seem worthwhile
to investigate a dozen or so randomly chosen block sites to see
if there is a significant change in any of the Life histories; if not,
the speculation becomes rather less likely. Has it been tried?
EN: does anyone have a handle on the number of these combinations? (also for R-pentomino and a single blinker); try:
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b2o$2o$bo$o$2o!
Anyone who plays life regularly knows that the alteration
in position of even a single bit in a pattern can alter
considerably the final census. Patterns which can be
so altered and still produce identical output we call
equivalent. For example, A is the glider predescessor
heptomino discovered by Thompson. B and C show how the
end bit can be moved around without destroying the
pattern's identity- for all three produce the same
glider in the game generation(4) occupying the same
position in the matrix.
D and E are another case in point. Both of these patterns
- differing from each other by the dislocation of a single
bit - produce a single glider fleeing a set of traffic
lights.
F is perhaps the most remarkable example I have to offer.
Structurally it is a glider connected to a latent block.
In Practice the latent block may as while not even exist,
for the glider is alone in the field in the sixth generation,
occupying the same position as it would have had it
started out alone.
Additionally, Curt Gibson of New York, N.Y. notes that: and
have identical results (traffic lites) in exactly the
same position and in exactly the same number of gens.
Tom Du Bois of Hawthorne, N.Y. has noted a surprising phenomenon
in Life regarding hollow block objects. In all cases investigated
up to order sixteen, the resultant census contains still lifes
composed of bits with either 2 or 3 neighbors but never both.
Eric A. Haines of Moorestown, N.J. has noted the same phenomenon
regarding solid block objects. In all cases investigated up to
order nine, the census never contained a common 2/3 type still life.
Henrik Bjurstrom of Uppsala, Sweden in studying all solid rectangular
objects up to ten by ten, has neverseen a census containing a
common 2/3 type still life.
These Lifexplainations are very unusual since still lifes are almost
always composed of bits with both 2 and 3 neighbors. In fact, of all
the 60,000 still lifes of 20 or less bits (conservative estimate),
there are only nine known to the writer. See table below showing
this distribution:
Still Life Structure Data
-SIZE-
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2 + 3
0
1
3
3
7
10
25
46
121
210
474
?
?
?
?
?
?
2 only
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3 only
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Totals
2
1
5
4
9
10
25
46
121
210
474
?
?
?
?
?
?
The smaller ones should be obvious to the seasoned Lifenthusiast. Can
you identify all nine? I'll print results of anyone with more in No. 11.
EN: how long can these generalities possibly last?
R.J. Best of Miami, Fla. reports that an
order twenty-one 'hooked cross' yields
in 87 generations, a group of four pulsars
with two extra beehives. Best ran this in
four seconds on homemade device that
outputs the results on a T-V like device.
COMING EVENTS:
Neal'sgame - an exciting and new biocolony simulation
