Lifeline Volume 7
| Lifeline Volume 7 | ||
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| Published in | November 1972 | |
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| Preceded by | Volume 6 | |
| Succeeded by | Volume 8 | |
| This page is a transcript of Volume 7 of the Lifeline newsletter |
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| 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• Editor and Publisher: Robert T. Wainwright •NUMBER 7NOVEMBER 1972
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In LIFELINE Number Six, I described two of Conway's conjectures regarding Garden of Eden configurations. JHC himself is offering $50 to the first person to settle either conjecture. To date no one has submitted a proof for either of these challenges and they still remain. I would now like to present another challenge which Conway lists as one of Life's 'problems'.
The Immovable Object Problem: is it possible to design an object (i.e. a pattern or configuration) inside a 1001 by 1001 square (say) which will protect the central cell (within the square) for all time against any invasion from outside? In other words, the state of the central cell must never change whatever we put outside the 1001-square.
Editor's note (EN): think of this as a game:
| You put your clever ob- ject in here, so that the change its state. |
I put whatever I like out here, and try to make the central cell change |
Fifty dollars for this as well. All decisions about validity of proofs to be Conway's alone. Now let us consider the related problem which is:
The Irresistible Force Problem: is it possible to design an object, that is, some kind of spaceship with a similar sort of property? This is easily proved impossible / just shoot two at each other! As Conway points out, you really do not need both an immovable object and an irresistible force to get a paradox / an irresistible force will do, if you opppose it to a copy of itself.
| Research in Occult Symbology - Part I by Curt Gibson, New York City |
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| In the late fall of 1970 someone told me of Conway's Life, and I immediately started experimenting. Before I got a copy of Scientific American's report by Martin Gardner I had already processed most of the smaller ominoes, discovered the glider, and 8 or 10 of the perms and perps, etc. (EN: these are the still-lifes and oscillators). |
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Of course, on graph paper, I was still far from accurate, and my rooster pento (EN: R-pentomino) ended career at 150 gens. But I was duly impressed, because as an occultist already knew the 12 pentominoes represent the 12 tribes of Israel (or signs of the Zodiac), a sort of perpetual or recurrent round table division of the race of man (and of the universe). And the rooster is the tribe of Benjamin, presently identified as the Jewish people. As seer I've seen many thousands of years into the future and found the Jews still a distinct people as today. So it is perfectly appropriate if their symbol gives a Life process far longer than any of the others. Similarly the two briefest pento careers were appropriately the zag
glyph (EN: Since 1962 or '63 I'd been somewhat of a specialist in the pentominoes. I had solved the maestro (or 'Hexed') puzzle (composing the 12 into a 6 by 10 field) 1600 ways, e.g. I'd invented the game called golomb without ever hearing of Prof. Golomb's game, and I still play it on the 6 by 10, and have four extra versions: space, anti-space, contact, and anti-contact. Anti-space is a mind boggler, and we call it Fraser, as I first played it with Keigh Fraser the chess expert. Just how Life processing gives valid symbological and prognostic results we can't say. I have theories but will not go into it here. It must all look wildly irrational to the average science-oriented reader. But I've had all sorts of interesting results thru a variety of modes of application, and will give a few examples. One of my first ventures into applying Life to symbology was prompted by the world's chamionship Frazier-Foster bout, with heavyweight Foreman in the sub-feature fight. I decided it would be interesting to process three f's chosen to represent these three great fighters. So I called the big F octomino (a top of next page) Frazier's, the shorter hepto (b) Foreman's, and the tall slim Septo (c) Foster's, as he is tall and slim. All three appropriately resulted in good sized careers, and Frazier's big F went too far and large for me to follow out. So I decided we should expect Frazier to beat Foster, and Foreman if they meet, and to hold his crown for a good while and leave a major mark on pug history. As you may know he has continued to prove himself one of the outstanding ring warriors of history, a veritable machine of destruction, at least as formidable as Louis and Marciano. Less colorful and interesting than the 'great John L', or Dempsey, or Gaseous Cassius, he's still the super-dreadnought of the whole lot. Try his F on a computer. It ought to be impressive. |
