Difference between revisions of "Lifeline Volume 8"
(New page: __NOTOC__{{LifeLine|vol=8|date=December 1972}} <center><pre>A QUARTERLY NEWSLETTER FOR ENTHUSIASTS OF JOHN CONWAY'S GAME OF LIFE O OOOOO OOOOO OOOOO O OOOOO O O OOOOO O O...) |
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__NOTOC__{{LifeLine|vol=8|date=December 1972}} | __NOTOC__{{LifeLine|vol=8|date=December 1972}} | ||
< | ====Page 1==== | ||
<small>''View [[:File:Lifeline vol 8.png|scan of this page]]''</small> | |||
[[Conway's Game of Life|Life]] is enjoying a revival of activity as evidenced by recent reader response containing many amazing new discoveries. Specific among these are included a basically new type of [[puffer train]] which can be used to generate all kinds of objects including [[glider|gliders]](!), some exotic collisions involving only gliders and [[block]]s which may be used to assemble new types of [[spaceship]] [[gun]]s as well as build the logical circuitry for a Life computer, and many exciting [[oscillator]]s including a [[predecessor]] for the [[tumbler]]! Some of this material is contained herein; however, additional time will be required in order to present all the findings in such a way so that they will compliment and reinforce work previously reported. | |||
{| class="wikitable" style="margin-left: auto; margin-right: auto;" | |||
! style="text-align:left" |[[Buckingham's combine|'Buckinghams Combine']] revisited . . . | |||
|- | |||
|{{LV:Viewer|{{LifeViewer config/lifeline|zoom=24|width=70|height=30}} | |||
#C [[ THUMBSIZE 3 ]] | |||
#C [[ LABEL -1.5 0 8 "a" ]] | |||
#C [[ LABEL 21.5 0 8 "b" ]] | |||
#C [[ LABEL 34 0 8 "c" ]] | |||
#C [[ LABEL 50 0 8 "d" ]] | |||
#C [[ LABEL 0 15 8 "e" ]] | |||
#C [[ LABEL 17 15 8 "f" ]] | |||
#C [[ LABEL 34 15 8 "g" ]] | |||
#C [[ LABEL 48 15 8 "h" ]] | |||
#C Note that pattern g fails (see Lifeline #9 page 3 for correction) | |||
2o16b2o3b2o4b2o9bo16bo$bo16bo5bo4bo9bobo13b5o$bobo12bobo5bob2obo8bobob | |||
o11bo5bo$2b2o12b2o7bo2bo9bo3bo8bo2bo2b3obo$7bo4bo13bo9b2o2bo2b2o5bobob | |||
obo4bo2bo$5b2ob4ob2o13bo6bo4bo4bo5bo2bo4bobobobo$7bo4bo11b2o8bobob2ob | |||
2obobo7bob3o2bo2bo$2b2o12b2o10b2o5bo4bo4bo9bo5bo$bobo12bobo6bo10b2o2bo | |||
2b2o11b5o$bo16bo8bo10bo3bo15bo$2o16b2o5bo2bo9bobobo$7bo16bob2obo9bobo$ | |||
6bobo15bo4bo10bo$7bo15b2o4b2o2$5b5o31b2o8b2o8b2o$4bo5bob2o6b2o5b2o13bo | |||
8bobo6bobo$3bob2o3bob2o6bo7bo10b3o11bo6bo$3bobo2bobo6b2obo7bob2o6bo3b | |||
3o6bob2o4b2obo$2obo3b2obo6b2obob5obob2o5bo3bo2bo4b3o2bo4bo2b3o$2obo5bo | |||
11bo2bo2bo9bobobobo4bo3bo8bo3bo$4b5o13b5o8b2o4bob2o4b3o2bo4bo2b3o$34bo | |||
2b4o10bob2o4b2obo$6bo17bo9b2o17bo6bo$5bobo15bobo13b2o10bobo6bobo$6bo | |||
17bo14b2o10b2o8b2o! | |||
|[[File:Lifeline vol08 101.png]] | |||
}} | |||
|} | |||
This profusion of material sent in as well as the torrent of reader replys<!--sic--> from [[Martin Gardner]]'s recent plug in Scientific American have really affected my plans to issue LIFELINE. However, with Number Eight now published and mailed, we are again back on schedule and I will resume the regular quarterly publication with Number Nine in March 1973. On the last page of this issue you will find a LIFESAVER form required for renewal of your LIFELINE subscription. | |||
====Page 2==== | |||
<small>''View [[:File:Lifeline vol 8 p2.jpg|scan of this page]]''</small> | |||
{| class="wikitable" | |||
|+ style="text-align:left" | Class E, Evolutionaries, Exercises, Events, Et cetera . . . | |||
|<div style="float:right">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=64|width=10|height=5}} | |||
#C [[ THUMBSIZE 4 ]] | |||
2o2bo$2obobo$4b2o! | |||
|[[File:Lifeline vol08 201.png]] | |||
}}</div> | |||
[[Paul Schick]] of Madison, Wi. notes the following interaction involving a [[block]] and a [[boat]] which in eight generations form a [[block]] and a [[beehive]]. The [[block]] and [[beehive]] in turn interacts as described on page five of [[Lifeline Volume 3|LIFELINE Number Three]] to form another [[block]] and [[beehive]]. (EN: also see [[Lifeline Volume 6#Page 2|No.6,p.2]]) | |||
|} | |||
{| class="wikitable" | |||
|+ style="text-align:left" | Class I, Still Lifes and Stable Forms . . . | |||
! style="text-align:left" | LIFEXPLAINATIONS<!--sic--> by [[Paul Dietz]] of Ellicott City, Md. | |||
|- | |||
|<div style="float:right">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=24|width=50|height=20}} | |||
#C [[ THUMBSIZE 3 ]] | |||
#C [[ GRIDMAJOR 10 ]] | |||
#C [[ X 2 ]] | |||
#C [[ ARROW 4.5 7.5 4.5 11 6 ]] | |||
#C [[ ARROW 14.5 7.5 14.5 11 6 ]] | |||
#C [[ ARROW 24.5 7.5 24.5 11 6 ]] | |||
#C [[ ARROW 34.5 7.5 34.5 11 6 ]] | |||
#C [[ ARROW 44.5 7.5 44.5 11 6 ]] | |||
#C [[ COLOR POLY White ]] | |||
#C [[ POLYALPHA 0.5 ]] | |||
#C [[ POLYT 0 0 0 ]] | |||
#C [[ POLYFILL {{PolyCell|x=6|y=3}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=16|y=3}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=16|y=6}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=26|y=3}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=23|y=6}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=36|y=3}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=36|y=6}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=33|y=6}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=46|y=3}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=46|y=6}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=43|y=6}} 64 ]] | |||
#C [[ POLYFILL {{PolyCell|x=43|y=3}} 64 ]] | |||
3$6bo9bo9bo9bo6bo2bo$4b2o8b2o8b2o8b2o8b2o$4b2o8b2o8b2o8b2o8b2o$16bo6bo | |||
9bo2bo6bo2bo7$5bo9bo9bo9bo8b2o$4bobo7bobo7bobo7bobo6bo2bo$4b2o8bobo6bo | |||
bo7bo2bo6bo2bo$15bo8bo9b2o8b2o! | |||
|[[File:Lifeline vol08 202.png]] | |||
}}</div> | |||
