Difference between revisions of "OCA:Maze"

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{{Rule|name=Maze|imgname=maze|s=12345|b=3|char=Explosive|animated=true}}
{{Rule
'''Maze''' is a [[cellular automaton#Well-known Life-like cellular automata|Life-like cellular automaton]] in which [[cell]]s survive from one [[generation]] to the next if they have at least 1 and at most 5 [[Moore neighbourhood|neighbours]]. Cells are born if they have exactly 3 neighbours.
|name           = Maze
 
|imgname         = maze
This rule is notable because random starting patterns tend to evolve into complex maze-like structures with well-defined walls outlining corridors.
|char            = Explosive
|b              = 3
|s               = 12345
|ruleinteger    = 31752
|reversal        = B0128/S01234678
|animated       = true
}}
'''Maze''' is a [[cellular automaton#Well-known Life-like cellular automata|Life-like cellular automaton]] in which [[cell]]s survive from one [[generation]] to the next if they have at least 1 and at most 5 [[Moore neighbourhood|neighbours]]. Cells are born if they have exactly 3 neighbours. This resembles [[Conway's Game of Life]] in some ways, but it is rather more difficult for cells to die off, and random starting patterns tend to evolve into complex growing maze-like structures with well-defined walls outlining corridors.


==Notable patterns==
==Notable patterns==
The maze rule is explosive, which means that most randomly-generated starting patterns will explode in all directions. Nonetheless, there are many [[still life]]s and [[oscillator]]s under this rule. It has no known [[spaceship]]s.<ref>{{cite web|url=http://fano.ics.uci.edu/ca/rules/b3s12345/ |title=Maze (B3/S12345) |publisher=David Eppstein|accessdate=March 16, 2009}}</ref>
The maze rule is [[Class three cellular automata|explosive]], which means that most randomly-generated starting patterns will explode in all directions. Nonetheless, there are many [[still life]]s and [[oscillator]]s under this rule. It has no known [[spaceship]]s.<ref>{{cite web|url=http://fano.ics.uci.edu/ca/rules/b3s12345/ |title=Maze (B3/S12345) |publisher=David Eppstein|accessdate=March 16, 2009}}</ref>


===Still lifes===
===Still lifes===
Below is a sampling of many small patterns that are still lifes in the maze rule. Several small still lifes from [[Conway's Game of Life]] are also still lifes in this rule, and they include [[block]], [[tub]], [[barge]], [[ship]], [[boat]], [[loaf]], [[beehive]], [[snake]], and [[aircraft carrier]].
Below are all still lifes with nine or fewer cells in the maze rule.<ref>Computed using the ''EnumStillLifes.c'' script located [http://www.conwaylife.com/forums/viewtopic.php?f=9&t=44 here].</ref> It is worth noting that, because the only difference between this rule and the standard [[Conway's Game of Life|Conway rule]] is that cells have more ways of staying alive, every pattern that is a still life in standard Life is also a still life in the maze rule. Similarly, every still life in the maze rule will also be a still life in the [[Life without death]] rule.
 
Other notable still lifes include the infinitely-extensible diagonal line. Also, any diamond in which every other cell is alive (i.e. any [[barge]] that is extended in either length and/or width) is a still life.


Other notable still lifes include the infinitely-extensible diagonal line. Also, any diamond in which every other cell is alive (i.e. any barge that is extended in either length ''or'' width) is a still life.
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
[[Image:maze_still_lifes.png|framed|center|Some small still lifes.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=mazestilllifes click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=mazestilllifes.rle click here] ]]
|-
! Size
! Count
! Image
! Links
|-
| 1
| 0
|
|
|-
| 2
| 2
| [[Image:maze2cellstilllifes.png]]
| {{JavaRLE|maze2cellstilllifes}}
|-
| 3
| 1
| [[Image:maze3cellstilllifes.png]]
| {{JavaRLE|maze3cellstilllifes}}
|-
| 4
| 5
| [[Image:maze4cellstilllifes.png]]
| {{JavaRLE|maze4cellstilllifes}}
|-
| 5
| 7
| [[Image:maze5cellstilllifes.png]]
| {{JavaRLE|maze5cellstilllifes}}
|-
| 6
| 18
| [[Image:maze6cellstilllifes.png]]
| {{JavaRLE|maze6cellstilllifes}}
|-
| 7
| 40
| [[Image:maze7cellstilllifes.png]]
| {{JavaRLE|maze7cellstilllifes}}
|-
| 8
| 197
| [[Image:maze8cellstilllifes.png]]
| {{JavaRLE|maze8cellstilllifes}}
|-
| 9
| 669
| [[Image:maze9cellstilllifes.png]]
| {{JavaRLE|maze9cellstilllifes}}
|}


