LifeWiki - User contributions [en]

Talk:Titanic toroidal traveler

2010-01-04T23:16:20Z

Axaj: /* Replicator */

== Replicator ==

The detached back part is a replicator, not just replicator-like. --[[User:Axaj|Axaj]] 19:09, 23 December 2009 (UTC)

It's not regular enough to be a replicator in the classical sense. Replicators in HighLife etc. return to the same (fixed) population after exponentially increasing periods of time. The Titanic Toroidal Traveller does not have this property. If you're still not convinced, note that this pseudo-replicator does not produce *exact copies* of itself, without leaving unwanted debris.

Maybe you're getting confused with the true replicator on a 6-cell cylinder, the T-tetromino.

Just for clarification, this is what the back part of the TTT looks like:

x = 17, y = 739, rule = S23/B3
b3o3b3o3b3o$$bobo3bobo3bobo$bbo5bo5bo10$bbo5bo5bo$bobo3bobo3bobo$$b3o
3b3o3b3o7$b3o3b3o3b3o5$b3o3b3o3b3o$bbo5bo5bo4$bbo5bo5bo$b3o3b3o3b3o8$b
3o3b3o3b3o$$o3bobo3bobo3bo$o3bobo3bobo3bo$o3bobo3bobo3bo$obobobobobobo
bobo$b3o3b3o3b3o$$b3o3b3o3b3o$o3bobo3bobo3bo$ooboobooboobooboo15$b3o3b
3o3b3o$$o3bobo3bobo3bo$o3bobo3bobo3bo$o3bobo3bobo3bo$$b3o3b3o3b3o3$oob
oobooboobooboo$ooboobooboobooboo8$b3o3b3o3b3o14$b3o3b3o3b3o$$o3bobo3bo
bo3bo4$b3o3b3o3b3o$b3o3b3o3b3o$$b3o3b3o3b3o$b3o3b3o3b3o4$o3bobo3bobo3b
o$$b3o3b3o3b3o6$ooboobooboobooboo$ooboobooboobooboo26$b3o3b3o3b3o$obob
obobobobobobo$o3bobo3bobo3bo$b3o3b3o3b3o4$ooboobooboobooboo$oobooboob
oobooboo12$ooboobooboobooboo$ooboobooboobooboo4$ooboobooboobooboo$oob
oobooboobooboo6$bbo5bo5bo$bobo3bobo3bobo$o3bobo3bobo3bo$bobo3bobo3bobo
$bbo5bo5bo$$bbo5bo5bo$bobo3bobo3bobo$o3bobo3bobo3bo$bobo3bobo3bobo$bbo
5bo5bo6$ooboobooboobooboo$ooboobooboobooboo6$bbo5bo5bo$b3o3b3o3b3o$obo
bobobobobobobo$ooboobooboobooboo$obobobobobobobobo$b3o3b3o3b3o$$b3o3b
3o3b3o$obobobobobobobobo$ooboobooboobooboo$obobobobobobobobo$b3o3b3o3b
3o$bbo5bo5bo$$bbo5bo5bo$b3o3b3o3b3o$obobobobobobobobo$oobooboobooboob
oo$obobobobobobobobo$b3o3b3o3b3o$bbo5bo5bo4$b3o3b3o3b3o$o3bobo3bobo3bo
$o3bobo3bobo3bo$o3bobo3bobo3bo$b3o3b3o3b3o$$bbo5bo5bo$b3o3b3o3b3o$oob
oobooboobooboo$b3o3b3o3b3o$bbo5bo5bo17$ooboobooboobooboo$$ooboobooboob
ooboo$$bbo5bo5bo19$bbo5bo5bo$bobo3bobo3bobo$bobo3bobo3bobo$bbo5bo5bo4$