I have noticed a surprising phenomenon in Life regarding the [[block|smallest and most compact stable object]]. In all cases where a single bit is placed on one or more corners of a [[block]], a new stable configuration is formed the next generation. Also to be noted is the fact that the size of the resulting object in all cases is equal to four (the size of the block) plus the total number of bits placed on the corners. These are shown at the right. | |||
EN: this generality also applies in at least three instances involving bit-pairs thereby adding credibility to Dietz's Lifexplaination<!--sic-->. Can you identify these? | |||
|- | |||
! style="text-align:left" | Ten-bit Still Lifes by [[Everett Boyer|V. Everett Boyer]] of San Diego, Ca. | |||
|- | |||
|<div style="float:right">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=64|width=14|height=7}} | |||
#C [[ THUMBSIZE 4 ]] | |||
b2o6bobo$o2bo4bob2o$obobo3bo$bobo5b3o$2bo8bo! | |||
|[[File:Lifeline vol08 203.png]] | |||
}}</div> | |||
There are at least 25 [[:Category:Strict still lifes with 10 cells|stable objects of size ten]], but these two are especially easy to miss. Will those who committed themselves to only 24 check their lists! | |||
EN: I have checked my list and it still contains only 24 objects! | |||
|} | |||
====Page | {| class="wikitable" | ||
[[ | |+ style="text-align:left" | Class II, Oscillators . . . | ||
|- | |||
| colspan=3 |The eight objects shown on the [[#Page 1|cover page]] of LIFELINE Number Eight were discovered and sent in by [[David Buckingham]], [[Mark Niemiec]], and [[Peter Raynham]] of Sarnia, Ontario, Canada. These were chosen by the writer from those sent in by this ingenious prolific group who have now reported over fifty new oscillators of periods greater than two! Since each of the obejcts shown on the cover are easy to track, I will leave for the reader the enjoyment of determining their periods which incidentally are all different. Like the collection presented on the cover of [[Lifeline Volume 5|LIFELINE Number Five]] this arrangement as shown will reappear again only after 2,520 generations. Details, credits etc. next issue. | |||
|- | |||
| style="border:none;vertical-align:top" | [[Paul Schick|Schick]] has submitted an arrangement of two simple objects which when properly bounded, on a small finite surface will evolve into a <u>[[tumbler]]</u>! Shown here is a row of sixteen bits with one bit removed.(cont. on [[#Page 5|page 5]]) | |||
| style="border:none;text-align:right;width:250px" | {{LV:Viewer|{{LifeViewer config/lifeline|zoom=48|width=20|height=11}} | |||
#C [[ THUMBSIZE 4 ]] | |||
#C [[ X 0 ]] | |||
<nowiki> | |||
x = 20, y = 11, rule = B3/S23:P20,11 | |||
5$b5ob10o! | |||
</nowiki> | |||
|[[File:Lifeline vol08 204.png]] | |||
}} | |||
| style="border:none" |11×20<br />finite<br />surface<br /> ↲ | |||
|} | |||
====Page 3==== | |||
<small>''View [[:File:Lifeline vol 8 p3.jpg|scan of this page]]''</small> | |||
{| class="wikitable" | |||
|+ style="text-align:left" | Reader Article . . . | |||
|- | |||
! <u>Progress on the "Life Codex"</u> | |||
by [[Hugh W. Thompson]] | |||
|- | |||
|[[Bob Wainwright]] has mentioned my work on my "Life Codex" several times in LIFELINE. Now that its format and ultimate scope have firmed up, I think it is appropriate for me to step to stage center and describe the thing in detail. | |||
The Codex itself simply contains pictures of the "Life" objects, from three cells on up, arranged by number of cells, with a sequence number assigned to each object. A sample page is shown (see page 5 ). The complete "Life Codex Number" (LC#) of an object is the number of cells, followed by the sequence number in parentheses. Thus our old friends "[[R-pentomino|r]]" and "[[Pi-heptomino|π]]" have the prosaic designations of 5(9) and 7(101), respectively; the "[[beehive]]" is 6(485). The Codex divides logically, but not physically, into two segments: a "fixed" portion and a "random" portion. The fixed portion consists of objects to which I have assigned sequence numbers, in a more or less logical manner, before their histories were known. It includes all possible objects from 3 to 6 cells, the 3031 7-cell "[[polyplet|tangoes]]", the 369 [[octomino]]es plus a few other 8-cell tangoes, the 1285 [[nonomino]]es, about 100 [[decomino]]es, the straight [[n-omino]]es (n-rows) for n = 11 thru 22, and all simple objects discussed in SCIENTIFIC AMERICAN and LIFELINE, a total of roughly 12,700 objects. (By "simple" objects I specifically exclude such esoterics as [[glider gun]]s, [[billiard table|billiard-table]] configurations, [[fuse]]s, [[agar]]s, etc.) The random portion consists of objects which occur as descendants of the "fixed" objects, those sent to me by other contributors, directly or thru [[Bob Wainwright|Bob]], any which show up in future issues of LIFELINE, and any others which look interesting. These are sequenced on a first-come-first-served basis. This random portion, of course, is growing by leaps and bounds as I add more life histories, so that the total Codex consists of nearly 23,000 objects to date (Jan. 10th), and will likely be well over 30,000 by the time the Codex is "finished". | |||
(A note about the word "tango" which I used above. This is a term coined by [[Curt Gibson]] to denote a kingwise-connected object, probably derived from the word "tangent". I would like to see it become common usage, since it is short, colorful and convenient. Gibson's word for a spatially-connected object, "incontinuo", is less pithy but could also be useful.) | |||
