Lifeline Volume 11
| Lifeline Volume 11 | ||
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| Published in | September 1973 | |
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| Preceded by | Volume 10 | |
| This page is a transcript of Volume 11 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 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 11SEPTEMBER 1973
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The unique letter published in LIFELINE Number Ten has triggered quite a few similar responses by other readers. In fact so many replies were received that I decided to extend this issue of LIFELINE to 24 pages to give proper credit. This overwhelming response is especially appreciated since as the masthead indicates, I have just recently moved and now find editorial time even more scarce. Repeating what was said in Number Ten, I certainly welcome any and all letters of this nature no matter how long or short!
As the contents of this issue testify, Life continues to yield more new and interesting discoveries.
| Thompson's piece de resistance (click above to open LifeViewer) |
Three years ago, before we even knew about Life, Conway was busy tracking the smaller ominoes and tabulating the outcomes of each. Had he continued his research, he would have made an amazing discovery for one of the nominoes spawns a lightweight spaceship which successfully escapes! This discovery, shown here on the cover page of LIFELINE Number Eleven, was just recently made by Hugh W. Thompson of Lefrak City, New York who has now successfully tracked all the ominoes up through and including the 1285 nonominoes. The final census of Thompson's 'piece de resistance' includes 13 blocks, 1 boat, 1 beehive, 1 ship, 4 blinkers, 2 trafic lites, 3 gliders (NW,SW,SE) and 1 lightweight spaceship (E)! Formed in generation 198, the 'natural light weight' is about 300 cells east of the debris which finally subsides by generation 800.
Now for some interesting and varied replies and articles sent in by the more energetic Lifenthusiasts and Lifanatics:
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Reader Reply . . .
Dear Mr.Wainwright
After weeks of long and frustrating effort,I have engineered the following
fuse, along with the two gliders that trigger it.
| (click above to open LifeViewer) |
The block section of the fuse can be extended to any length whatsoever,
or eliminated altogether,placing the pond in conjunction with the second part
of the fuse.
The first glider,shown about to collide with the pond,converts it into
a ship in 3 generations. The ship(FIG.1)remains until the second glider hits
it,and in 4 generations,they are mutually annihilated. However,the fading
debris the ship,converts the adjacent
block into a latent beehive(FIG.2),and
this sets off the first part of the fuse.
| FIG.1 (click above to open LifeViewer) |
| FIG.2 (click above to open LifeViewer) |
The beehive interacts
vigorously with the upper block
and in 8 generations,only the
upper block remains,intact.In
generation 5,however,a spark from
the destruction of the beehive
converts the next block in the lower wave,into a latent beehive,and causes
the cycle of the first part of the fuse to repeat.(FIG.3).EN: see No.1,p.5.
The first part of the fuse has a period of 6.
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| FIG.3 (click above to open LifeViewer) |
| FIG.4 (click above to open LifeViewer) |
When the first
part of the fuse
has reached the
second part
(Midgard Serpent)
the igniting spark
lights the horizontal portion
(FIG.4),and converts it into a
honeyfarm,producing beehives at the rate of one per 12 generations.
In developing this configuration,I spent weeks experimenting with fly-by fuses,and ways to spark off the honeyfarm fuse from the Midgard Serpent. I had serious trouble with the tendency towards unwanted and destructive interactions. Only in the past few days did I find the block and beehive interaction that would light the fuse,and in one day,I developed the double wave of blocks,and then the pond-glider collision that sets off the entire fuse. That took some brief experimenting with glider still life collisions.
In the course of my experiments in the above,I uncovered a collision of six gliders that produces a beehive and nothing else. The diagram shows the six gliders about to interact.After 36 generations,the beehive is alone in the field. (FIGURE 5) The beehive is indicated in its position after completion.
| FIG.4 (click above to open LifeViewer) |
A pond is formed in the 6th generation from gliders A and B. Gliders C and D crash to form an adjacent block in generation 7. Glider E reduces the pond to a ship,in generation 14,and after a consider wait,glider F collides with the ship in generation 31 to remove both itself and the ship. The fading debris of this crash converts the block into the beehive (indicated by X-signs).
This seems to be a lot of gliders,just to make a beehive.
Last of all,I desire the addresses of LIFE clubs in New York City, so I can try out various problems of mine, and get acquainted with people who know what I'm talking about,when I talk about LIFE.
- Yours Truly,
- Paul Wilson
- Paul Wilson
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Reader Article . . .
The Explosive World of Kinkbombs
By Mark Horton
I became interested in LIFE about a year ago and wanted to do
somothing original. Then I was hit by an idea: suppose I have a stable
pattern that depends on a fuse for stability? That is, a pattern which
is class I, that hag 1 or more fuses extending from it to infinity. What
happens when the fuse burns down? I wanted to find a pattern that would
blow up, a bomb that creates a spectacular explosion when the lit fuse
burns down. Thus I started looking for families of patterns fitting the
definition of stability with fuses, or Stable Fuse Ends. (SFE's) The
simplest such pattern is the fencepost. (1) This pattern becomes a block,
but in how many generations? I needed a starting point, a defined generation
0. Hence I defined Effective Age (EA) of a SFE to be the age of a pattern
which 1) is a successor to the given pattern with a long fuse, 2) is
identical to the pattern and has either a short or no fuse, and 3) has the
shortest possible fuse consistant with 1 and 2. Thus the given pattern
for the fence post is [insert image here] and it's ea is 1.
