Langton's loops

Langton's loops are a particular "species" of artificial life in a cellular automaton created in 1984 by Christopher Langton. They consist of a loop of cells containing genetic information, which flows continuously around the loop and out along an "arm" (or pseudopod), which will become the daughter loop. The "genes" instruct it to make three left turns, completing the loop, which then disconnects from its parent.

In 1952 John von Neumann created the first cellular automaton (CA) with the goal of creating a self-replicating machine. This automaton was necessarily very complex due to its computation- and construction-universality. In 1968 Edgar F. Codd reduced the number of states from 29 in von Neumann's CA to 8 in his. When Christopher Langton did away with the universality condition, he was able to significantly reduce the automaton's complexity. Its self-replicating loops are based on one of the simplest elements in Codd's automaton, the periodic emitter.

Langton's Loops run in a CA that has 8 states, and uses the von Neumann neighborhood with rotational symmetry. The transition table can be found here: [1].

As with Codd's CA, Langton's Loops consist of sheathed wires. The signals travel passively along the wires until they reach the open ends, when the command they carry is executed.

Because of a particular property of the loops' "pseudopodia", they are unable to reproduce into the space occupied by another loop. Thus, once a loop is surrounded, it is incapable of reproducing, resulting in a coral-like colony with a thin layer of reproducing organisms surrounding a core of inactive "dead" organisms. Unless provided unbounded space, the colony's size will be limited. The maximum population will be asymptotic to ${\displaystyle \textstyle \left\lfloor {\frac {A}{121}}\right\rfloor }$, where A is the total area of the space in cells.

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