ooboobooboobooboo$ooboobooboobooboo7$ooboobooboobooboo$oobooboobooboob
oo6$bbo5bo5bo$bobo3bobo3bobo$bobo3bobo3bobo$bbo5bo5bo3$bbo5bo5bo$bbo5b
o5bo$b3o3b3o3b3o20$bbo5bo5bo$b3o3b3o3b3o$ooboobooboobooboo$b3o3b3o3b3o
$bbo5bo5bo4$b3o3b3o3b3o$b3o3b3o3b3o$bobo3bobo3bobo$$ooboobooboobooboo$
ooboobooboobooboo$o3bobo3bobo3bo$bobo3bobo3bobo$bbo5bo5bo4$bbo5bo5bo$
ooboobooboobooboo$o3bobo3bobo3bo$ooboobooboobooboo$bbo5bo5bo6$bbo5bo5b
o$bbo5bo5bo$$bbo5bo5bo$bbo5bo5bo27$ooboobooboobooboo$ooboobooboobooboo
5$ooboobooboobooboo$bobo3bobo3bobo$bbo5bo5bo4$ooboobooboobooboo7$ooboo
booboobooboo10$bbo5bo5bo$bobo3bobo3bobo$o3bobo3bobo3bo$bobo3bobo3bobo$
bbo5bo5bo9$bbo5bo5bo$bbo5bo5bo$bbo5bo5bo9$bbo5bo5bo$bobo3bobo3bobo$bob
o3bobo3bobo$bbo5bo5bo13$ooboobooboobooboo$ooboobooboobooboo3$bbo5bo5bo
$bobo3bobo3bobo$bobo3bobo3bobo$bbo5bo5bo5$b3o3b3o3b3o$bbo5bo5bo3$bbo5b
o5bo$bobo3bobo3bobo$$bobo3bobo3bobo$b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob
5o12$b3o3b3o3b3o$ooboobooboobooboo$$bobo3bobo3bobo$$b3o3b3o3b3o$bbo5bo
5bo8$ooboobooboobooboo$ooboobooboobooboo15$bbo5bo5bo$bbo5bo5bo$bbo5bo
5bo5$bbo5bo5bo$bbo5bo5bo$bbo5bo5bo$$bbo5bo5bo$bbo5bo5bo$bbo5bo5bo$$bbo
5bo5bo$bobo3bobo3bobo$bobo3bobo3bobo$bbo5bo5bo9$ooboobooboobooboo$oob
oobooboobooboo$$bbo5bo5bo$bobo3bobo3bobo$o3bobo3bobo3bo$o3bobo3bobo3bo
$ooboobooboobooboo22$b3o3b3o3b3o$o3bobo3bobo3bo$$o3bobo3bobo3bo$b3o3b
3o3b3o4$b3o3b3o3b3o$b3o3b3o3b3o$o3bobo3bobo3bo$o3bobo3bobo3bo$o3bobo3b
obo3bo$b3o3b3o3b3o$$b3o3b3o3b3o$o3bobo3bobo3bo$o3bobo3bobo3bo$o3bobo3b
obo3bo$b3o3b3o3b3o$b3o3b3o3b3o5$bbo5bo5bo$bobo3bobo3bobo$bobo3bobo3bob
o$bbo5bo5bo13$b3o3b3o3b3o$bbo5bo5bo15$bbo5bo5bo$bobo3bobo3bobo$bobo3bo
bo3bobo$bbo5bo5bo4$bbo5bo5bo$bobo3bobo3bobo$o3bobo3bobo3bo$bobo3bobo3b
obo$bbo5bo5bo7$bbo5bo5bo$b3o3b3o3b3o$ooboobooboobooboo$oobooboobooboob
oo3$ooboobooboobooboo$5ob5ob5o$b3o3b3o3b3o4$bbo5bo5bo$bbo5bo5bo$bobo3b
obo3bobo$bbo5bo5bo$bbo5bo5bo18$bbo5bo5bo$bbo5bo5bo$bobo3bobo3bobo$bbo
5bo5bo$bbo5bo5bo$$bbo5bo5bo$bbo5bo5bo$bobo3bobo3bobo$bbo5bo5bo$bbo5bo
5bo8$bbo5bo5bo$b3o3b3o3b3o$b3o3b3o3b3o$bbo5bo5bo$$ooboobooboobooboo$b
3o3b3o3b3o$bbo5bo5bo$$bbo5bo5bo$b3o3b3o3b3o$ooboobooboobooboo$$bbo5bo
5bo$b3o3b3o3b3o$b3o3b3o3b3o$bbo5bo5bo8$bbo5bo5bo$bbo5bo5bo$bobo3bobo3b
obo$bbo5bo5bo$bbo5bo5bo$$bbo5bo5bo$bbo5bo5bo$bobo3bobo3bobo$bbo5bo5bo$
bbo5bo5bo!