I then discovered that it is possible to place "kinks" in a diagonal
fuse without affecting its stability. The kink can go either way, as in
(2) and (3). Any number of kinks can be placed in a fuse, and if they are
sufficiently spaced, they do not effect it's stability. I can now consider
the entire conglomeration of kinks, fuses, and fencepost as the fuse end,
with 1 fuse extending from it.
Then I needed a classification system for these patterns, or "kinkbombs",
as I call them. I do this by a series of numbers, separated by dashes.
The first number is the number of kinks. There are then that many numbers,
each telling how many extra bits (besides the 6 required for each kink and
the 3 for the fencepost) are between that kink and the next. To attain a
universal orientation, I hold the first kink positive, and allow the fencepost
and all other kinks to turn either way. A number in the series may be
negated to indicate a negative kink, or a turned down fencepost. Each
number indicates the direction of the kink after the bits whose number it
indicates. The last one is for the fencepost. See some examples in the
illustrations:
4 ORDER 1 - 0 KINKBOMB
5 ORDER 1 - 7 KINKBOMB
6 ORDER 1 - (-2) KINKBOMB
7 ORDER 2 - 2 - 2 KINKBOMB
8 ORDER 2 - (-2) - 2 KINKBOMB
9 ORDER 2 - (-2) - (-2) KINKBOMB
The fencepost can be considered the order 0 kinkbomb.
I have been working on the single kink kinkbombs from order 1 - (-10)
through 1 - 10. All are known except the 1 - 7.
The order 1 - 7 has gone over 3000 generations and is still going strong. The average EA of the 18 known (1 - (-0) and 1 - (-1) are not spaced far enough apart to be SFE's) kinkbombs is 218 generations. So I seem to have a gold mine of bombs. I define a "Dud" as a SFE that terminates within 10 generations of when the fencepost is reached, a "Firecracker" as one with an EA less than 200 which is not a "Dud", and a "Bomb" as one with an EA over 200. Out of the 18 known Kinkbombs, 4 are duds, 9 are firecrackers, and 5 are Bombs. The 1 - 7 and 1 - (-10) are also bombs. The 1 - (-2) and 1 - (-6) both form a block and a blinker, both are duds, but the blinker is 1 cell different. They also form differently. (See illustrations 10 & 11).
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| FIG.3 (click above to open LifeViewer) |
Note: the number of bits in the upper left fuse is irrelevant, when actually run, there are none, as in 10 and 11. These patterns were run on a UNIVAC 1108 with 65K of core in 5 minute segments.
Results
Class Order EA Pop Census
Dud 0 1 4 b
FC 1-0 16 3 +
FC 1-1 23 0 Θ
FC 1-2 187 55 +,2 t.lite/2,6 B, 2 pond (pi)
FC 1-3 87 0 Θ
Dud 1-4 16 4 b
FC 1-5 116 9 b,g
FC 1-6 100 16 4b
EN: *BOMB 1-7 >3200
BOMB 1-8 428 56 S,2g,7b,2+,B
FC 1-9 137 16 3/4 t.lite, L
FC 1-10 54 12 2B
Dud 1-(-2) 8 7 b,+
BOMB 1-(-3) 984 282 4g,19b,5+,2 3/4 t.lite,10B,1 hf/2,3L,1 tub,3 boats,3S,pond
Dud 1-(-4) 16 4 b
BOMB 1-(-5) 278 45 5b,3+,2g,S
Dud 1-(-6) 16 7 b,+
BOMB 1-(-7) 1192 173 2g,16b,4+,1½ t.lite,5B,4L,barge,boat
FC 1-(-8) 75 6 B
BOMB 1-(-9) 204 24 2B,b,+,boat
BOMB 1-(-10) 580 122 7+,1 3/4 t.lite,8b,3B,L,pond,3 boats
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Robert T. Wainwright
Editor, Lifeline
Dear Bob:
In the June 1973 issue of Lifeline, Mr. D. G. Petrie asked
about collisions of objects having different symbols, wherein
the resultant configuration contained some of both symbols.
The following examples of this type were discovered while investigating
glider—glider collisions. The initial and final
configurations are shown in the attached set of figures. In
these figures, the configurations are horizontally true and the
same vertical row is marked by an arrow.
EN: also see pages 12 and 13
- Sincerely Yours,
- William P. Webb
- William P. Webb
| (click above to open LifeViewer) |
| (click above to open LifeViewer) |
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June 10, 1973
Reader Reply(s):
Robert T. Wainwright
Lifanatic-in-chief
Dear Sir: Besides the 14-bit naturally occuring objects you mentioned, 14.322
(bookends) and the 18-bit "dead spark coil" have been reported as puffer product.