The Codex has four companion volumes. The first, the Life History and Cross-Reference, lists each object by LC#, followed by the LC#'s of its successive generations until one of three things happens: (1) an object occurs (or a pattern) whose history has already been recorded; (2) a stable object or pattern occurs in 50 generations or less; (3) at least 20 generations have been recorded for a [[methuselah]] (51 gens. or more). Option (2) includes objects which die, since an empty universe is about as stable as you can get. Then follows an indication of the eventual terminus – stable object or pattern, death, or methuselah constellation – and the LC# of the first ancestor of the | |||
|} | |||
====Page 4==== | |||
<small>''View [[:File:Lifeline vol 8 p4.jpg|scan of this page]]''</small> | |||
{| class="wikitable" | |||
|object (if any). The second, the Terminus Cross-Reference, lists, for each stable object, pattern or [[methuselah]] constellation,all objects whose terminus is the given object or pattern. The stable objects and "short-life" patterns are arranged by [[Bob Wainwright|Bob]]'s original classification scheme, with a separate book (Class V-A) for objects that die. [[Methuselah]] constellations are arranged by the LC# of the "primary" (usually the first object, i.e. lowest LC#, to result in the given constellation). Listed for each object with a given terminus are the LC#, number of generations, first (lowest LC#) father, if any, and son. Listed also for methusaleh "secondaries" are the first ancestor and the generation numbers of the secondary and primary, respectively, which are identical. The third book is the [[Methuselah]] extract, giving, on a separate page for each primary, a picture of the primary, a picture, if available, of the final constellation, the number of generations, and such other demographic data as the maximum and final populations and the class of the final constellation (static, periodic, dead, or containing gliders). The fourth "book" is a codex of the "short-life" patterns which have occurred as termini of Life objects. These are pictured on 4x6 index cards, with descriptive notes as needed. The LC# for these consists of the <u>total</u> number of cells, followed by the letter P, followed by a sequence number which is merely the order in which the pattern was encountered in the History. "[[Traffic light]]s", for example, is 12P1. | |||
As of this writing, the Life History and the other subsidiary volumes are complete thru about the first third of the nonominoes, leaving perhaps 1300 objects in the Codex whose history is unknown. | |||
What is the use of all this compilation? Well, what was the "use" of climbing Mount Everest, or tabulating the first million prime numbers? apart from keeping me amused, and leading to the discovery of many objects with remarkable, and even esthetically<!--sic--> pleasing, life histories, the Codex and its satellite volumes have already seen some use as a quesiton-answerer. A correspondent will write in with an object whose history is unknown to him, and after a look at the Life History, I can reply "Your object becomes a [[beehive]] in 35 moves", or whatever. Eventually I expect the Codex, etc., to become a compendium of all known simple objects, with their life histories. Eventually also, I expect <u>my</u> task to consist primarily of logging in the results obtained by others. Accordingly I am taking the fearful risk of listing my address with this article. If you have an object you wish to add to the Codex (or to find out if it's already there), send it on. Also, I reproduced this particular page of the Codex for a reason – except for 10(1), which becomes the [[pentadecathlon]], <u>all</u> of these decominoes are "unknown" to me, anyway. If you want to track a few histories and lay them on me, feel free. | |||
EN: see Lifequote on [[#Page 7|page seven]]! | |||
|} | |||
====Page 5==== | |||
<small>''View [[:File:Lifeline vol 8 p5.jpg|scan of this page]]''</small> | |||
{| class="wikitable" | |||
| colspan=3 style="text-align:center" | Sample "Life Codex" page | |||
[[File:Lifeline vol08 501.png]] | |||
|- | |||
| style="border:none;vertical-align:top;" | (cont. from [[#Page 2|page 2]]) | |||
The five-bit row is the familiar [[traffic light|traffic lite]]<!--sic--> precursor and the ten-bit row the familiar pentadecathlon predecessor. Together as shown within the 11 by 20 bounded area they evolve in 29 generations into two [[blinker]]s and a [[tumbler]]! During the process, the north, south, and west border must by 'inducted'. If four mirror pairs of these rectangles are laid side by side (120 bits in all), they will evolve into 4 [[block]]s, 12 [[blinker]]s, and 2 [[tumbler]]s. EN: the [[T-tetromino]] is proving to be a virile ingredient for [[oscillator]]s ([[traffic light|t.lite]], [[pulsar]], [[tumbler]], and [[pentadecathlon]]) . . . any others? | |||
| style="border:none;text-align:right;width:250px" | {{LV:Viewer|{{LifeViewer config/lifeline|zoom=32|width=41|height=47}} | |||
#C [[ THUMBSIZE 4 ]] | |||
5$3b10ob5o3b5ob10o12$3b10ob5o3b5ob10o12$3b10ob5o3b5ob10o12$3b10ob5o3b | |||
5ob10o! | |||
|[[File:Lifeline vol08 502.png]] | |||
}} | |||
| style="border:none" |47×41<br />unbounded<br />area<br /> ↲ | |||
|} | |||
{| class="wikitable" | |||
|+ style="text-align:left" | <span class="anchor" id="Procrastination Quotient"></span>Reader Briefs . . . | |||
|<div style="float:left">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=64|width=9|height=5}} | |||
#C [[ THUMBSIZE 4 ]] | |||
o3bo$5o$o! | |||
|[[File:Lifeline vol08 503.png]] | |||
}}</div> | |||
<div style="float:right">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=64|width=9|height=6}} | |||
#C [[ THUMBSIZE 4 ]] | |||
3o$2bo$2bo2bo$4bobo! | |||
|[[File:Lifeline vol08 504.png]] | |||
}}</div> | |||
