HighLife is a cellular automaton

Cellular automaton

A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...

 similar to Conway's Game of Life

Conway's Game of Life

The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970....

. It was devised in 1994 by Nathan Thompson. It is a two-dimensional, two-state cellular automaton in the "Life family

Life-like cellular automaton

A cellular automaton is Life-like if it meets the following criteria:* The array of cells of the automaton has two dimensions....

" and is described by the rule B36/S23; that is, a cell is born if it has 3 or 6 neighbors and survives if it has 2 or 3 neighbors. Because the rules of HighLife and Conway's Life (rule B3/S23) are similar, many simple patterns in Conway's Life function identically in HighLife. More complicated engineered patterns for one rule, though, typically do not work in the other rule.

Replicator

The main reason for interest in HighLife comes from the existence of a pattern called the replicator. After running the replicator for twelve generations, the result is two replicators. The replicators will repeatedly reproduce themselves, all on a diagonal line. Whenever two replicators try to expand into each other, the pattern in the middle simply vanishes. The behavior of a row of Replicators interacting with each other in this way simulates the one-dimensional Rule 90

Rule 90

Rule 90 is an elementary cellular automaton based on the exclusive or function. It consists of a one-dimensional array of cells, each of which can hold either a 0 or a 1 value; in each time step all values are simultaneously replaced by the exclusive or of the two neighboring values...

 cellular automaton, where a single replicator simulates a nonzero cell of the Rule 90 automaton and a blank space where a replicator could be simulates a zero cell of Rule 90. Replicators can be used to engineer other more complex patterns, such as glider guns and high period oscillators. It is also possible to make slow spaceships using the replicator, but no explicit examples have yet been found. Nevertheless, a simple c/6 diagonal spaceship has been found, known as the bomber.

It has been proven that replicators exist in Conway's Life as well.

External links

• Life lexicon: replicator
• HighLife - An Interesting Variant of Life (ZIP file of a single text file)