I can help answer the question of the probability of occurence of various objects,
because I have been doing a large-scale statistical survey of exactly that. The method
is to collect the census results for all reported configurations which require
≥200 generations to settle down, and add them up. In the case of symmetric patterns,
when 2, 4, or 8 objects are symmetrically equivalent they are counted as one. A
table of the findings to date is enclosed. I would appreciate hearing results for
all long-lasting methuselahs so that they may be added to the survey. Desired
data for each object history is initial pattern (picture or description), age, final
census, and all occurences of constellations such as TL or HF; and for symmetric
patterns, the degree of symmetry and a special note if any objects are located directly
on a line of symmetry.
A comparison between my census table (page nine) and Thompson's data on small objects
(#4 p. 10-12) shows that for most objects the frequency of natural occurrence is
(roughly) inversely proportional to its area and directly proportional to the number
of small ancestors. One noted exception: The ship is much more common than
would be expected; on examination it turns out that most natural ships occur as descendants
of the very common B-heptomino. The pond and loaf are both rarer than
expected, for what reason I know not. EN: is the loaf rare?
- June 17, 1973
Robert T. Wainwright
Lifeline Ed.
Dear Sir:
The question of determining the degree of "naturalness" of objects is a tricky one
and an important one. In line with the material in my June 10 letter I have been
trying to develop a numerical measure of naturalness/artificiality which would range
from, say 1 for the block (the most common object) to ∞ for GoE patterns. The inverse
of the cumulative census count (1/C) gives a direct measurement of artificiality,
but with the present amount of data it is only valid for the top 10 or 12 objects
and patterns. After some study I have found 5 measurable variables associated with
Life patterns that seem to be useful: (S) the size (population) of the pattern; (N)
the number of ancestors of size ≤6; (A) the area occupied by the pattern (obtained
by counting all live cells and all cells which have at least one neighbor); (M) the
size of the minimum predecessor other than itself (thus for blinker M=4); and (G)
the minimum number of gliders required to construct it. (As you can sec, your recent
suggestions were quite useful.)
First of all (S) was eliminated because it measures basically the same thing
as (A) does, but with less precision. The available data is somewhat limited, but
it appears that the quantity 1/C varies directly with (A), inversely with (N), exponentially
with (M), and exponentially with (G). (N) can be used only for patterns
with a 6-bit ancestor, but (A) can quickly be found for any pattern, and thanks to
the activities of a multitude of Life-freaks (G) is known for many of the "interesting"
patterns and (M) is known for almost all of them. When (G) is not known the
approximation G=½M will do, and when (M) is not known some quick backtracking by
hand will usually yield something close to it.
With all that in mind, I suggest the following tentative definition for the
"artificiality factor":
- AF = (A/16)e(M+G-5)
- AF = (A/16)e(M+G-5)
Since adding 1 to M or G will multiply AF by 2.7, this cannot be an exact measure, but it does provide a good order-of-magnitude estimate. Except in three cases (ship,
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pond, and HF), the AF corresponds reasonably well to the observed census data, and
using AF has the advantage that it can easily be applied to Class IV and V patterns
for which other measurements do not work. Some typical AF values are: block 1.00,
blinker 3.58, boat 10.1, TL 13.1, tub 26.4, B-heptomino 32.7. eater 95.9, HF 147 (an
anomaly there), pentadecathlon 8950, and P30 glider gun 2.8x1013.
Making a couple of further assumptions, I have been guesstimating the sizes of
random broths necessary in order to expect to see natural occurrences of various rare
patterns (for instance, 108x108 for the P30 gun). I would like to know if the as-
sumptions were justified, and since you seem to have done the most with random-broth
experiments I turn to you for information. When the pattern has reached a steady-state
situation (i.e. swirling around at more-or-less constant density), what is the
density on the average? Also, what percentages of the live bits belong respectively
to terminal forms, easily recognizable nonterminals (pi, r, etc.), and amorphous
masses? Finally, what is the half-life for terminals once they have been formed in
the field? For Class I and II objects I imagine the expected lifetime within a broth
would equal (constant)/(area), but I have no idea what it might be for the glider or
how to calculate it for other moving objects. Can you supply this information, if
available, please?
This whole line of investigation has an important bearing on some intriguing
speculations by Conway. He has suggested that, given a sufficiently large random
pattern, it is likely that by pure chance Life computers and self-replicating animals
would form out of the broth, that thru interaction with the surrounding random
debris these patterns would mutate and evolve, and that in this way a large Life pattern
would in fact be a simulation of real-life biological processes. If AF or some
similar measurement proves to be a reliable indicator, we might then be able to calculate
how large a starting pattern and how many generations would be needed to create
a truly "living" Life-form. It would be interesting to see how these numbers might
compare with, say, the atomic weight of an amoeba and the length of time it took for
the first amoeba to evolve on Earth.
I expect shortly to have computer access, so hopefully I can start running some large-scale patterns. Most of the previously-sent items were found by hand, and I have been living in deathly fear that someone would run one of my collisions and discover it didn't work. I will try to run as many methuselahs as possible, so that in a couple of months I can send you some updated and expanded results for the cumulative census.
