This page is a transcript of Volume 9 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 record of such errors can be found at Lifeline/Errata.
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
This issue of LIFELINE brings the newsletter back on schedule again
and I am pleased to report that even more new and exiting discoveries
have been made in this incredible game. We welcome the several hundred
new readers who responded to Martin Gardner's recent column in
Scientific American mentioning this endeavor.
As in previous issues, I will attempt to present a cross-section of
the many new findings still being made and sent in.
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Local Lifeclub News . . .
On February 27 th, a meeting of the Michigan State University Lifenthusiasts
(and several dozen Life-neophytes) was held. Chris Scussel
arranged and conducted the meeting which was held in the Engineering
building on the East Lansing campus. The agenda included a brief explaination
of the rules of Life given by Scussel. The heart of the
meeting involved a demonstration of a 4K (16-bit word) program which
runs on a standalone device (IMLAC). Developed by Bryan Drake, this
program has the capability to compute and display Life on a 124 square
display. The group enjoyed watching the notorious R-pentomino evolve
through its history in less than five minutes on Drake's display.
Next, the group saw a showing of the 17 minute film created at M.I.T.
by Bill Gosper and thoughtfully loaned by Mike Beeler to the writer
who also presented some unpublished Life discoveries and answered
miscellaneous questions. Incidentally, the most frequently asked
question regards the practicality and/or possible pragmatic application
of Life. This is a difficult one to answer and I will publish the best
responses sent in by any reader.
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EN: when the writer left East Lansing, Dave Filpus and
Kevin Karplus were still humped over the IMLAC tracking
the glider-blocks collision shown here which had just
passed the 1500 generation mark before exceeding Drake's
area limit. By that time, ten gliders had sucessfully
escaped from this original arrangement that Karplus had
discovered while experimenting for only a few minutes at
the input keyboard!
Class E, Evolutionaries, Exercises, Events, Et. cetera . . .
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Previously (No.7,p.3), we examined several Lifevents involving pairs
of objects which after N (say) generations, retained their identity.
That conservation of structure was only temporary however because each
of these objects then went on to become something else. In issue No.3,
page 15, we saw an event where a beehive and a block conservatively
interact on a permanent basis. This reaction is also
time limited however because, as before, we must start
at generation 0 with just the right arrangement. An
'ideal' conservation of structure would involve (say)
a glider and an object (Class I, II, or III) which
after collision would become a glider and that object
either or both of which could be displaced in time and
or space. The only example of this ever published was
that Lifevent involving a glider striking and being
reflected (180) by a pentadecathalon as reported in issue No.1, page 5.
I would now like to present another Lifevent involving two gliders
and a block which the writer considers an even more spectacular display
of structure conservation. The arrangement shown here will, in 15
generations, be identical in structure: that is, a block (same location)
and two gliders altered somewhat in space and time! Peter Raynham of
Sarnia, Ontario, Canada who made this discovery notes that the two
gliders can be reflected either 90° or 180°. (EN: this will be very
useful in our yet to be built Life computer)
To avoid further confusion regarding the ten-bit still lifes, Buckingham
has obligingly submitted the set of 25 shown on the next page which
includes the one (m) that was not in my original list. Gosper suggested
searching for even a 26th to make an alphabet of stable objects.
EN: Lee Skinner of Albuquerque, N.M. submitted a set of 43 eleven-bit
stable objects which recently has been increased to 46 by Buckingham
who also has identified 119 of the twelves, 210 of the thirteens, and
474 of the fourteens! A subscription to LIFELINE will be awarded to
anyone submitting a set of 47 or more eleven-bit still lifes.
The cover page of LIFELINE Number Eight illustrated a
set of oscillators with periods of 9, 2, 3, 8, 7, 4,
5(*), and 6 (a thru h respectively)! (g) was meant to
be a period five oscillator but will not work as shown.
This was first pointed out by Gosper and later by
Buckingham who more recently submitted (g.v) shown to
the right which will work with a period of five.
Again, to insure appropriate credit and authorship,
I will now indicate the specific constructor and exact
name as coined by same.
There are 104 unique arrangements (excluding rotations and reflections)
of bits within a square nine-cell matrix. Can you track all of these?
EN: these are presented here with row and column identification for
reference in future issues.
The last page of LIFELINE Number Five presented the first LIFESAVER
Form which included a questionnaire about organizing for local Life
activities. Here is a summary of the questions and responses from
those 262 readers who bothered to reply:
Does the idea of forming a local group in your area for participation in Life activities appeal to you?
No Maybe Yes
23% 42% 35%
Could or would you be able to offer a good computing facility to a local group?
