Difference between revisions of "OCA:Maze"
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−  {{Rulename=Mazeimgname=maze  +  {{Rule 
−  '''Maze''' is a [[cellular automaton#Wellknown Lifelike cellular automataLifelike cellular automaton]] in which [[cell]]s survive from one [[generation]] to the next if they have at least 1 and at most 5 [[Moore neighbourhoodneighbours]]. Cells are born if they have exactly 3 neighbours.  +  name = Maze 
+  imgname = maze  
+  char = Explosive  
+  b = 3  
+  s = 12345  
+  ruleinteger = 31752  
+  reversal = B0128/S01234678  
+  animated = true  
+  }}  
+  '''Maze''' is a [[cellular automaton#Wellknown Lifelike cellular automataLifelike cellular automaton]] in which [[cell]]s survive from one [[generation]] to the next if they have at least 1 and at most 5 [[Moore neighbourhoodneighbours]]. 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 mazelike structures with welldefined walls outlining corridors.  
−  +  ==Notable patterns==  
+  The maze rule is [[Class three cellular automataexplosive]], which means that most randomlygenerated 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 weburl=http://fano.ics.uci.edu/ca/rules/b3s12345/ title=Maze (B3/S12345) publisher=David Eppsteinaccessdate=March 16, 2009}}</ref>  
−  +  ===Still lifes===  
+  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 LifeConway 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 infinitelyextensible 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.  
+  
+  { class="wikitable" style="marginleft:auto;marginright:auto;"  
+    
+  ! Size  
+  ! Count  
+  ! Image  
+  ! Links  
+    
+   1  
+   0  
+    
+    
+    
+   2  
+   2  
+   [[Image:maze2cellstilllifes.png]]  
+   {{JavaRLEmaze2cellstilllifes}}  
+    
+   3  
+   1  
+   [[Image:maze3cellstilllifes.png]]  
+   {{JavaRLEmaze3cellstilllifes}}  
+    
+   4  
+   5  
+   [[Image:maze4cellstilllifes.png]]  
+   {{JavaRLEmaze4cellstilllifes}}  
+    
+   5  
+   7  
+   [[Image:maze5cellstilllifes.png]]  
+   {{JavaRLEmaze5cellstilllifes}}  
+    
+   6  
+   18  
+   [[Image:maze6cellstilllifes.png]]  
+   {{JavaRLEmaze6cellstilllifes}}  
+    
+   7  
+   40  
+   [[Image:maze7cellstilllifes.png]]  
+   {{JavaRLEmaze7cellstilllifes}}  
+    
+   8  
+   197  
+   [[Image:maze8cellstilllifes.png]]  
+   {{JavaRLEmaze8cellstilllifes}}  
+    
+   9  
+   669  
+   [[Image:maze9cellstilllifes.png]]  
+   {{JavaRLEmaze9cellstilllifes}}  
+  }  
+  
+  ===Oscillators===  
+  The smallest [[period]] 2 oscillator is an [[onoff]] that has several different possible [[stator]]s, some of which are shown below.  
+  [[Image:maze_p2.gifframedcenterSome 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===  
+  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.gifframedcenterA 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==  
+  The most wellknown 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.  
+  
+  {  
+    
+  [[Image:Mazectric.pngframedleftGeneration 235 of the evolution of a 10×10 square of random cells under the mazectric rule]]  
+  }  
==References==  ==References==  
<references />  <references />  
+  
+  == External links ==  
+  {{LinkEppsteinRuleb3s12345}}  
+  {{LinkCatagolueRuleb3s12345}} 
Revision as of 20:05, 5 April 2019
Maze  


View animated image  
Rulestring  12345/3 B3/S12345 


Rule integer  31752  
Character  Explosive  
Black/white reversal  B0128/S01234678 
Maze is a Lifelike 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 mazelike structures with welldefined walls outlining corridors.
Contents
Notable patterns
The maze rule is explosive, which means that most randomlygenerated 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 infinitelyextensible 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  Download RLE: click here  
3  1  Download RLE: click here  
4  5  Download RLE: click here  
5  7  Download RLE: click here  
6  18  Download RLE: click here  
7  40  Download RLE: click here  
8  197  Download RLE: click here  
9  669  Download RLE: click here 
Oscillators
The smallest period 2 oscillator is an onoff that has several different possible stators, some of which are shown below.
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.
Similar rules
The most wellknown 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.
References
 ↑ "Maze (B3/S12345)". David Eppstein. Retrieved on March 16, 2009.
 ↑ Computed using the EnumStillLifes.c script located here.
External links
 Maze at David Eppstein's Glider Database
 Maze at Adam P. Goucher's Catagolue