===Oscillators===
===Oscillators===
The smallest [[period]] 2 oscillator has several different possible [[stator]]s, some of which are shown below.
The smallest [[period]] 2 oscillator is an [[on-off]] that has several different possible [[stator]]s, some of which are shown below.
[[Image:maze_p2.gif|framed|center|Some small period 2 oscillators.]]
[[Image:maze_p2.gif|framed|center|Some small period 2 oscillators.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=mazeperiod2 click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=mazeperiod2.rle click here] ]]


===Other patterns===
===Other patterns===
One [[wickstretcher]] that commonly appears from random starting configurations is shown below. Its period is 12 and it travels at [[speed]] c/3. It can be stabilized on the left edge in many different ways.
One [[wickstretcher]] that commonly appears from random starting configurations is shown below. Its period is 12 and it travels at [[speed]] c/3. It can be stabilized on the left edge in many different ways.
[[Image:maze_wick.gif|framed|center|A common wickstretcher.]]
[[Image:maze_wick.gif|framed|center|A common wickstretcher.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=mazewickstretcher click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=mazewickstretcher.rle click here] ]]


==Similar rules==
==Similar rules==
Line 31: Line 90:
==References==
==References==
<references />
<references />
== External links ==
{{LinkEppsteinRule|b3s12345}}
{{LinkCatagolueRule|b3s12345}}

Revision as of 01:55, 15 February 2019

Maze
x=0, y = 0, rule = B3/S12345 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated pseudorandom soup
Rulestring 12345/3
B3/S12345
Rule integer 31752
Character Explosive
Black/white reversal B0128/S01234678

Maze is a Life-like cellular automaton in which cells survive from one generation to the next if they have at least 1 and at most 5 neighbours. Cells are born if they have exactly 3 neighbours. This resembles Conway's Game of Life in some ways, but it is rather more difficult for cells to die off, and random starting patterns tend to evolve into complex growing maze-like structures with well-defined walls outlining corridors.

Notable patterns

The maze rule is explosive, which means that most randomly-generated starting patterns will explode in all directions. Nonetheless, there are many still lifes and oscillators under this rule. It has no known spaceships.[1]

Still lifes

Below are all still lifes with nine or fewer cells in the maze rule.[2] It is worth noting that, because the only difference between this rule and the standard Conway rule is that cells have more ways of staying alive, every pattern that is a still life in standard Life is also a still life in the maze rule. Similarly, every still life in the maze rule will also be a still life in the Life without death rule.

Other notable still lifes include the infinitely-extensible diagonal line. Also, any diamond in which every other cell is alive (i.e. any barge that is extended in either length and/or width) is a still life.

Size Count Image Links
1 0
2 2 Maze2cellstilllifes.png Download RLE: click here
3 1 Maze3cellstilllifes.png Download RLE: click here
4 5 Maze4cellstilllifes.png Download RLE: click here
5 7 Maze5cellstilllifes.png Download RLE: click here
6 18 Maze6cellstilllifes.png Download RLE: click here
7 40 Maze7cellstilllifes.png Download RLE: click here
8 197 Maze8cellstilllifes.png Download RLE: click here
9 669 Maze9cellstilllifes.png Download RLE: click here

Oscillators

The smallest period 2 oscillator is an on-off that has several different possible stators, some of which are shown below.

Some small period 2 oscillators.
Manipulate via Java: click here
Download RLE: click here

Other patterns

One wickstretcher that commonly appears from random starting configurations is shown below. Its period is 12 and it travels at speed c/3. It can be stabilized on the left edge in many different ways.

A common wickstretcher.
Manipulate via Java: click here
Download RLE: click here

Similar rules

The most well-known related rule is known as mazectric, which has rulestring 1234/3. That is, it is the same as the maze rule except that cells don't survive if they have 5 neighbours. This results in maze patterns that tend to have longer and straighter corridors.

Generation 235 of the evolution of a 10×10 square of random cells under the mazectric rule

References

  1. "Maze (B3/S12345)". David Eppstein. Retrieved on March 16, 2009.
  2. Computed using the EnumStillLifes.c script located here.

External links

Maze at David Eppstein's Glider Database Maze at Adam P. Goucher's Catagolue