It has occurred to me that the census count for TL and HF may be slightly low because several results reported in Lifeline apparently lumped these patterns together with the blinkers and beehives. I would like to know (if the data exists) if there were any instances of TL or HF in these final censuses: glider-cigar crash (#4 p.5), Y34 fuse ignition smoke (#4 p.7), Horton's "five" (#7 p.8), and the nonominoes N-1 and N-2 (#10 p.2).
That's all I can think of right now. I hope the preliminary suggestions I have made will be helpful. As you can tell from my requests for data, there is still a great deal about the "naturalness" question that I am unsure of. Can you think of any other useful measurements? EN: I think this is an excellent beginning - any ideas from other readers?
- Doug Petrie
- Douglas G. Petrie
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CUMULATIVE CENSUS OF NATURALLY-OCCURING OBJECTS
| |
single objects | common constellations |
--------------------------------------+-----------------------------+
o | o |
c | c |
c | c |
u | u o |
r | r b n |
r | r j o |
e | e e . |
n | n c | total
c | c t o | census
e | e s f | count
| | |L.L. | s | | s | | for
name |size|class|ref. | | name | | | object
----------------+----+-----+-----+----+------------------+---+------+---------
blinker 3 II 204 |{traffic lights 42 150}| 354
|{interchange 0 0}|
block 4 I 361 | | 361
tub 4 I 10 | | 10
boat 5 I 66 | | 66
glider 5 III 87 | | 87
beehive 6 I 163 | honey farm 13 49| 212
ship 6 I 25 | | 25
barge 6 I 3 | | 3 +-----------
aircraft carrier 6 I #2 p.12 0 | | 0 | (14.488)
snake 6 I 0 | | 0 | OO
toad 6 II 0 | | 5 | O O
clock 6 II 5 | | 0 | OO O
loaf 7 I 0 | | 48 | O OO
long boat 7 I 48 | | 2 | O O
eater 7 I 2 | | 0 | OO
(7.1) 7 I #3 p.2 0 | | 0 |
beacon 7 II 1 | | 1 |
pond 8 I 9 | | 9 | dead
long barge 8 I 1 | | 1 | spark coil
cigar (8,3) 8 I #3 p.2 1 | | 1 | OO OO
long ship 8 I 0 | | 0 | O O O O
bipole 8 II #3 p.3 0 | | 0 | O O
(10y) 10 I #9 p.3 1 | | 1 | O O O O
l. spaceship 10.5 III 0 | | 0 | OO OO
m. spaceship 11.5 III 0 | | 0 |
half-fleet 12 I #7 p.4 0 | fleet 2 4| 4 |
bookends 14 I #3 p.7 1 | | 1 | half-bakery
half-bakery 14 I -> 0 | bakery 0 0| 0 | OO
S-14 14 I #4 p.5 0 | | 0 | O O
(14.488) 14 I -> 0 | | 0 | O O
dead spark coil 18 I -> 0 | | 0 | OO O
spark coil 19 II #3 p.3 1 | | 1 | O O
pentadecathlon 20.9 II 1 | | 1 | O O
pulsar 58.7 II 0 | | 0 | O
--------------------------------------+-----------------------------+-----+-----------
Notes and comment: --This table consists of the sum of the final censuses of all
Class V patterns known to me whose age is at least 200 generations.
--Objects with a census count of 0 are considered to be "natural" and included in
the table if they have appeared temporarily in an intermediate stage of some more-or-less
random pattern, if they result from the interaction of two commonly-seen
objects (for instance, glider + preblock ⇒ spaceship), or if they have an ancestor
of 7 bits or less.
--For traffic lights and honey farm the number of objects is less than 4 times the
number of constellations because of the inclusion of several ½TL, ¾TL, and ¾HF.
--"Size" of Class II and III objects is defined as average population over all phases.
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Reader Article . . .
AN INTRODUCTION TO GLIDER LOGIC
by V. Everett Boyer, San Diego with counsel from Doug Petrie and J. H. Conway
Glider logic involves simulation by Life of digital electronics, with gliders substituting for electric pulses. Straight wires, basic timing, and power are then provided by the ether and by glider guns. Most logic is accomplished by right-angle crossings of glider streams. The question of whether a glider has escaped a collision represents a bit of information. Gliders and holes must then react appropriately.
[insert image here]
To deal efficiently with the many different arrangements of two glider streams, collisions are classified by delay and parity. The parity is obtained from the separation between the two paths. Even separation and parity is designated by a plus (+), odd by a minus (-). The delay is the number of generations by which one glider trails a glider on the intersecting path. There is no collision if the delay is at least 19 but thus with P(period)-30 streams, delays above 11 are ambiguous and demand extra care. Here is a partial list of basic glider collisions, coded by delay and parity:
code age result |code age result 0- 4 twin blocks | 3+ 7 pond 1- 152 'B' LL#3p12 | 4+ 5 - 2- 6 blinker | 9+ 14 eater 3- 33 - (dies) | 10+ 5 block 5- 7 - | 11+ 5 - 6- 14 - | 12+ 6 beehive 7- 11 - | 17- 9 glider 8- 9 - | 15- 5 - 10- 26 blinker | 14- 14 - 12- 5 block | 13- 12 -
More than one third of the 38 right-angle collisions are simple enough to be good for glider logic. The vanish reaction, the most common, is surprisingly useful. And the kickback (17-) reaction also is valuable. More important may be the three ternary (9+, 10+, 12-) reactions, in which the resultant object vanishes quickly with the next glider to come along, from either stream. A ternary crossing of P-30 streams is the minimum known P-60 gun. Other useful reactions appear later.