[[Don Woods]] of Princeton, N.J. who first suggested measuring age to initial size (see [[Lifeline Volume 1#Page 6|No.1,p.6]]) has allowed for tracking just about all previously defined ratios and statistics in his general purpose program. One more that I would add is the 'procrastination quotient' as suggested by [[Everett Boyer|Boyer]]. Boyer defines this measure as the age divided by the product of the initial and final populations where the initial configuration must be a single object (see [[Lifeline Volume 2#Page 12|No.2,p.12]]). For all three-bit objects this value is maximum for the [[Pre-block|block predecessor]] (PQ = 1/3x4 = 0.083) since all other patterns die. For all four-bit objects this measure is maximum for the familiar [[T-tetromino]] grandfather (PQ = 0.229). A five-bit [[R-pentomino]] grandfather has a value of 1.905. The familiar [[procrastinator]] (see [[Lifeline Volume 4#Page 4|No.4,p.4]]) holds the record for all seven-bit objects with a value of 1.810. [[Hugh Thompson|Thompson]] reports the eight-bit object above left which is active for 78 generations before stabilizing into a single blinker (PQ = 78/8x3 = 3.250). Another eight-bit pattern reported by Thompson however runs for 189 generations before forming a [[beehive]]. This sets the current record for <u>all</u> objects with a procrastination quotient of 3.937. | |||
|} | |||
====Page 6==== | |||
<small>''View [[:File:Lifeline vol 8 p6.jpg|scan of this page]]''</small> | |||
{| class="wikitable" style="text-align:left" | |||
|+ style="text-align:left" |Lifearticle . . . | |||
|- | |||
| colspan=2 |<pre> ooooooooooooooooooooooooooooo oooo Systems | |||
ooooooooooooooooooooooooooooooooo oooo Dimensions | |||
ooooooooooooooooooooooooooooooooooooooo Limited | |||
oooo oooooooo | |||
oooooooooooooooo oooo ooooooo | |||
oooooooooooooooo oooo ooooooo SYSTEMLETTER | |||
ooooooooooooooooooo ooooooo | |||
ooooooo ooooooooo | |||
ooooooooooooooooooooooooooooooooooo ooooooooooooooooo Fall 1972 | |||
ooooooooooooooooo oooooooooooooooo oooooooooooooooo | |||
oooooooooooooooo oooooooooooooo oooooooooooooo | |||
page 5</pre> | |||
|- | |||
| rowspan=3 |'''THE GAME OF LIFE''' | |||
"the Game Of Life" (Scientific Arnerican, <s>November</s> October | |||
1970) can be basically described as a set of rules which | |||
determine the growth pattern of any given cell structure. | |||
Hence, a particular cell structure may grow and multiply | |||
with succeeding generations and another structure may | |||
in fact die after several generations. The algorithms for | |||
cell propogation have been applied to some serious | |||
research projects dealing with human cell structure, but | |||
they have also been used for recreational programming. | |||
The Iverson Computer Science Club (group of high | |||
school students which meets at SDL, Ottawa, Saturday | |||
mornings) have applied the Game of Life to a cell structure | |||
which approximates the SDL Logo. After 75 | |||
generations the logo has grown to (and stabilized at) the | |||
cell structure pictured below. | |||
<center>{{LV:Viewer|{{LifeViewer config/lifeline|zoom=24|width=73|height=36}} | |||
#C [[ THUMBSIZE 3 ]] | |||
#C [[ STARTFROM 75 ]] | |||
#C [[ X 5.5 Y -2 ]] | |||
#C [[ ZOOM 5 ]] | |||
3b29o3b4o$b33ob4o$39o$4o27b8o$16o2b4o10b7o$b16ob4o10b7o$3b19o10b7o$15b | |||
7o9b9o$35ob17o$17ob16o3b16o$16o2b14o7b14o! | |||
|[[File:Lifeline_vol08_601.png]] | |||
}}</center> | |||
Since the logo symbolically represents SDL as a company | |||
it's interesting to speculate what this new structure | |||
might represent. If you have any ideas we would like to | |||
hear from you. | |||
If you would like a free copy of the program and instructions | |||
on how to apply it to your corporate symbol | |||
please contact Dot Romhild, Secretary, Cus<!--prevent spam filter editing block-->tomer Service | |||
and Education, Ottawa. Your Board of Directors | |||
might be interested in a look into the future. | |||
! style="text-align:left" | | |||
Excursions Into the Universe | |||
of [[OCA:3-4 Life|'3-4' Life]] . . . | |||
|- | |||
| | |||
The following period two | |||
oscillators all operate by | |||
having four '[[rotor|active bits]]' | |||
vibrating around respectively | |||
three, six, and nine [[stator|stable | |||
bits]]. | |||
|- | |||
| | |||
III by Tom Webster | |||
of La Mesa, Ca. | |||
<center>{{LV:Viewer|{{LifeViewer config/lifeline|zoom=30|width=20|height=10}} | |||
#C [[ THUMBSIZE 3 ]] | |||
#C [[ GRIDMAJOR 10 ]] | |||
#C [[ AGESTATES 1 ]] | |||
#C [[ COLOR BACKGROUND White ]] | |||
#C [[ COLOR ALIVE Black ]] | |||
#C [[ COLOR ALIVERAMP Gray ]] | |||
#C [[ STARTFROM 2 ]] | |||
<nowiki> | |||
x = 20, y = 10, rule = B34/S34 | |||
3$5bo8bo$3bobo9b2o$4b3o6b3o$4bo10bo! | |||
</nowiki> | |||
|[[File:Lifeline_vol08_602.png]] | |||
}}</center> | |||
VI by Anonymous | |||
of L.A., Ca. | |||
<center>{{LV:Viewer|{{LifeViewer config/lifeline|zoom=30|width=20|height=10}} | |||
#C [[ THUMBSIZE 3 ]] | |||
#C [[ GRIDMAJOR 10 ]] | |||
#C [[ AGESTATES 1 ]] | |||
#C [[ COLOR BACKGROUND White ]] | |||
#C [[ COLOR ALIVE Black ]] | |||
#C [[ COLOR ALIVERAMP Gray ]] | |||
#C [[ STARTFROM 2 ]] | |||
<nowiki> | |||
x = 20, y = 10, rule = B34/S34 | |||
3$4b2o8b2o$2b2obo8bob2o$3bob2o6b2obo$3b2o10b2o! | |||
</nowiki> | |||
|[[File:Lifeline_vol08_603.png]] | |||
}}</center> | |||
IX ('cluster') | |||
by [[David Buckingham|Buckingham]] | |||
<center>{{LV:Viewer|{{LifeViewer config/lifeline|zoom=30|width=20|height=10}} | |||
#C [[ THUMBSIZE 3 ]] | |||
#C [[ GRIDMAJOR 10 ]] | |||
#C [[ AGESTATES 1 ]] | |||
#C [[ COLOR BACKGROUND White ]] | |||
#C [[ COLOR ALIVE Black ]] | |||
#C [[ COLOR ALIVERAMP Gray ]] | |||
#C [[ STARTFROM 2 ]] | |||
#C [[ Y 1 ]] | |||
<nowiki> | |||
x = 20, y = 10, rule = B34/S34 | |||
3$4b2o8b2o$2b2obo8bob2o$2bobobo6bobobo$3bob2o6b2obo$3b2o10b2o! | |||
</nowiki> | |||
|[[File:Lifeline_vol08_604.png]] | |||
}}</center> | |||
|} | |||