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One of the great symbols is the Great Dipper and Polar Star, or the throne and dog of the Celestial King. Note that if you place a mono directly behind the throne hexo thus (d) they die in only three gen. But as the Dipper lip slants out, and Polaris is far off 90 degrees to its lay, the appropriate heptino is thus (e), which in re 1 (EN: Gen 1) becomes the rattler hexo with 1103 re, 6 gliders and a lot of perms and perps. I believe this symbolizes a truth: if royalty lets its dogs of war share its royal dais their reign will be cursed, their dynasty brief, like Nebuchadnezzar's or the Macedon's. Violence, or force, has its place, but only absolutely subject to reason and right. Now note that if the mono is subjected still further, thus (f) you soon grade into the same career as the rooster-rattler's, via a 6, 9, 8, 9 series instead of the foregoing 6, 7, 9, 8, 9 series (EN: this is the population count beginning from generation one). I take this to represent a throne and hound, i.e. a peaceful reign like Solomon's compared to the previous which would represent a warrior king like David. Its series skips 7, the number of Judgment and the house of enemies, and its first re (g) represents the realm of science (ideas celestial and terra: 'as in heaven so on earth') or universal law, like the wisdom of Solomon. Continued in Part II: Alphabetic Grid-cycling of Names. EN: a colorful description of some familiar Life histories! |
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The following similar events were recently submitted by two different Life groups. They both illustrate a 'one-shot' repulsive action by a pair of identical objects. | |
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Kerry K. Tatlow of Chicago, Illinois representing the U. of I. Life Group (incl. Bernard K. Kuehlhorn and Alan McGhee) notes that: | |
| Gen:0
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Gen:30
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David Buckingham of Sarnia, Ontario, Canada representing his own Group (incl. Mark Niemiec and Peter Raynham) notes that: | |
| Gen:0
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Gen:11
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And of course, we can add to this set the familiar Pulsar predecessor: | |
| Gen:0
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Gen:4
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| More LIFEXPLAINATIONS by Raynham | |
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Certain lifeforms can multiply, (curiously always by a factor of 4) by adding one bit to the object. Several examples are shown below. | |
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Lifequote: |
| 'Ob-la-di, ob-la-da, Life goes on - bra, la-la how the Life goes on . . .' . . . Paul and John
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Lifecomic by Richard Holmes of Fayetteville, N.Y.
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| Fly-by Fuses, a Second Flight by Donald Woods of Natick, Mass.
Having recently completed analysis of two dozen new "fly-by fuses", I report here some of the more interesting results. First, for those readers who may have missed the description of fly-by fuses in LIFELINE #3, p. 23, a brief synopsis. A fly-by fuse consists of a heavyweight spaceship and a formation (or number of formations), stable or oscillating, strewn in its path in the proper orientation. The object(s) must include a block in the north, thus: (see a) | |
| a | b |
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In tracing such fuses, I have established generation 0 as the generation when the spaceship's sparks first interact with the "charge". This is shown above (b) with a second example of a fly-by fuse. | |
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Most seasoned Lifreaks are probably well aware of the immense differences which can be brought about by a relatively minor change, but to add to the library of examples, consider these four f.b. fuses: #1 is a flasher (period-2 billiard table oscillator) whose alter ego is #2. #3 and #4 are merely rotations. Consider first the effect of the change in timing by having ignition occur on an even or an odd generation. #1 becomes a lone blinker at g59. #2 becomes a glider (heading northwest), 3/4 of a set of traffic lights, 2 loaves, a honey farm, and a block, at g777. Rotating #1 into #3, it goes to a northeast glider, 2 southeast gliders, 2 sets of traffic lights, 3 boats, 4 beehives, a loaf, a ship, and 10 blocks, at g804. #4 turns into a southeast glider, a loaf, a blinker, and 3 blocks at g359. EN: More fly-by fuse activity will be presented in later issues. |
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Niemiec and Riley have independently reported the smallest 3-4 Life oscillator. Shown here the 'bleeper' (Niemiec's term) of only four bits in size remains within a mere 2 by 3 area during both of its phases. Other four-bit period two objects submitted include the 'flip-flop' (Niemiec) and the 'blinker' (Riley) termed after their respective counterparts in Life. | ||
| bleeper
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flip-flop
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blinker
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Using blinkers for boundries, the writer constructed a 3-4 Life form analogous to the infinitely extensible barber pole: | ||
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The writer also submits the following period five wick which burns like a clean fuse at each end but not at the same speed! Can the reader determine the two burn rates? |
Lifecomic by Traw  |
| Regarding the 'Titanic Toroidal Traveler' by W. P. Webb of San Rafael, Ca. |