| a 'twogun' (period 60) (click above to open LifeViewer) |
The next five questions, completing the fundamentals of digital electronics, involve bridging, bending, timing, gating, and branching. P-30 streams cannot cross without reacting. Newgun P-46 streams can, but use of slightly smaller twogun P-60 guns makes bridging easier and takes advantage of P-30 streams where there is no bridging. A NOT gate which turns a corner is provided by a vanish reaction with a full stream, but simple bending is done with a special reaction. The best known solutions use a two-bit spark from a junkie or a twin bee (LL#3p14). Special effort is also required to make streams arrive at just the right time. Inserting pairs of NOT gates preserves the information, and the number of vanish reactions (4+, 11+, 5-, 6-, 7-, 8- for P-30 logic) provides
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| (click above to open LifeViewer) |
the freedom to reposition and time information exactly. Give all the foregoing, gating information becomes trivial. All boolean functions are easily performed by vanish reactions. Two guns can produce either AND or OR outputs from three parallel inputs. The final problem is of copying information, and Conway and M.I.T. were greatly troubled, as is seen by Conway's 12-gun solution, which would copy P-240 data. The problem is better answered with ternary reactions; branching a P-60 stream takes only a P-30 gun and twogun. Bridging or branching a P-30 stream is done by dividing it into P-60 streams to be treated separately and merged afterwards.
[insert image here]
Since exactly plotting large numbers of glider guns detracts from logical design, various simple symbols are used instead, and designers deal with generalizations; the exact positioning of each glider gun is put off. Streams are shown by lines and each component is symbolized, as shown or otherwise. When required, reactions can be marked with delay, parity, and a mark by the advanced stream which leaves the delay by the delayed stream. Every time glider streams close a loop, the sum of the parities must be even, and the four delays must check out appropriately. A special case, for a new glider is actually created, is the kickback reaction. The primary use of the (17-) reaction is in thinguns, where the release of a glider every 120 generations, of a multiple of 120 generations, is caused by a pair of repeating kickback reactions. The new glider is delayed in a (5-) relation to the original stream. The two streams from the siamese gun have a (15+) relationship. Therefore, the parity of the vanish reaction is even, the delay is odd, so it must be an (11+) reaction. Also, by chance, a minimum thingun can use a ternary reaction (9+), which allows closer packing of the subparts.
[insert image here]
Three other symbols used show where streams have been (+) delayed or (o) advanced a 30-generation cycle.
As an example for study, a P-30-stream branch is shown here, with a P-60 analysis of all information flow. Imagine a cell-by-cell plot.
- EN: (!)
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Reader(s) Reply . . .
Dear Bob,
Our group has found an assortment of interesting information in a wide variety of classes, most of which is contained herein.
| (click above to open LifeViewer) |
The reaction to the right between two gliders and a pentadecathlon reflects the two gliders by 90 degrees, and the gliders just barely escape the pentadecathlon. (Dave Buckingham's idea) Another interesting pentadecathlon-glider interaction is shown to the right, where four gliders delay the pentadec. by 6 generations, thus making it period 21 for one cycle. Could this be used in the construction of odd-period oscillators or puffer trains , breeders, guns etc. ?
| (click above to open LifeViewer) |
I have also followed the fates of all the glider-glider collisions, and some of the glider-object collisions in immigration-LIFE. All that resulted in a mixed census are shown below. Some, too complex to trace by hand, I will leave to those with access to large computing facilities. Also Pete Raynham has supplied a house-tub-tub interaction which releases two hybrid gliders.
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Here are the rest of the immigration collision. Also included are some four-glider collisions to produce unusual still-lifes or oscillators. As four gliders are usually use used, the most representative combination is shown. The others can be easily figured out. Can you find any use for the one that makes two B- heptominoes? (i.e. something like the 'Twin Bees')
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Dave has found several interesting glider collisions, all of which involve four gliders coming in from different directions. One of these forms a 'quick toad' in only three(!) generations. Another forms a fleet, and the 'third forms an odd fourteen- bit still life consisting of two honeyfarm predecessors inducting one another. Pete also discovered a way of making the fourteen bit 'paperclip' (everybody's term) from two gliders and a middle-wt. s.ship.
I have found yet another 'Cha-cha' oscillator, comprising 32 bits. (see below)
As for still lifes, Dave has pointed out that there are four, and not two,twenty-bit still lifes in which all bits have two neighbours. The complete list up to twenty bits with 2 or 3 neighbours is shown below.
| (click above to open LifeViewer) |
| (click above to open LifeViewer) |
| (click above to open LifeViewer) |
| (click above to open LifeViewer) |
| (click above to open LifeViewer) |
| (click above to open LifeViewer) |
EN: yet even more 14- bit still lifes (!) see No.10, p.2.