No Maybe Yes
63% 28% 9%
Does the idea of acting as a LIFELINE associate editor for such a group or contributing to one appeal to you?
No Maybe Yes‑contr. Yes‑assoc.
34% 34% 24% 9%
Would you be interested in contacting others in your area and starting a group if provided with an address list of readers near you?
No Maybe Yes
41% 32% 27%
Additionally, I polled the reader base to determine the extent to
which any individual would, within his own reason, be willing to pay
for a 'custom built computer' which would display Life on an ordinary
TV set. Here is a summary of those responses:
Schick found that by placing
a mere T-tetrominoNo.8,p.5) between a mirror
pair of tightly packed lightweight spaceships, he was
able to 'pull' the elegantly symmetric clean engine
along with a period of 12!!
By placing additional combinations of one or more spaceships alongside and slightly
behind this arrangement, he
was able to construct an
endless variety of puffer
trains with periods of a
multiple of 12!
A few of these are shown
here to the right. Arrangement I deposits a
block every 12 generations,
Arrangement II creates twin
toads every 24 generations,
and Arrangement III generates a rearward glider every
24 generations.
The BREEDER (No.3,p.7) lays
down a Gun every 64 generations. These are spaced
32 cells apart. It is possible to pack them as close as
24 cells apart. Do you suppose we could construct a
period 48 NEWBREEDER???
Arrangement I
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2o$b2o2$9b6o$9bo5bo$9bo$10bo4bo$12b2o!
Arrangement II
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#C This mistake is preserved from the original document.
9b6o$9bo5bo$9bo$10bo4bo$bo2bo7b2o$o23bo12bo$o3bo7bo9bo2bo9bo2bo$4o4bo
3b3o7bo2bo9bo2bo$6b2o5b2o8bo12bo$6b3o6bo$6b2o5b2o8bo12bo$4o4bo3b3o7bo
2bo9bo2bo$o3bo7bo9bo2bo9bo2bo$o23bo12bo$bo2bo7b2o$10bo4bo$9bo$9bo5bo$
9b6o!
Arrangement III
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9b2o$bo2bo2b2o8bobo$o$o3bo$4o$15b2o$13bo4bo$12bo$12bo5bo$12b6o!
Both Raynham and P. Burton of Preston, England report that a glider
will interact with a toad and result in an
allied glider if they initially had different states. This is shown here. Recall
that in this three state variation births
are governed by the majority state.
EN: interesting grist for a sci-fi scenerio
regarding intergalatic civilizations.
Gen:0
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x = 7, y = 6, rule = Immigration
.2A$A$3.A$.2A2.2B$4.2B$6.B!
Gen:6
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x = 7, y = 6, rule = Immigration
.2A$A$3.A$.2A2.2B$4.2B$6.B!
Ratios, Quotients, Factors, and Miscellaneous Measures . . .
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V. Everett Boyer of San Diego, Ca. previously (No.8,p.5) defined the
procrastination quotient as the ratio of age to the product of the
initial and final populations. By this measure, a procrastinator is
an object whose PQP is large but finite. Unfortunately, this does not apply to patterns like the
'diehard' shown here (also see No.2,p.13) because
the final census is total extinction which therefore gives an infinite measure of PQP. (EN: the
diehard PQP = 118/8x0 = inf.). To get around this
problem, Gosper has suggested another related
measure which is equal to the age divided by the sum of the initial
and final populations. This ratio is somewhat more comprehensive
since it credits long age as well as minimum (even zero) final population for patterns that procrastinate. It does not, however, properly credit small initial patterns. Note that the diehard has a PQS
= 118/8+0 = 14.750 which now tops the structurally similar object reported
last issue with a PQS = 189/8+6 = 13.500.
EN: can you identify the special set of objects of size = n whose
PQS is maximum for n = 3, 4, 5, ... ?
Reader Briefs . . .
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Hugh W. Thompson of Lefrak City, N.Y.
notes that the nonomino:
which looks more like
the Greek letter Pi than
the oft-mentioned pi-heptomino, terminates in the
'pi' constellation in exactly the same
number of moves!
EN: recall this is 6 blocks, 2 ponds, and 5 blinkers after 173 gens.
Wainwright has experimented with
various infinite fields of regular stable
patterns, which he calls agars—rich culture mediums. When, for instance, a single "virus," or bit, is placed in the agar
of blocks shown in the illustration at
bottom left so that it touches the corners
of four blocks, the agar eliminates the
virus and repairs itself in two moves. If,
however, the alien bit is positioned as
shown (or at any of the seven other symmetrically equivalent spots), it initiates
an inexorable disintegration of the pattern. The portion eaten away contains
active debris that has overall bilateral
symmetry along one axis and a roughly
oval border that expands, probably forever, in the four compass directions at
the speed of light.