By comparison, this is what the true replicator looks like:

x = 17, y = 263, rule = S23/B3
b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b3o3b3o$$b3o3b
3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b3o3b3o6$bbo5bo5bo$b
obo3bobo3bobo$$bbo5bo5bo14$bbo5bo5bo$$bobo3bobo3bobo$bbo5bo5bo6$b3o3b
3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b3o3b3o$$b3o3b3o3b3o
$o3bobo3bobo3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b3o3b3o18$b3o3b3o3b3o$o3bo
bo3bobo3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b3o3b3o$$b3o3b3o3b3o$o3bobo3bob
o3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b3o3b3o6$bbo5bo5bo$bobo3bobo3bobo$$bb
o5bo5bo14$bbo5bo5bo$$bobo3bobo3bobo$bbo5bo5bo6$b3o3b3o3b3o$o3bobo3bobo
3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b3o3b3o$$b3o3b3o3b3o$o3bobo3bobo3bo$5o
b5ob5o$o3bobo3bobo3bo$b3o3b3o3b3o18$b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob
5o$o3bobo3bobo3bo$b3o3b3o3b3o$$b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3b
obo3bobo3bo$b3o3b3o3b3o6$bbo5bo5bo$bobo3bobo3bobo$$bbo5bo5bo14$bbo5bo
5bo$$bobo3bobo3bobo$bbo5bo5bo6$b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3b
obo3bobo3bo$b3o3b3o3b3o$$b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3bobo3bo
bo3bo$b3o3b3o3b3o18$b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3bobo3bobo3bo
$b3o3b3o3b3o$$b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b
3o3b3o6$bbo5bo5bo$bobo3bobo3bobo$$bbo5bo5bo14$bbo5bo5bo$$bobo3bobo3bob
o$bbo5bo5bo6$b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b
3o3b3o$$b3o3b3o3b3o$o3bobo3bobo3bo$5ob5ob5o$o3bobo3bobo3bo$b3o3b3o3b3o
!

--[[User:Calcyman|Calcyman]] 13:01, 24 December 2009 (UTC)

:I don't think it needs to be regular to be a replicator. For instance, the replicator in B36/S245 grows ver irregularly, but is still classified as a replicator. --[[User:Axaj|Axaj]] 23:16, 4 January 2010 (UTC)

Talk:Titanic toroidal traveler

2009-12-23T19:09:56Z

Axaj: Replicator

== Replicator ==

The detached back part is a replicator, not just replicator-like. --[[User:Axaj|Axaj]] 19:09, 23 December 2009 (UTC)

User:Axaj

2009-12-23T19:08:27Z

Axaj:

Well, I don't see much to say here. I have mostly dabbled in Life (duh), LogRep, and D&N.

Titanic toroidal traveler

2009-12-18T15:49:35Z

Axaj:

{{Pattern|type=Superstring|name=Titanic toroidal traveler|discoverer=Robert Wainwright|discoveryear=1971|pname=titanictoroidaltraveler|bx=∞|by=2|life105=true|life106=true|plaintext=true|rle=true}}
'''Titanic toroidal traveler''' is a [[superstring]] with a 6-[[cell]] repeating segment that was first described in [[Lifeline Volume 4]]. The front part repeats with [[period]] 16, but the detached back part is a [[replicator]], and replicates at 7c/40.

A similar situation arises when the twin bees shuttle is iterated on a cylinder of width 12.

==External links==
{{LinkLexicon|lex_t.htm#titanictoroidaltraveler}}

Speed

2009-12-01T00:58:20Z

Axaj: added "see also"

{{Glossary}}
The '''speed''' of a [[pattern]] is a measure of the number of generations that it takes for some effect to travel some given distance. Speeds are almost always measured in reference to the '''speed of light''' (or '''speed of life'''), denoted by ''c'', which is a rate of one [[cell]] per [[generation]]. The speed of light is the fastest possible speed at which any effect can propagate.

==Spaceships==
[[Image:lwss.gif|framed|left|The lightweight spaceship has speed c/2 because it moves 2 cells in 4 generations]]
For [[spaceship]]s, the speed describes the number of cells that it has been displaced by after it has gone through one [[period]]. Speed is reported in the form dc/p where d is the displacement and p is the period. It is most common to reduce this "fraction" to lowest terms. For example, even though the period of a [[lightweight spaceship]] is 4, it moves 2 cells during those generations, giving it a speed of 2c/4 = c/2.

For spaceships that move diagonally, speed is defined the same as above, but where "the number of cells that is has been displaced by" refers to the maximum of the x or y displacement; not their sum. So, for example, a [[glider]] has a speed of c/4, since it takes 4 generations to move one cell in the x direction and one cell in the y direction.