====Page 7==== | |||
<small>''View [[:File:Lifeline vol 8 p7.jpg|scan of this page]]''</small> | |||
{| class="wikitable" style="text-align:left" | |||
|+ style="text-align:left" |Reader Reply . . . | |||
|- | |||
|'''<u>Reregarding the '[[Titanic toroidal traveler|Titanic Troidial<!--original spelling--> Traveler]]' by David Buckingham</u>''' | |||
In Lifelines [[Lifeline Volume 4|4]] & [[Lifeline Volume 7|7]] the second 'Titanic Troidial Traveler was | |||
mentioned but was not given a proven census or period. The | |||
debris however, even though never becoming periodic, quickly | |||
develops into a [[pentadecathlon]] [[agar]], which can exist on a | |||
6 x N torus. | |||
It has been noted by David Buckingham and Mark Niemiec that a | |||
pentadec/2 expands indefinitely with a speed of almost C/5 in | |||
both directions. This idea can also be increased to create another | |||
class of oscillating agars. Thus, the exhaust of the | |||
TT II can never achieve a stable period. This idea is based | |||
on the following ideas: first of all the TT II creates TL's | |||
at the end which move in the direction opposite to the wick | |||
and they themselves are spaceships. After working with the | |||
pentadecathlon agars I have found that the only possible | |||
products in the field are [[bi-block|twin blocks]] [[File:Lifeline_vol08_701.png]], beehives, blinkers, | |||
and traffic lights and predicessors<!--sic--> thereto. If the stable | |||
debris is hit with a traffic light,or<!--sic--> some form thereof, it | |||
will eventually form a traffic light or die and therefore | |||
will not form a stable centre. If the stable centre does not | |||
form and the 2 part s<!--sic--> of the wick move further and further | |||
apart then more and more different debris forms. | |||
A simple example which comes to mind is this: since the inside | |||
(between the wick and the outer traffic light) will never | |||
stabilize, it will behave as an infinitely expanding pentadecathlon | |||
agar or the inside will die out. Therefore the wick | |||
and traffic light will create traffic lights that move towards | |||
each other causing a mutual annihalation<!--sic--> which will | |||
take an increasing number of generations to cause since the | |||
wick and the outer traffic light will constantly move further | |||
apart. I think that this concludes a proof that the second | |||
TTT has no finite period but possibly someone might figure | |||
out an exponential period for it. | |||
|} | |||
{| class="wikitable" style="text-align:left" | |||
|+ style="text-align:left;" |Lifequote submitted by Mark Linimon of Houston, Tx: | |||
|- | |||
|'Life is one long process of getting tired.' | |||
<div style='text-align: right;'>. . . Samuel Butler</div> | |||
|} | |||
'''LIFE SAVER''' | |||
{| style="text-align:center" | |||
| style="padding-right: 1em;" |LIFELINE back issue and subscription rates: | |||
| style="padding-left: 1em;padding-right: 1em;" | U.S. & Canada | |||
| style="padding-left: 1em;padding-right: 1em;" | Foreign | |||
|- | |||
| style="padding-left: 2em;padding-right: 1em;text-align:left" |1971 (Nos. 1-4) 70 pages total, per set | |||
| $10 || $15 | |||
|- | |||
| style="padding-left: 2em;padding-right: 1em;text-align:left" |1972 (Nos. 5-8) 32 pages total, per set | |||
| $4 || $6 | |||
|- | |||
| style="padding-left: 2em;padding-right: 1em;text-align:left" |1973 (Nos. 9-12) new subscription | |||
| $2 || $3 | |||
|} | |||
====Page 8==== | |||
<small>''View [[:File:Lifeline vol 8 p8.jpg|scan of this page]]''</small> | |||
{| class="wikitable" style="text-align:left" | |||
|+ style="text-align:left" |Reader Reply . . . | |||
|- | |||
! colspan=8 |Regarding Those 'Titanic Toroidal Travelers' by [[Bill Gosper|R. Wm. Gosper, Jr.]] | |||
|- | |||
| colspan=8 | | |||
The smoke puff emitted by A (see diagram below) before it becomes a | |||
spaceship is itself a puffer train equivalent to several B with | |||
different ages and displacements. Following one of these, calling | |||
C generation zero, we find a complex, nonperiodic puffer expanding | |||
in both directions at 7C/40 which consists of merely two C's whenever | |||
generation = 200x2exp.n. Two of those out of phase with each | |||
other will repeatedly react, causing their wave fronts to occasionally | |||
lurch forward at 9C/46, apparently at ever decreasing frequency. | |||
D moves at C/2, sends the same pattern in the opposite direction, | |||
and fills the intervening space with C's of various ages (mind | |||
boggling complexity). | |||
|- style="vertical-align: top" | |||
| style="border:none" |A | |||
| style="border:none" |{{LV:viewer|{{LifeViewer config/lifeline|zoom=64|width=10|height=6}} | |||
#C [[ THUMBSIZE 4 ]] | |||
#C [[ X 0 ]] | |||
<nowiki> | |||
x = 6, y = 2, rule = B3/S23:T6,0 | |||
6o$3o! | |||
</nowiki> | |||
|[[Image:Lifeline_vol08_801.png]] | |||
}} | |||
| style="border:none" |B | |||
| style="border:none" |{{LV:viewer|{{LifeViewer config/lifeline|zoom=64|width=10|height=6}} | |||
#C [[ THUMBSIZE 4 ]] | |||
#C [[ X 0 ]] | |||
<nowiki> | |||
x = 6, y = 2, rule = B3/S23:T6,0 | |||
3o$bo! | |||
</nowiki> | |||
|[[Image:Lifeline_vol08_802.png]] | |||
}} | |||
| style="border:none" |C | |||
| style="border:none" |{{LV:viewer|{{LifeViewer config/lifeline|zoom=64|width=10|height=7}} | |||
#C [[ THUMBSIZE 4 ]] | |||
#C [[ X 0 ]] | |||
<nowiki> | |||
x = 6, y = 3, rule = B3/S23:T6,0 | |||
3o$obo$3o! | |||
</nowiki> | |||
|[[Image:Lifeline_vol08_803.png]] | |||
}} | |||
| style="border:none" |D | |||
| style="border:none" |{{LV:viewer|{{LifeViewer config/lifeline|zoom=64|width=16|height=7}} | |||
#C [[ THUMBSIZE 4 ]] | |||
#C [[ X 0 ]] | |||
<nowiki> | |||
x = 12, y = 3, rule = B3/S23:T12,0 | |||