Gardner discusses some of the work that the writer did with seeded
agars. For reference, I have included this material here on the
bottom of page six. Robert R. Korfhage of Dallas, Tx. has been experimenting with seeded finite block agars and submits a particular
arrangement that evolves into the period three pulsar. Korfhage
notes that an arrangement of a dozen blocks when properly seeded
(see area outlined in Scientific American reference), will in 61
generations, form the pulsar. The final result is shown at the
bottom right of page six in a printout supplied by Robert Bison of
Hopewell Jct., N.Y.. (Bison references the original pattern with (O)
and shows the final pattern with (X)).
EN: the pi grandson is really a small seeded agar!
Lifequote:
'May you never have less than two neighbors, nor more than three!'
New and interesting developments in this variation of Life continue
to be reported by many readers. One of these readers, Tom Webster
of La Mesa, Ca. has reported the greatest variety of new material
than any other single reader. I would now like to present a sample
of Webster's findings. (EN: recall the simple rules in this variation; 3 or 4 bits for birth and 3 or 4 bits for survival. In
otherwords, a cell will be occupied in the next generation if and
only if it now has 3 or 4 neighbors regardless if it is now empty
or occupied).
'I have been doing extensive work with 3-4 Life and am very excited
with its possibilities. I have tracked all ominoes up through and
including order eight and now have them catalogued. However, 29 of
the octominoes grow too large for my 72 by 72 matrix. Of the rest,
126 die, 58 become a period two clock (my term) and 43 become a T
(my term). Only 2 become blocks. The others become one of twenty
different oscillators.'
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 THUMBLAUNCH ]]
#C [[ COLOR LABEL Gray LABELZOOMRANGE -2048 2048 LABELSHADOW OFF ]]
#C [[ COLOR ARROW Black ARROWZOOMRANGE -2048 2048 ARROWSHADOW OFF ]]
#C [[ COLOR POLY Black POLYZOOMRANGE -2048 2048 POLYSHADOW OFF POLYALPHA 0.15 ]]
#C [[ THUMBZOOM 64 ]]
#C [[ WIDTH 960 ]]
#C [[ HEIGHT 384 ]]
#C [[ SUPPRESS ]]
#C [[ THUMBSIZE 4 ]]
#C [[ LABEL -5 0 12 "octomino" ]]
#C [[ X -2.5 ]]
#C Note that this octomino does not evolve into the
#C "double small T in 13" as claimed. Instead, the
#C following is the unique octomino that evolves into
#C the double small T (and it does so in 13 generations):
#C
#C oooo
#C o ooo
#C
x = 4, y = 4, rule = B34/S34
o$3o$obo$2b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 THUMBLAUNCH ]]
#C [[ COLOR LABEL Gray LABELZOOMRANGE -2048 2048 LABELSHADOW OFF ]]
#C [[ COLOR ARROW Black ARROWZOOMRANGE -2048 2048 ARROWSHADOW OFF ]]
#C [[ COLOR POLY Black POLYZOOMRANGE -2048 2048 POLYSHADOW OFF POLYALPHA 0.15 ]]
#C [[ THUMBZOOM 64 ]]
#C [[ WIDTH 960 ]]
#C [[ HEIGHT 448 ]]
#C [[ SUPPRESS ]]
#C [[ THUMBSIZE 4 ]]
#C [[ LABEL -4 0 12 "double\nsmall T\nin 13" ]]
#C [[ X -2.5 ]]
#C The following is the unique octomino that evolves into
#C the double small T (and it does so in 13 generations):
#C
#C oooo
#C o ooo
#C
x = 7, y = 5, rule = B34/S34
5bo2$3ob3o2$bo!
M#1
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 THUMBLAUNCH ]]
#C [[ COLOR LABEL Gray LABELZOOMRANGE -2048 2048 LABELSHADOW OFF ]]
#C [[ COLOR ARROW Black ARROWZOOMRANGE -2048 2048 ARROWSHADOW OFF ]]
#C [[ COLOR POLY Black POLYZOOMRANGE -2048 2048 POLYSHADOW OFF POLYALPHA 0.15 ]]
#C [[ THUMBZOOM 64 ]]
#C [[ WIDTH 640 ]]
#C [[ HEIGHT 448 ]]
#C [[ SUPPRESS ]]
#C [[ THUMBSIZE 4 ]]
#C [[ ZOOM 8 ]]
x = 4, y = 3, rule = B34/S34
2o$b2o$2b2o!