More formally, if a spaceship in any 2D [[cellular automaton]] is translated by (x,y) after n generations then its speed v may be defined as:
[[Image:speed_formula.png|center]]

This definition can be generalized in a straightforward manner to cellular automata with dimension other than two.

==See also==
*[[:Category:speeds|List of important speeds]]

==External links==
*[http://en.wikipedia.org/wiki/Spaceship_(cellular_automaton) Spaceships] at Wikipedia
*[http://www.argentum.freeserve.co.uk/lex_s.htm#speedoflight Speed of light] at the Life Lexicon

Talk:Block on cover

2009-11-30T02:17:13Z

Axaj: Eating capabilities

== Eating capabilities ==

Could this eat objects in a similar way that Eater 2 does? --[[User:Axaj|Axaj]] 02:17, 30 November 2009 (UTC)

Talk:Infinite growth

2009-10-25T15:03:25Z

Axaj:

== Fastest? ==

"quadratic growth is the fastest possible growth rate"

I don't believe this is correct. Is there some reason you can't have a factory that produces MMM breeders? --[[User:Axaj|Axaj]] 02:33, 20 October 2009 (UTC)

: Quadratic is the fastest possible because patterns can't possibly expand at a speed faster than c. Thus, if the bounding box is x-by-y to begin with, after k generations it is at most (x+2k)-by-(y+2k), which has area xy+2k(x+y)+4k^2, which is quadratic in k. Since the area of the bounding box is an upper bound on the number of alive cells in the pattern, the number of alive cells can't grow any faster than quadratically. [[User:Nathaniel|Nathaniel]] 03:28, 20 October 2009 (UTC)

::Okay, I see now. Thanks! --[[User:Axaj|Axaj]] 15:03, 25 October 2009 (UTC)

Polyomino

2009-10-21T21:46:19Z

Axaj: added Haplominoes

{{Glossary}}
A '''polyomino''' (or simply '''omino''') is a finite collection of orthogonally connected [[cell]]s. The mathematical study of polyominoes was initiated by Solomon Golomb in 1953. Conway's early investigations of [[Conway's Game of Life|Life]] and other [[cellular automaton|cellular automata]] involved tracking the histories of small polyominoes, this being a reasonable way to ascertain the typical behaviour of different cellular automata when the patterns had to be evolved by hand rather than by computer. Polyominoes have no special significance in Life, but their extensive study during the early years lead to a number of important discoveries and has influenced the terminology of Life.

[[Image:Cross_small.png|framed|right|A cross.]]During the course of its evolution a polyomino could regain its original form, thereby constituting one phase of an [[oscillator]], as seen in the (infinite) [[cross]] family. The only other known examples are the [[block]] (which has [[period]] 1), the [[blinker]], the [[toad]], the [[star]] and (in two different phases) the [[pentadecathlon]]. Were a recurring polyomino displaced, it would be participating in a spaceship, though the only known examples are the [[lightweight spaceship]], the [[middleweight spaceship]], and the [[heavyweight spaceship]]. Of course, its evolution could follow other trajectories, possibly very long lived.

==Sizes of polyominoes==
Polyominoes of with n cells for n = 1, 2, 3, 4, ... are called haplominoes, dominoes, triominoes, tetrominoes, pentominoes, hexominoes, heptominoes, octominoes, and n-ominoes in general. The number of distinct polyominoes with n cells for n = 1, 2, 3, ... is given by the sequence 1, 1, 2, 5, 12, 35, 108, 369, 1285, ... (Sloane's [http://www.research.att.com/~njas/sequences/A000105 A000105]).

===Haplominoes===
There is only one '''haplomino''' (also called monomino or dot) and by itself it dies after one [[generation]]. Several objects, such as the middleweight spaceship, produce dot [[spark]]s.

===Dominoes===
There is also only one '''domino''' and by itself it too dies after one generation. A number of objects, such as the heavyweight spaceship and the pentadecathlon, produce domino sparks.

===Triominoes===
There are exactly two distinct '''triominoes'''. The term is rarely used in Life, because the two objects in question are simply the [[blinker]] and the [[pre-block]].

===Tetrominoes===
There are five distinct '''tetrominoes''', each of which is shown below. The first is the [[block]], the second is the [[T-tetromino]], and the remaining three rapidly evolve into [[beehive]]s. The fourth is commonly referred to as a [[tail]] and is often attached to small [[still life]]s.