3o3b3o$o2bobo2bo$o7bo! | |||
</nowiki> | |||
|[[Image:Lifeline_vol08_804.png]] | |||
}} | |||
|} | |||
Lifecomic by Harry J. Riley of Trenton, N.J. | |||
[[Image:Lifeline_vol08_805.png|600px|take me to your leader!]] | |||
{| class="wikitable" style="text-align:left" | |||
|+ style="text-align:left" |Lifequote: | |||
|- | |||
|'One way to get the most out of Life is to look upon it as an adventure'. | |||
<div style='text-align: right;'>. . . William Feather</div> | |||
|} | |||
'''<u>COMING EVENTS</u>:''' | |||
* some amazing pi-heptomino reactions | |||
* a host of clock predecessors | |||
* a new period thirty shuttle device | |||
* a period nine billiard tab le<!--sic--> construction | |||
* 'healthy patterns' that eradicate foreign implanted bits | |||
* a brand new series of 12n period puffer trains! | |||
* [[Lifeline Volume 9|LIFELINE Number Nine]] will be issued on schedule in March | |||
Yes, I would like to continue receiving LIFELINE. I am subscribing | |||
for my 1973 subscription as a: | |||
: ▢Regular member (now encloing<!--sic--> payment) | |||
: ▢Participating member (will contribute to newsletter) | |||
My correct mailing address is:<br /> | |||
Name:_________________________________________________________________<br /> | |||
Address:______________________________________________________________<br /> | |||
City:_______________________________State:_______________Zip:_________ | |||
==Page Scans== | ==Page Scans== |
Latest revision as of 16:03, 15 June 2023
Lifeline Volume 8 | ||
Published in | December 1972 | |
---|---|---|
Preceded by | Volume 7 | |
Succeeded by | Volume 9 |
This page is a transcript of Volume 8 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• Editor and Publisher: Robert T. Wainwright •NUMBER 8DECEMBER 1972
Page 1
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Life is enjoying a revival of activity as evidenced by recent reader response containing many amazing new discoveries. Specific among these are included a basically new type of puffer train which can be used to generate all kinds of objects including gliders(!), some exotic collisions involving only gliders and blocks which may be used to assemble new types of spaceship guns as well as build the logical circuitry for a Life computer, and many exciting oscillators including a predecessor for the tumbler! Some of this material is contained herein; however, additional time will be required in order to present all the findings in such a way so that they will compliment and reinforce work previously reported.
'Buckinghams Combine' revisited . . . |
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This profusion of material sent in as well as the torrent of reader replys from Martin Gardner's recent plug in Scientific American have really affected my plans to issue LIFELINE. However, with Number Eight now published and mailed, we are again back on schedule and I will resume the regular quarterly publication with Number Nine in March 1973. On the last page of this issue you will find a LIFESAVER form required for renewal of your LIFELINE subscription.
Page 2
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Paul Schick of Madison, Wi. notes the following interaction involving a block and a boat which in eight generations form a block and a beehive. The block and beehive in turn interacts as described on page five of LIFELINE Number Three to form another block and beehive. (EN: also see No.6,p.2) |
LIFEXPLAINATIONS by Paul Dietz of Ellicott City, Md. |
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I have noticed a surprising phenomenon in Life regarding the smallest and most compact stable object. In all cases where a single bit is placed on one or more corners of a block, a new stable configuration is formed the next generation. Also to be noted is the fact that the size of the resulting object in all cases is equal to four (the size of the block) plus the total number of bits placed on the corners. These are shown at the right. EN: this generality also applies in at least three instances involving bit-pairs thereby adding credibility to Dietz's Lifexplaination. Can you identify these? |
Ten-bit Still Lifes by V. Everett Boyer of San Diego, Ca. |
There are at least 25 stable objects of size ten, but these two are especially easy to miss. Will those who committed themselves to only 24 check their lists! EN: I have checked my list and it still contains only 24 objects! |
The eight objects shown on the cover page of LIFELINE Number Eight were discovered and sent in by David Buckingham, Mark Niemiec, and Peter Raynham of Sarnia, Ontario, Canada. These were chosen by the writer from those sent in by this ingenious prolific group who have now reported over fifty new oscillators of periods greater than two! Since each of the obejcts shown on the cover are easy to track, I will leave for the reader the enjoyment of determining their periods which incidentally are all different. Like the collection presented on the cover of LIFELINE Number Five this arrangement as shown will reappear again only after 2,520 generations. Details, credits etc. next issue. | ||
Schick has submitted an arrangement of two simple objects which when properly bounded, on a small finite surface will evolve into a tumbler! Shown here is a row of sixteen bits with one bit removed.(cont. on page 5) | 11×20 finite surface ↲ |
Page 3
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Progress on the "Life Codex" |
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Bob Wainwright has mentioned my work on my "Life Codex" several times in LIFELINE. Now that its format and ultimate scope have firmed up, I think it is appropriate for me to step to stage center and describe the thing in detail.