'Of the 29 unknown octominoes, 19 become at
some point the pattern I call M#1, which is
the smallest omino methuselah somewhat
analogous to the R-pentomino. I ran M#1 for
271 generations and to a population of 1444
at which time it grew out of my matrix! I
would appreciate the final census of this
omino from anyone with a program capable of
larger sizes.' (EN: the writer strongly suspects that 3-4 LIFE does
not meet Conway's first desiderata! A shame).
becomes a T in
the position
shown with (X)
in generation 26.
'One more item in conclusion: a way of shooting a spaceship at a fuse
that breaks the fuse, lets it burn from the inside, and reverses the
spaceship and shoots it back out in generation seven leaving the
small T stabilizers behind.'
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 THUMBLAUNCH ]]
#C [[ COLOR LABEL Gray LABELZOOMRANGE -2048 2048 LABELSHADOW OFF ]]
#C [[ COLOR ARROW Black ARROWZOOMRANGE -2048 2048 ARROWSHADOW OFF ]]
#C [[ COLOR POLY Black POLYZOOMRANGE -2048 2048 POLYSHADOW OFF POLYALPHA 0.15 ]]
#C [[ THUMBZOOM 56 ]]
#C [[ WIDTH 1680 ]]
#C [[ HEIGHT 448 ]]
#C [[ SUPPRESS ]]
#C [[ THUMBSIZE 3 ]]
x = 28, y = 6, rule = B34/S34
3o2b2o2b2o2b2o2b2o2b2o2b3o$3b2o2b2o2b2o2b2o2b2o2b2o$bo24bo2$13b2o$12b
4o!
COMING EVENTS:
This space is reserved for
your unknown pattern or any
challenge that you want
published for the readers:
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 THUMBLAUNCH ]]
#C [[ COLOR LABEL Gray LABELZOOMRANGE -2048 2048 LABELSHADOW OFF ]]
#C [[ COLOR ARROW Black ARROWZOOMRANGE -2048 2048 ARROWSHADOW OFF ]]
#C [[ COLOR POLY Black POLYZOOMRANGE -2048 2048 POLYSHADOW OFF POLYALPHA 0.15 ]]
#C [[ THUMBZOOM 24 ]]
#C [[ WIDTH 624 ]]
#C [[ HEIGHT 480 ]]
#C [[ SUPPRESS ]]
#C [[ THUMBSIZE 2 ]]
#C [[ GRIDMAJOR 10 ]]
#C [[ X 5 Y 0 ]]
!
EN: mail it in too!
a summary of Life ratios and measures and the set of record holders
null cells and permanent cells and their implications!
results of straight rows of n-bits up thru n = 50
a set of period 2, 4, 6, 8, 10 , 12 oscillators from the 3-4 universe
Thompson has now tracked about half of the 1285 nonominoes and in doing so came across these two which he could not track therefore they are still unk:
N-1
N-2
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 THUMBLAUNCH ]]
#C [[ COLOR LABEL Gray LABELZOOMRANGE -2048 2048 LABELSHADOW OFF ]]
#C [[ COLOR ARROW Black ARROWZOOMRANGE -2048 2048 ARROWSHADOW OFF ]]
#C [[ COLOR POLY Black POLYZOOMRANGE -2048 2048 POLYSHADOW OFF POLYALPHA 0.15 ]]
#C [[ THUMBZOOM 64 ]]
#C [[ WIDTH 576 ]]
#C [[ HEIGHT 384 ]]
#C [[ SUPPRESS ]]
#C [[ THUMBSIZE 4 ]]
#C [[ ZOOM 2 ]]
o$5o$o3bo$4bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 THUMBLAUNCH ]]
#C [[ COLOR LABEL Gray LABELZOOMRANGE -2048 2048 LABELSHADOW OFF ]]
#C [[ COLOR ARROW Black ARROWZOOMRANGE -2048 2048 ARROWSHADOW OFF ]]
#C [[ COLOR POLY Black POLYZOOMRANGE -2048 2048 POLYSHADOW OFF POLYALPHA 0.15 ]]
#C [[ THUMBZOOM 64 ]]
#C [[ WIDTH 640 ]]
#C [[ HEIGHT 384 ]]
#C [[ SUPPRESS ]]
#C [[ THUMBSIZE 4 ]]
#C [[ ZOOM 2 ]]
#C [[ Y 1 ]]
o2bo$5o$4b2o!
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