[[Image:Tetrominoes.png|framed|center|The five distinct tetrominoes. From left to right: O, T, I, J, Z.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=tetrominoes click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=tetrominoes.rle click here] ]]

===Pentominoes===
There are 12 distinct '''pentominoes'''. [[:Category:Patterns found by John Conway|John Conway]] assigned them all letters in the range O to Z, loosely based on their shapes, and they are all shown below in order.
* The O-pentomino is a [[traffic light]] [[predecessor]], though not one of the more common ones.
* The P-pentomino is a common [[spark]] that dies in [[generation]] 4.
* The Q-pentomino is a traffic light predecessor.
* The [[R-pentomino]] is a [[methuselah]] and by far the most well-known pentomino.
* The S-pentomino dies in generation 5.
* The T-pentomino is a common [[parent]] of the [[T-tetromino]].
* The U-pentomino dies in generation 4.
* The V-pentomino evolves into a [[loaf]] in generation 3.
* The W-pentomino is a common loaf predecessor.
* The X-pentomino is a traffic light predecessor.
* The Y-pentomino dies in generation 3.
* The Z-pentomino dies in generation 3.

{|
|-
|[[Image:Opentomino_small.png|framed|center|O]]
|[[Image:Ppentomino_small.png|framed|center|P]]
|[[Image:Qpentomino_small.png|framed|center|Q]]
|[[Image:Rpentomino_small.png|framed|center|R]]
|[[Image:Spentomino_small.png|framed|center|S]]
|[[Image:Tpentomino_small.png|framed|center|T]]
|-
|[[Image:Upentomino_small.png|framed|center|U]]
|[[Image:Vpentomino_small.png|framed|center|V]]
|[[Image:Wpentomino_small.png|framed|center|W]]
|[[Image:Xpentomino_small.png|framed|center|X]]
|[[Image:Ypentomino_small.png|framed|center|Y]]
|[[Image:Zpentomino_small.png|framed|center|Z]]
|}

===Hexominoes===
There are 35 distinct '''hexominoes''', the majority of which behave in uninteresting ways. The most interesting and well-known examples are [[century]], [[stairstep hexomino]], [[table]], [[toad]] and [[Z-hexomino]].

===Heptominoes===
There are 108 distinct '''heptominoes'''. Those with names in common use are the [[B-heptomino]], the [[bullet heptomino]], the [[C-heptomino]], the [[Herschel]] and the [[pi-heptomino]].

===Octominoes===
There are 369 distinct '''octominoes'''. Despite the abundance of octominoes, the following fairly common octomino (or its two-generation successor) is often referred to as simply ''the'' octomino:
[[Image:Octomino.png|framed|center|The octomino and its two-generation successor.]]

==Switch Engine==
[[Charles Corderman]] discovered the [[switch engine]] by running an exhaustive computer search on all decominoes. The machine that discovered the decomino seed was unique, possessing an unusual architecture.

==Nomenclature==

The name is a back-formation from 'domino', which explicitly refers to a pair of orthogonally connected live cells. According to the Life Lexicon, the pluralised name can be spelt two different ways: 'polyominos' and 'polyominoes' are both equally acceptable. The same applies to the systematic names of each of the polyomino sizes.

==See also==
*[[Polyplet]]

==External links==
{{LinkWeisstein|Polyomino.html}}
{{LinkLexicon|lex_p.htm#polyomino}}

Talk:Infinite growth

2009-10-20T02:33:12Z

Axaj: Fastest?

Talk:Phoenix

2009-10-06T02:27:59Z

Axaj:

== Spaceships not phoenixes? ==

Spaceships can definitely be phoenixes. Just look at this Seeds (2/) spaceship:

000000
001100
010010
000000

If it means specifically for 23/3, then it should say so. Correct? --[[User:Axaj|Axaj]] 02:25, 6 October 2009 (UTC)

Talk:Phoenix

2009-10-06T02:25:30Z

Axaj: Spaceships not phoenixes?

Talk:Reflector

2009-10-02T04:51:41Z

Axaj: p138

== p138 ==

Is there a period 138 90° reflector? --[[User:Axaj|Axaj]] 04:51, 2 October 2009 (UTC)

User:Axaj

2009-10-02T03:11:12Z

Axaj: New page: Well, I don't see much to say here. I have mostly dabbled in 23/3 (duh) and 3/0 (my own creation, called "Leather Belt"). I have also been doing some stuff in Generations.

Well, I don't see much to say here. I have mostly dabbled in 23/3 (duh) and 3/0 (my own creation, called "Leather Belt"). I have also been doing some stuff in Generations.