The Codex itself simply contains pictures of the "Life" objects, from three cells on up, arranged by number of cells, with a sequence number assigned to each object. A sample page is shown (see page 5 ). The complete "Life Codex Number" (LC#) of an object is the number of cells, followed by the sequence number in parentheses. Thus our old friends "r" and "π" have the prosaic designations of 5(9) and 7(101), respectively; the "beehive" is 6(485). The Codex divides logically, but not physically, into two segments: a "fixed" portion and a "random" portion. The fixed portion consists of objects to which I have assigned sequence numbers, in a more or less logical manner, before their histories were known. It includes all possible objects from 3 to 6 cells, the 3031 7-cell "tangoes", the 369 octominoes plus a few other 8-cell tangoes, the 1285 nonominoes, about 100 decominoes, the straight n-ominoes (n-rows) for n = 11 thru 22, and all simple objects discussed in SCIENTIFIC AMERICAN and LIFELINE, a total of roughly 12,700 objects. (By "simple" objects I specifically exclude such esoterics as glider guns, billiard-table configurations, fuses, agars, etc.) The random portion consists of objects which occur as descendants of the "fixed" objects, those sent to me by other contributors, directly or thru Bob, any which show up in future issues of LIFELINE, and any others which look interesting. These are sequenced on a first-come-first-served basis. This random portion, of course, is growing by leaps and bounds as I add more life histories, so that the total Codex consists of nearly 23,000 objects to date (Jan. 10th), and will likely be well over 30,000 by the time the Codex is "finished". (A note about the word "tango" which I used above. This is a term coined by Curt Gibson to denote a kingwise-connected object, probably derived from the word "tangent". I would like to see it become common usage, since it is short, colorful and convenient. Gibson's word for a spatially-connected object, "incontinuo", is less pithy but could also be useful.) The Codex has four companion volumes. The first, the Life History and Cross-Reference, lists each object by LC#, followed by the LC#'s of its successive generations until one of three things happens: (1) an object occurs (or a pattern) whose history has already been recorded; (2) a stable object or pattern occurs in 50 generations or less; (3) at least 20 generations have been recorded for a methuselah (51 gens. or more). Option (2) includes objects which die, since an empty universe is about as stable as you can get. Then follows an indication of the eventual terminus – stable object or pattern, death, or methuselah constellation – and the LC# of the first ancestor of the |
Page 4
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object (if any). The second, the Terminus Cross-Reference, lists, for each stable object, pattern or methuselah constellation,all objects whose terminus is the given object or pattern. The stable objects and "short-life" patterns are arranged by Bob's original classification scheme, with a separate book (Class V-A) for objects that die. Methuselah constellations are arranged by the LC# of the "primary" (usually the first object, i.e. lowest LC#, to result in the given constellation). Listed for each object with a given terminus are the LC#, number of generations, first (lowest LC#) father, if any, and son. Listed also for methusaleh "secondaries" are the first ancestor and the generation numbers of the secondary and primary, respectively, which are identical. The third book is the Methuselah extract, giving, on a separate page for each primary, a picture of the primary, a picture, if available, of the final constellation, the number of generations, and such other demographic data as the maximum and final populations and the class of the final constellation (static, periodic, dead, or containing gliders). The fourth "book" is a codex of the "short-life" patterns which have occurred as termini of Life objects. These are pictured on 4x6 index cards, with descriptive notes as needed. The LC# for these consists of the total number of cells, followed by the letter P, followed by a sequence number which is merely the order in which the pattern was encountered in the History. "Traffic lights", for example, is 12P1.
