Lifeline Volume 8
|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 Number 8 DECEMBER 1972• Editor and Publisher - Robert T. Wainwright •
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 . . .|
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.
Class E, Evolutionaries, Exercises, Events, Et cetera . . .
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 No.6,p.2)
Class I, Still Lifes and Stable Forms . . .
LIFEXPLAINATIONS [sic] by Paul Dietz of Ellicott City, Md.
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 [sic]. 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!
Class II, Oscillators . . .
The eight objects shown on the ocver 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)
Reader Article . . .
Progress on the "Life Codex"
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 methusaleh (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 methusaleh constellation – and the LC# of the first ancestor of the
object (if any). The second, the Terminus Cross-Reference, lists, for each stable object, pattern or methusaleh 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. Methusaleh 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 Methusaleh 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 [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 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.
- Hugh W. Thompson
- 98-25 Horace Harding Expway, Apt 16B
- Lefrak City, New York, 11368
EN: see Lifequote on page seven!
Sample "Life Codex" page
(cont. from page 2)
The five-bit row is the familiar 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 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?
Reader Briefs . . .
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.
(to be continued)