Evolutionary factor in Conway's life
jani.i...@gmail.com
find any information on evolutionary factors of life patterns. I found
out that Bunnies have a factor of nearly 2000. Is this the greatest
factor known? Also, has it been proven that arbitrarily large factors
can exist?
Jani Iltanen
Dave Greene
> find any information on evolutionary factors of life patterns. I found
> out that Bunnies have a factor of nearly 2000. Is this the greatest
> factor known?
No, not quite -- or depending on what kind of Life patterns you're
looking at, not nearly. Have a look at Dean Hickerson's summary page
for methuselahs:
http://www.math.ucdavis.edu/~dean/RLE/methuselahs.html
The evolutionary factor works out to 1944.5 for the following pattern,
versus 1925+ or 1934+ for 'bunnies' and other 'rabbits' friends-and-
relations:
#C Runs for 23334 gens. Initial pop = 12. Final pops = 2898/2895
#C May be the longest-lived 12-cell pattern within a 12x12 square.
#C Emits a LWSS in gen 13811.
#C Found by Tomas G. Rokicki, some time before Feb 21, 2005.
x = 8, y = 5
4b3o$3bo$o5bo$b2o2bobo$bobo!
> Also, has it been proven that arbitrarily large factors can exist?
Sure. As Hickerson points out, a glider aimed at a faraway blinker or
preblock has only 8 cells, but can be arranged to run as long as you
want. To disqualify cases like that, you have to come up with an
arbitrary definition for "methuselah" that includes some kind of
bounding box or connectedness rule... and ultimately arguing about
which definition to use isn't very interesting, which may be why the
evolutionary-factor metric dropped out of use.
(It seems especially odd to call something a "factor" when you aren't
even dividing apples by apples, so to speak: time to stabilization
divided by initial cell count seems like a strange numerological
exercise. Before I looked it up, I expected the definition would be
final divided by initial population.)
There's a hard upper limit on how long a Life pattern can possibly run
before it stabilizes, if it stays inside a given bounding box. But
it's a very generous limit: any two-state CA inside an N-cell
bounding box must have repeated a cell configuration by time 2^N, so
if it's still running then it must be an oscillator.
-- That leaves a lot of room for improvement! For example, adding or
subtracting a few cells would allow this 297x227 oscillating pattern
to stabilize eventually, with an evolutionary factor somewhere over
sixty-three million:
http://pentadecathlon.com/lifenews/2006/05/primeperiod_oscillator_p103079.html
Here are a couple of more interesting examples from Nick Gotts, with
evolutionary factors of 46,000+ and something over 220,000,
respectively. Notice that (if memory serves) the ark doesn't stop
growing after "stabilization" -- it's just that the glider stream
heading northwest punches through the startup debris, and after that
you know what the pattern will look like at any future time without
having to run it any further. These are included as "ark1" and "ark2"
in Golly 1.3's "Methuselahs" folder:
#C ark-ohnp: 16 cells, stabilizes at 736692.
#C This is the 16-cell ark that takes longest to stabilize.
#C Nick Gotts, 24 February 2005.
x = 32, y = 29, rule = S23/B3
27bo$28bo$29bo$28bo$27bo$29b3o20$oo$bbo$bbo$3b4o!
#C ark-nhaa-gbi6x376: 19 cells, stabilizes between 2^22 and 2^23.
#C Nick Gotts, 24 February 2005.
x = 53, y = 44, rule = S23/B3
50b3o28$12bo$12bo$13boo$15bo$15bo$15bo$15bo6$oo$bbo$bbo$3b4o!
For much more along these lines, take a look at http://nickgotts-eventful.blogspot.com/
.
Keep the cheer,
Dave
Dave Greene
593. History of China.--I believe only the histories, whose witnesses got
themselves killed.
Which is the more credible of the two, Moses or China?
It is not a question of seeing this summarily. I tell you there is in it
something to blind, and something to enlighten.
By this one word I destroy all your reasoning. "But China obscures," say
you; and I answer, "China obscures, but there is clearness to be found; seek
it."
Thus all that you say makes for one of the views and not at all against the
other.
So this serves, and does no harm.
We must, then, see this in detail; we must put the papers on the table.
594. Against the history of China.--The historians of Mexico, the five suns,
of which the last is only eight hundred years old.
The difference between a book accepted by a nation and one which makes a
nation.
595. Mahomet was without authority. His reasons, then, should have been very
strong, having only their own force. What does he say, then, that we must
believe him?
596. The Psalms are chanted throughout the whole world.
Who renders testimony to Mahomet? Himself. Jesus Christ desires His own
testimony to be as nothing.
The quality of witnesses necessitates their existence always and everywhere;
and he, miserable creature, is alone.
597. Against Mahomet.--The Koran is not more of Mahomet than the Gospel is
of Saint Matthew, for it is cited by many authors from age to age. Even its
very enemies, Celsus and Porphyry, never denied it.
The Koran says Saint Matthew was an honest man. Therefore Mahomet was a
false prophet for calling honest men wicked, or for not agreeing with what
they have said of Jesus Christ.
598. It is not by that which is obscure in Mahomet, and which may be
interpreted in a mysterious sense, that I would have
jani.i...@gmail.com
will the heretics say?
In order to know whether an opinion is a Father's...
863. All err the more dangerously, as they each follow a truth. Their fault
is not in following a falsehood, but in not following another truth.
864. Truth is so obscure in these times, and falsehood so established, that,
unless we love the truth, we cannot know it.
865. If there is ever a time in which we must make profession of two
opposite truths, it is when we are reproached for omitting one. Therefore
the Jesuits and Jansenists are wrong in concealing them, but the Jansenists
more so, for the Jesuits have better made profession of the two.
866. Two kinds of people make things equal to one another, as feasts to
working days, Christians to priests, all things among them, etc. And hence
the one party conclude that what is then bad for priests is also so for
Christians, and the other that what is not bad for Christians is lawful for
priests.
867. If the ancient Church was in error, the Church is fallen. If she should
be in error to-day, it is not the same thing; for she has always the
superior maxim of tradition from the hand of the ancient Church; and so this
submission and this conformity to the ancient Church prevail and correct
all. But the ancient Church did not assume the future Church and did not
consider her, as we assume and consider the ancient.
868. That which hinders us in comparing what formerly occurred in the Church
with what we see there now is that we generally look upon Saint Athanasius,
Saint Theresa, and the rest, as crowned with glory and acting towards us as
gods. Now that time has cleared up things, it does so appear. But at the
time when he was persecuted, this great saint was a man called Athanasius;
and Saint Theresa was a nun. "Elias was a man subject to like passions as we