OCA:HighLife
HighLife  


View animated image  
Rulestring  23/36 B36/S23 


Character  Chaotic 
HighLife is a Lifelike cellular automaton in which cells survive from one generation to the next if they have 2 or 3 neighbours, and are born if they have 3 or 6 neighbours. It was named by John Conway and was first considered in 1994 by Nathan Thompson. It is mainly of interest due to a simple replicator that it allows.
Because its rulestring is so similar to that of Conway's Game of Life, many simple patterns exhibit the same behavior in both rules; it's only when patterns get complex that their behavior differs. Nonetheless, it exhibits such rich structure that John Conway himself stated
"It seems to me that 'B36/S23' is really the game I should have found, since it's so rich in nice things." ^{[1]}
Contents
Notable patterns
All of the most common still lifes, oscillators and spaceships from the standard Life rules behave the exact same under the HighLife rules, including the block, beehive, blinker, toad, beacon, glider, lightweight spaceship, middleweight spaceship, and heavyweight spaceship. On the other hand, even though traffic lights and honey farms themselves behave the same in both rules, they do not occur naturally in HighLife with any sort of regularity due to their common predecessors being unstable.
The replicator
By far the most notable pattern in HighLife is the simple replicator, shown to the right. It is by far the most wellknown replicator in any Lifelike cellular automaton. It repeatedly copies itself along a diagonal line. It copies itself the first time after 12 generations, then produces another two copies after another 24 generations, followed by another four copies after another 48 generations, and so on. In general there are 2^{n} copies of the replicator at generation 12(2^{n}  1) and their centers are evenly spaced 4 cells apart. The two ends of the replicator line expand at a speed of c/6.
Because of the way the replicator duplicates itself, it can be considered a sawtooth with expansion factor 2 and a minimum repeating population of 22. Because the replicator is so small, it often occurs naturally from soup. This contrasts with the standard Game of Life, where all known sawtooths are complex, preciselyengineered patterns.
Still lifes
Because the only difference between the HighLife rules and the standard Life rules is that there is another way for cells to be born (when they have exactly six alive neighbours), all still lifes in the HighLife rule are necessarily still lifes under Conway's rules as well. Also, very few still lifes under the standard Life rules have dead cells with six alive neighbours, so the list of still lifes for the two rules are almost identical for small cell counts. The smallest patterns that are still lifes in the standard Life rules but not in HighLife are ship (with 6 cells) and hat (with 9 cells). Also, any pattern involving a bun or a cap that is a still life under the standard rules is not a still life in HighLife.
Size  Count  Image  Links 

≤3  0  
4  2  Download RLE: click here  
5  1  Download RLE: click here  
6  4  Download RLE: click here  
7  4  Download RLE: click here  
8  9  Download RLE: click here  
9  9  Download RLE: click here  
10  25  Download RLE: click here  
11  44  Download RLE: click here  
12  111  Download RLE: click here  
13  218  Download RLE: click here 
Change in Frequency
From the same random starting conditions, HighLife usually settles into fewer objects than in Life. This chart shows the change in frequency of common or notable objects in Life and in HighLife. In the chart, frequency is measured by number of objects per cell rather than total objects. This is because the frequency of total objects also changes between Life and HighLife.
SpaceshipsAll of the standard spacehips from the standard Life rules work in HighLife, but the only nonstandard spaceships that are known to work in HighLife are the turtle, 86P9H3V0, and some flotillae of the standard spaceships. There are also several known spaceships that are specific to HighLife^{[2]}, the most wellknown of which is the bomber. Bomber
The bomber is a replicatorbased spaceship that occurs naturally and was discovered by Nathan Thompson. It can be formed by placing a blinker in the path of the replicator as shown below. The spaceship itself has a period 48 and travels diagonally at speed c/6. The blinker reacts with one of the spawned replicators such that it destroys itself and the spawned replicator while leaving another blinker on the other side of the spaceship. It is thus a glide symmetric spaceship with mod equal to 24. References