Many still lifes have
been successfully used
in the construction of
spaceships, oscillators,
puffer trains, other
still lifes, etc. Some
still lifes, however,
which might be potentially
very useful are
virtually impossible to
form by ordinary means.
We have devised a method of adding bits
and pieces to some of the less exotic still
lifes. For example, the eater can be transformed
into the tub with tail, etc. with the
use of several gliders. Some of these require
the use of many gliders, but in time this
number can be out down. (See next page for
a partial list of the still lifes that can be
formed from gliders.)
EN: really amazing!
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As in LIFE, there are an infinite number of flip-f1ops in 3-4 LIFE, which are either of period two, such as the first three examples shown above, or period four, such as the remaining three examples. It should be noted that these are only representatives of some of the varied activities that occur in these flip-flops. Also, many LIFE flip-flops, in which all the original bits die, can be used in 3-4 LIFE with much the same effects.It may be possible to insert other oscillating machinery into these to change the period to something like 8, but Dave believes this to be unlikely, as he did not come accross anything promising while designing the above examples. As for pragmatic applications, flip-flops might be used to stabilize transfinite oscillators. (see LIFELINE #9)
Below is yet another one of Dave's "Sombrero" constructions. Essentially period six, the sombrero supplies a bit every six generations to the object beneath it. In this case, the object is the period four construction shown as a wick in LIFELINE #3. The added bit extends the period to six, thus making the entire thing oscillate. Unfortunately, it is as yet impossible to make the period four construction finite, and hence the same applies to the period six sombrero construction. Thus a wick form is needed.
On the next page are some variations of the eater- subclass oscillators "Confused Eater", and "Honeyfarm w/tail"
In the first example, a confused eater is used to confuse another eater. In the second example, a confused eater is used to stabilize a h.farm w/tail
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| (click above to open LifeViewer) |
The idea of using a confused eater toeat other oscillators can be extended indefinitely (i.e. a confused eater which is eating a confused eater which is eating ... ) The use of this technique, however is restricted to oscillators with a period of four.
Below is an interesting example of a shuttle- bound oscillator. The centre behaves much like the period 30 (pentadec./2) agar, except that it is not inducted on the sides, and tends to expand out the sides. As in the development of the pulsar, each traffic- light pred. doubles itself, and three of the shuttles produce beehives to kill the preds. on one side. Then the process repeats, and the preds. move back, the other side being wiped out by the other three shuttles. It can also be done with pentadecathlons if they are positioned strategically enough to eliminate the preds. fast enough.
| Dave Buckingham's Period 30 Pseudo- Shuttle (click above to open LifeViewer) |
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| (click above to open LifeViewer) |
At present, there are two basic shuttles: The period 30 "Queen Bee" shuttle, (etc.),and the period 46 "Twin Bees" shuttle, (etc.). Now, for a new addition to this class, Dave Buckingham reports the period 28 (!) "Newshuttle". (Shown below) This is similar in principle to the pseudo-shuttle shown on the previous page, in that it follows the evolution of the pulsar. Normally, however, when two t-tetrominoes are placed 3 spaces apart, they replicate fifteen generations later, allowing for a period 30 shuttle. However, if the outer blinker is somehow removed, the t-tetrominoes re-appear in only fourteen generations. This reduces the period to 28. Because of the extra machinery needed to eat the extra blinkers off the sides of the forming pulsars, it has been necessary to induct eight pairs of t-tetrominoes, forming the grotesquely huge object shown below. As of yet, nobody has been able to cut down the size of this, or even to use it in a possible period 28 gun (any ideas?)
Above is a beriod 29 agar (residing on a 29x29 torus), which is a comb- ination of the period 14 and 15 movements. Also, the period 28 and 30 oscillators can also be made into agars in the same way.
| (click above to open LifeViewer) |
We would appreciate it if anyone finding any uses of the above, or ways of making the periods 292or 30 agars finite, to contact one of us. (The period 30 can be stabilized with shuttles or with pentadecathlons.) If some Class I objects could be used, then they would be true shuttle oscillators.
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Concerning your definition of an object: The pattern shown at right consists of four blocks, The block made out of 'x'es is an object, because all the bits are connected. The blocks made out of 'o's make an object, because they cause a birth which does not normally occur on blocks. However, when these two objects are placed together as shown, the birth will not occur. Therefore this is an object. But according to your definition, this is not an object because no births are caused on the blocks. IS THIS CONFIGURATION AN OBJECT OR NOT ??????????
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- EN: see No.1,p12.
Due to lack of space, i have been forced to withhold some of our recent discoveries. We will send these in at a later date. We have a great assortment of glider collisions to produce some interesting results: Twin Bees(4 gliders), pair of bookends(6),glidersomino(4),shooting a pentadec. 9 gens. out of phase, ass opposed to 6(4), etc.
By the way, what ever happened to most of the COMING EVENTS?
- EN: pre-empted by new stuff!