As of this writing, the Life History and the other subsidiary volumes are complete thru about the first third of the nonominoes, leaving perhaps 1300 objects in the Codex whose history is unknown. What is the use of all this compilation? Well, what was the "use" of climbing Mount Everest, or tabulating the first million prime numbers? apart from keeping me amused, and leading to the discovery of many objects with remarkable, and even esthetically pleasing, life histories, the Codex and its satellite volumes have already seen some use as a quesiton-answerer. A correspondent will write in with an object whose history is unknown to him, and after a look at the Life History, I can reply "Your object becomes a beehive in 35 moves", or whatever. Eventually I expect the Codex, etc., to become a compendium of all known simple objects, with their life histories. Eventually also, I expect my task to consist primarily of logging in the results obtained by others. Accordingly I am taking the fearful risk of listing my address with this article. If you have an object you wish to add to the Codex (or to find out if it's already there), send it on. Also, I reproduced this particular page of the Codex for a reason – except for 10(1), which becomes the pentadecathlon, all of these decominoes are "unknown" to me, anyway. If you want to track a few histories and lay them on me, feel free. EN: see Lifequote on page seven! |
Page 5
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Sample "Life Codex" page | ||
(cont. from page 2)
The five-bit row is the familiar traffic lite precursor and the ten-bit row the familiar pentadecathlon predecessor. Together as shown within the 11 by 20 bounded area they evolve in 29 generations into two blinkers and a tumbler! During the process, the north, south, and west border must by 'inducted'. If four mirror pairs of these rectangles are laid side by side (120 bits in all), they will evolve into 4 blocks, 12 blinkers, and 2 tumblers. EN: the T-tetromino is proving to be a virile ingredient for oscillators (t.lite, pulsar, tumbler, and pentadecathlon) . . . any others? |
47×41 unbounded area ↲ |
Don Woods of Princeton, N.J. who first suggested measuring age to initial size (see No.1,p.6) has allowed for tracking just about all previously defined ratios and statistics in his general purpose program. One more that I would add is the 'procrastination quotient' as suggested by Boyer. Boyer defines this measure as the age divided by the product of the initial and final populations where the initial configuration must be a single object (see No.2,p.12). For all three-bit objects this value is maximum for the block predecessor (PQ = 1/3x4 = 0.083) since all other patterns die. For all four-bit objects this measure is maximum for the familiar T-tetromino grandfather (PQ = 0.229). A five-bit R-pentomino grandfather has a value of 1.905. The familiar procrastinator (see No.4,p.4) holds the record for all seven-bit objects with a value of 1.810. Thompson reports the eight-bit object above left which is active for 78 generations before stabilizing into a single blinker (PQ = 78/8x3 = 3.250). Another eight-bit pattern reported by Thompson however runs for 189 generations before forming a beehive. This sets the current record for all objects with a procrastination quotient of 3.937. |
Page 6
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ooooooooooooooooooooooooooooo oooo Systems ooooooooooooooooooooooooooooooooo oooo Dimensions ooooooooooooooooooooooooooooooooooooooo Limited oooo oooooooo oooooooooooooooo oooo ooooooo oooooooooooooooo oooo ooooooo SYSTEMLETTER ooooooooooooooooooo ooooooo ooooooo ooooooooo ooooooooooooooooooooooooooooooooooo ooooooooooooooooo Fall 1972 ooooooooooooooooo oooooooooooooooo oooooooooooooooo oooooooooooooooo oooooooooooooo oooooooooooooo page 5 | |
THE GAME OF LIFE
"the Game Of Life" (Scientific Arnerican, The Iverson Computer Science Club (group of high school students which meets at SDL, Ottawa, Saturday mornings) have applied the Game of Life to a cell structure which approximates the SDL Logo. After 75 generations the logo has grown to (and stabilized at) the cell structure pictured below. Since the logo symbolically represents SDL as a company it's interesting to speculate what this new structure might represent. If you have any ideas we would like to hear from you. If you would like a free copy of the program and instructions on how to apply it to your corporate symbol please contact Dot Romhild, Secretary, Customer Service and Education, Ottawa. Your Board of Directors might be interested in a look into the future. |
Excursions Into the Universe of '3-4' Life . . . |
---|---|
The following period two oscillators all operate by having four 'active bits' vibrating around respectively three, six, and nine stable bits. | |
III by Tom Webster of La Mesa, Ca. VI by Anonymous of L.A., Ca. IX ('cluster') by Buckingham |
Page 7
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Reregarding the 'Titanic Troidial Traveler' by David Buckingham
In Lifelines 4 & 7 the second 'Titanic Troidial Traveler was mentioned but was not given a proven census or period. The debris however, even though never becoming periodic, quickly develops into a pentadecathlon agar, which can exist on a 6 x N torus. It has been noted by David Buckingham and Mark Niemiec that a pentadec/2 expands indefinitely with a speed of almost C/5 in both directions. This idea can also be increased to create another class of oscillating agars. Thus, the exhaust of the TT II can never achieve a stable period. This idea is based on the following ideas: first of all the TT II creates TL's at the end which move in the direction opposite to the wick and they themselves are spaceships. After working with the pentadecathlon agars I have found that the only possible products in the field are twin blocks , beehives, blinkers, and traffic lights and predicessors thereto. If the stable debris is hit with a traffic light,or some form thereof, it will eventually form a traffic light or die and therefore will not form a stable centre. If the stable centre does not form and the 2 part s of the wick move further and further apart then more and more different debris forms. A simple example which comes to mind is this: since the inside (between the wick and the outer traffic light) will never stabilize, it will behave as an infinitely expanding pentadecathlon agar or the inside will die out. Therefore the wick and traffic light will create traffic lights that move towards each other causing a mutual annihalation which will take an increasing number of generations to cause since the wick and the outer traffic light will constantly move further apart. I think that this concludes a proof that the second TTT has no finite period but possibly someone might figure out an exponential period for it. |
'Life is one long process of getting tired.'
. . . Samuel Butler
|
LIFE SAVER
LIFELINE back issue and subscription rates: | U.S. & Canada | Foreign |
1971 (Nos. 1-4) 70 pages total, per set | $10 | $15 |
1972 (Nos. 5-8) 32 pages total, per set | $4 | $6 |
1973 (Nos. 9-12) new subscription | $2 | $3 |
Page 8
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Regarding Those 'Titanic Toroidal Travelers' by R. Wm. Gosper, Jr. | |||||||
---|---|---|---|---|---|---|---|
The smoke puff emitted by A (see diagram below) before it becomes a spaceship is itself a puffer train equivalent to several B with different ages and displacements. Following one of these, calling C generation zero, we find a complex, nonperiodic puffer expanding in both directions at 7C/40 which consists of merely two C's whenever generation = 200x2exp.n. Two of those out of phase with each other will repeatedly react, causing their wave fronts to occasionally lurch forward at 9C/46, apparently at ever decreasing frequency. D moves at C/2, sends the same pattern in the opposite direction, and fills the intervening space with C's of various ages (mind boggling complexity). | |||||||
A | B | C | D |
Lifecomic by Harry J. Riley of Trenton, N.J.
'One way to get the most out of Life is to look upon it as an adventure'.
. . . William Feather
|
COMING EVENTS:
- some amazing pi-heptomino reactions
- a host of clock predecessors
- a new period thirty shuttle device
- a period nine billiard tab le construction
- 'healthy patterns' that eradicate foreign implanted bits
- a brand new series of 12n period puffer trains!
- LIFELINE Number Nine will be issued on schedule in March
Yes, I would like to continue receiving LIFELINE. I am subscribing for my 1973 subscription as a:
- ▢Regular member (now encloing payment)
- ▢Participating member (will contribute to newsletter)
My correct mailing address is:
Name:_________________________________________________________________
Address:______________________________________________________________
City:_______________________________State:_______________Zip:_________