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Mr. R. T. Wainwright, in the December 1971 issue of Lifeline, described an initial configuration on a six cell wide torus which traveled at the speed of light but left a complicated exhaust in its wake. He wondered if it could be tracked to a final proven period and census. This configuration has now been followed through 716 generations on an infinitely long, six unit wide, torus surface, using an IBM 1130 computer. The two original questions cannot be answered at this time, but an interesting development occurred which is reported herein. The starting configuration is shown in the attached figure. As the front edge proceeds to the right a continuous exhaust is left behind which slowly evolves and expands. For example this configuration at the 25th generation extends from cell row number 5 to cell row number 27, at the 50th generation from cell row number 4 to cell row number 52, and at the 75th generation from 1 to 77. At generation 96, the exhaust begins to divide into two parts. The right hand portion, 78 cell rows long proceeds to the right at the speed of light with a recycle period of 16. The configuration at generation 96 is shown on top of page 8. The entire 16 cycle repeat unit (train?) appears to be made up of five nearly spearate areas or substructures. Each of the substructures then evolves in 16 generations into the substructure next adjacent to the left, and in effect the entire portion moves to the right. The substructures are not completely independent, but require some contact with each other to achieve the result described above. The trailing edge varies from 78 to 86 cell rows behind the leading edge. The cell count varies from 105 to 126. The remainder of the exhaust, (the left hand portion after separation) 22 cell rows long at generation 96, slowly grows in both directions until at generation 716 it is 238 cell rows long. A plot of the length at several generations showed that both edges are moving outward at a constant rate of about 1/6 cell row per generation. There is no reason to expect anything but continued growth at this rate. The left and right edges are not the same, hence there is no verticle line of symmetry. The initial configuration as shown on the figure results in structures that are horizontally symetrical about the 2nd horizontal row. The 5th horizontal row remains unoccupied after about 10 cell rows behind the advancing wave front. |
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Recently, using a program written by David Tetenbaum, a Senior at the Hinsdale Central High School, we stumbled upon an interesting scenario involving a glider and a pentadecathalon. Generation 0 is shown below. The glider interacts with the pentadecathalon in generation 5, and, in generation 12, reappears shortly going in the opposite direction and two spaces downward. The damage done to the pentadecathalon, though, is irreperable, and by generation 17, it disappears entirely, as shown below. | ||
| Gen:0
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Gen:12
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Gen:17
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The concept of a three-state Life will, I think, prove to be quite significant. For example, in a collision, one could 'mark' one object with a separate state. Using the rules of the three-state IMMIGRATION game, one could determine whether an object resulting from the crash was truly a product of both objects or primarily a product of one, e.g., a fly-by fuse is not a product of both the wick and the spaceship, but primarily a product of the wick. Illusion of motion (IoM) can also be more easily distinguished from real spaceship motion. For example, if a single element of the following channel is marked as shown in 5 generations the configuration is exactly the same. Thus, the marked spaceship does not move! Real spaceship motion, as in a glider, does not have this property, and the marked ship appears to move. We hope in the future to have a similar result dealing with the above collision of a glider with a pentadecathalon. By marking the glider with @ symbols, we hope to see if the glider heading back is the same, a product of the pentadecathalon, or a combination of both objects. | ||
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Generation: 96 Cell Count: 155 |
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Dean Hickerson of Davis, Ca, submits the following billiard table construction: |
Mark Horton of Cardiff by Sea, Ca. a 'five' which forms 10 blocks, 1 tub, 1 boat, 5 beehives, 4 loaves, 1 pond, 14 blinkers, and 3 gliders after 1059 generations: |
| Editor's Errors and Embarassment . . . | Buckingham's 'five' forms a glider headed N.E. in 3: |
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Due to the keen observation of several readers, I am obligated to report these errata from earlier issues of LIFELINE: Harry J. Riley of Trenton, N.J. notes that the configuration on p.6 of issue No.4 is not a Gun predecessor but rather a mere period thirty oscillator. Either the left 10 bits should be moved up one cell or the right 11 bits should be moved down one cell in order for the configuration to operate as a Gun. George H. Wells, Jr. of Pomona, Ca. was the first reader to point out the error which was corrected on page 4 of the last issue. |
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Answers to reader query given on page six: The period five wick as shown will burn on the left at the speed of light and on the right at 3/4 of that speed. |
| Lifecomic by Niemiec
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COMING EVENTS: Hugh W. Thompson of Lefrak City, N.Y. has discovered and sent in such a large volume of new material that it will require additional time to prepare this for the newsletter. In addition to those attractions stated in previous issues but not yet covered we can add:
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