- EN: pre-empted by new stuff!
o o ooo
o o
o ours o ruly,
- Mark Niemiec *
P.S. Below is a collision which forms a tub in six gens. The glider on the extreme left becomes the tub.
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- EN: representing Buckingham's
Combine (Dave Buckingham,
Mark Niemiec, and Peter
Raynham) of Sarnia Ontario,
Canada.
EN: in addition to Niemiec's tub forming collision, Raynham reports a four glider collision which forms a pentadecthlon in twelve generations and Buckingham reports a three glider collision which forms a heavyweight spaceship in seven generations(!). These initial arrangements are shown on the top of page 19. Also see the cover page of No. 10.
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- Petrie replys:
The new collision results are quite impressive. . . . Regarding 4 blinkers + tub ⇒ (20-bit object), there ought to be a way to make that with gliders, since the blinker-forming collisions need not interfere with the central tub. . . . Cross-fertilization lives! Combining Raynham's new l.w.S.S. generator with my own collision discoveries, I have been able to synthesize Schick's Flying Machine from 11 gliders. See enclosed graph. . . . If someone can find a way to produce the clock as well as ([insert image here]), that would mean that all terminal forms smaller than size 8 can be constructed with gliders. (By "terminal" I mean any pattern of class I, II, III, or IV.)
"flying machine" synthesis
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Dear Sir:
Figure 1 shows an infinitely extensible period 2 billiard table configuration which I have discovered.
The object shown in Figure 2a becomes that of Figure 2b in 8 generations. Note that the configuration in 2b contains that of 2a shifted 2 units south-east. Unfortunately, the extra 4 bits prevent the object from appearing again, and it becomes 4 blocks in generation 18. Perhaps someone could make a glider or puffer-train out of this. EN: speed = C/4!
I have experimented with 3 state life and have found that there are exactly 2 alliances for the clock and 3 for the toad. These are shown in Figures 3 and 4 respectively. I have tried to increase the number of states in the 3-4 version of life, but have been unable to invent any natural rules for it. In ordinary life, however, I have managed to invent some simple rules for a 5 state version, which I will now describe.
The states are the "off" state, denoted by a blank, and 4 "on" states denoted "1", "2", "3", and "4". As in the 3 state version, ordinary life rules are used to take care of deaths and survivals, and new rules are needed only for birth cells. If at least 2 of the 3 neighbors of a birth cell have the same state, the cell will have that state in the next generation. If the 3 states are all different, the cell will have the 4th "on" state. For example, if the neighbors of a birth cell have states 1, 3, and 4, then the cell will have state 2 in the next generation.
Note that if each "on" cell in one generation has state 1 or 2, then this will be true of all succeeding generations, and the rules become simply the 3 state ones. (Of course,there is nothing special about states 1 and 2; any pair of "on" states would work as well.)
I have examined all possible gliders in 5 state life and have found that there is exactly 1 alliance which is not actually a 3 state one. (By "exactly one", I mean except for permutations of the states.) As shown in Figure 5, this alliance has period 12 rather than 4.
There are at least 6 (there might be more, but I doubt it) 5 state alliances for the toad. These are shown in Figure 6. (To save space, I have shown only 1 phase of each.) Surprisingly, each of these alliances has period 4 rather than 2.
In Lifeline Number 5, you presented some oscillators discovered by "Buckinghams Combine". In Lifeline Number 6, page 3, you stated that object (e) has period 6 and object (g) has period 7. Actually, (e) has period 7 and (g) has period 6.
- EN: thanks, its strange that no one else mentioned this.
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On page 1 of Lifeline Number 6, you mentioned Conway's "Unique Father Problem". You illustrated this by asking if the "tick" was the only predecessor of the "tock". This example is somewhat inappropriate, since the clock is not stable, as required in the problem. However,to answer the clock problem, Figure 7 shows another predecessor to the "tock". (There must be something simpler than this.) EN: see page 24.
In Lifeline Number 9, page 4, you asked for the final censuses of all objects which are contained in a 3 by 3 square. These are given below. As noted in Lifeline Number 10, page 5, A10=D11 and E11=H10. In addition, we have the following equalities (,though the relevant objects are not in the same positions in the square).
