From LifeWiki
Revision as of 04:38, 16 October 2011 by Bloonsio (talk | contribs)
Jump to navigation Jump to search
HighLife rule
Rulestring 23/36
Character Chaotic

HighLife is a Life-like 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]

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 well-known replicator in any Life-like 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 2n copies of the replicator at generation 12(2n - 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, precisely-engineered patterns.

A 3-generation predecessor of the replicator
RLE: here
The replicator itself
RLE: here
The replicator after 12 generations
The replicator after another 24 generations

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 Highlife4cellstilllifes.png Download RLE: click here
5 1 Highlife5cellstilllifes.png Download RLE: click here
6 4 Highlife6cellstilllifes.png Download RLE: click here
7 4 Highlife7cellstilllifes.png Download RLE: click here
8 9 Highlife8cellstilllifes.png Download RLE: click here
9 9 Highlife9cellstilllifes.png Download RLE: click here
10 25 Highlife10cellstilllifes.png Download RLE: click here
11 44 Highlife11cellstilllifes.png Download RLE: click here
12 111 Highlife12cellstilllifes.png Download RLE: click here
13 218 Highlife13cellstilllifes.png 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.

Object Frequency in Life Change in Frequency Frequency in HighLife Notes
All Objects 6.64×10-3 -35% 4.30×10-3 The overall decrease of objects causes HighLife to stabilize over twice as fast on average.
Blinker 2.15×10-3 -68% 6.88×10-4 Blinkers are much less common (third) since the traffic light does not form from predecessors in HighLife.
Block 2.11×10-3 -13% 1.83×10-3 Although the block are less common in HighLife, it is still the most common object.
Beehive 1.25×10-3 -40% 7.46×10-4 Beehives are also less common, but more common than the blinker.
Loaf 3.89×10-4 +8% 4.19×10-4 Loaves are slightly more common in HighLife, but still far behind the beehive.
Boat 3.58×10-4 +16% 4.14×10-4 In HighLife, a hat, as well as other predecessors, will evolve into a very common formation of four boats.
Tub 8.00×10-5 +21% 9.73×10-5 Tubs experience a 21% increase - the largest of the top ten most common objects.
Pond 7.53×10-5 -54% 3.49×10-5 Ponds, which are almost as common as tubs in Life, are almost three times rarer than tubs in HighLife.
Ship 4.92×10-5 -100% 0 The center cell of a ship has six living neighbors and is born in HighLife. This birth causes it all to die.
Aircraft carrier 5.00×10-7 +2516% 1.30×10-5 They're 26 times more common. Pi1.png This evolves into two aircraft carriers and a blinker.
Elevener 4.55×10-9 +5395% 2.50×10-7 Eleveners appear 55 times as often in HighLife! It's probably because of a common predecessor.


All of the standard spacehips from the standard Life rules work in HighLife, but the only non-standard 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 well-known of which is the bomber.


For other uses of the term 'bomber', see Bomber (disambiguation).

The bomber is a replicator-based 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.

A predecessor of the bomber
RLE: here
The bomber itself


  1. HighLife - An Interesting Variant of Life by David Bell (.zip file)
  2. "HighLife (B36/S23)". David Eppstein. Retrieved on April 15, 2009.