A2=D2 A3=B3 A4=D4 A5=D5 B1=C1=D1 B4=B5=C4 B6=B7 C2=C3 C6=D6 C8=C9 C10=D10 D8=D9 E8=G8 F8=H8
The final censuses are:
dead |A1 dies in 1 |A2,A3,A13,B1,B2,B3,C1,C2,C3,D1,D2,D3,D12 dies in 2 |A5,A6,A7,A11,B6,B7,B12,C5,C6,C7,C11,C12,D5,D6,D7,E3,H4 dies in 3 |B8,B11,E9,F13,G12 dies in 4 |E5,E6,E8,F5,F8,G8,G11,H8 dies in 5 |B10 dies in 6 |F2,F6 dies in 7 |H3 dies in 9 |H5 blinker |A4,D4 block |B9 block in 1 |B4,B5,C4 block in 2 |A9,A12,C10,D10 tub |B13 tub in 1 |E13,G13 boat |H12 boat in 1 |F11,G10 pond in 2 |G5 pond in 3 |H7 pond in 4 |D13 beehive in 1 |E4,G6 beehive in 2 |A10,D11 beehive in 3 |D8,D9 loaf in 1 |E2,F4 loaf in 2 |H9 loaf in 3 |G9,H2 loaf in 4 |E7,G1 ship |H6 t.l. in 5* |E1,H1 t.l. in 6 |H13 t.l. in 8 |F3,G2 t.l. in 9 |C8,C9 t.l. in 10 |E12,C13 t.l. in 11 |A8,F9 glider |F10,H11 glider in 1 |E11,H10 R pentomino |F12 R in 1 |E10 PI heptomino |G3 PI in 1 |F7 Also, G4=R in 1 and F1 in 3=G7 in 5=PI in 3 *t.l.=traffic lights
I have experimented a little with 3-4 life and have found 2 periodic objects which have not been mentioned in Lifeline. They are shown, in 1 phase only, in Figures 8 and 9. Their periods are 12 and 6, respectively.
In Lifeline Number 10 page 8, you requested information on still lifes in which each bit has the same number of neighbors (, either 2 or 3). The ones with fewer than 9 bits are: the block, the tub, the beehive, the aircraft carrier, the loaf, the pond, and the object shown in Figure 10. Figure 11 shows 2 20-bit still lifes in which each bit has exactly 2 neighbors. I have not found any others with 20 or fewer bits, but some larger ones are shown in Figure 12. In these, each bit has exactly 2 neighbors. I have not found any still lifes except the block in which each bit has exactly 3 neighbors, and I conjecture that there are none. So far, however, I have only been able to prove that such an object must contain a block. EN: see page 14
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| Figure 11 (click above to open LifeViewer) |
Figure 12 Larger still lifes
- EN: yes, but sadly out of date.
Does the Lifefile still exist? There has been no mention of it since Lifeline Number 4. If it does, please send me any information you can concerning collisions between 2 gliders, a glider and a block, or a glider and a blinker.
- Sincerely,
- Dean Hickerson
- Dean Hickerson
- P.O. Box 31
- Yreka, California 96097
P.S.: Figure 1 3 contains some 5 state alliances for a lightweight spaceship. Spaceships a, b, c, d, e, and f have periods 4, 4, 4, 8, 8, 16, respectively. Only 1 phase of each is shown.
[insert viewer here]
Figure 13
Lightweight spaceship alliances
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Reader Reply . . . August, 1973
Robert T. Wainwright
LIFELINE Editor
Dear Sir,
Some assorted comments and discoveries:
A lightweight spaceship can also (#1 p4, #3 p24) convert gliders to R's, as shown.
| Figure 11 (click above to open LifeViewer) |
Hexlife (#2 p15) includes a period nine oscillator I call the "magician", with a three-cell grandfather:
[the Hexlife in LifeViewer doesn't seem to be the same one as is described here]
Petrie notes that the V.C age record (#4 p4) is set by "Pike", which, from a glider collision with a ship or a boat, takes 997 generations to leave 9 blinkers, 7 blocks, 2 boats, 9 beehives, and a toad.
| Figure 11 (click above to open LifeViewer) |
A glider-toad collision (#4 p6) reflects a glider 90° but doesn't work for glider streams. These three collisions each reflect the solid glider down at 90°, and likewise destroy the target, but each target is unstable and is easy to recreate. This is especially useful in glider logic.
| Figure 11 (click above to open LifeViewer) |
| Figure 11 (click above to open LifeViewer) |
| Figure 11 (click above to open LifeViewer) |
[insert viewer here]
No five-cell tangoes yield twin blocks, but the three at left yield ponds (#4 p10).
| Figure 11 (click above to open LifeViewer) |
At right is a clock father (#6 p1).
| Figure 11 (click above to open LifeViewer) |
Gibson's application of the occult was not to blame for his faulty boxing forecast (#7 p3). The computer shows Frazier's octomino active 14 re, while Foreman's heptomino is active 18 re. Each yields a beehive, which presumably symbolizes the boxing crown.
Although the variety of mixed still lifes (i.e. with cells with two and three neighbors, #10 p8) is tremendous, only the boat and ship can be called common, hence the supposedly strange results.
Petrie suggests the "Pearl Harbor" fuse, at left, is the only fuse we know to occur "naturally". It is found in a collision of a glider with a light spaceship.
| Figure 11 (click above to open LifeViewer) |
Here is a new V.F fuse, the "infinity bomb". The baker goes out at c, but its loafs burn at 4/5 c with period 40n. The result thru 530 generations is cloudy. The ignition is also messy.
| Figure 11 (click above to open LifeViewer) |
My long-awaited article follows...
- Sincerely[insert image here]
- V. Everett Boyer
- V. Everett Boyer
Lifequote submitted by the Editor:
'Whatever you have received more than others-in health, in talents
in ability, in success, in a pleasant childhood, in harmonious
conditions of home life—all this you must not take to yourself as
a matter of course. In gratitude for your good fortune, you must
render in return some sacrifice of your own life for another life.'
-Albert Schweitzer
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