Langton loop

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Two long tone loops as a schematic graphic. The strand bent to a small “d” shows the protective cover on the outside, cells of different colors can be seen on the inside.
2 Langton loops after replication (parent loop on the left, daughter loop on the right)

Langton loops are a form of artificial life in theoretical biology . They were designed by Christopher Langton in 1984 . The “organisms” with the ability to self-replicate , which are simulated in a cellular automaton , consist of a ring-shaped arrangement of cells that contain the “genetic information”. These cells are surrounded by a protective shell in which they constantly rotate. At a certain point, the cell cord with the “genes” breaks open the shell, and the organism forms an arm here (quasi a pseudopodium ) into which a complete copy of the gene sequence enters. This causes the arm to grow, close into a new ring (the daughter ring) and eventually detach itself from the parent ring. After that, the two genetically identical organisms are ready to replicate again.

history

In 1947 John von Neumann presented the Universal Constructor for the first time, a universal cellular automaton with the ability to self-replicate, which could reproduce any pattern, including itself. Because of its universality, this automaton was necessarily very complex, in 1968 Edgar F. Codd was able to reduce the number of cell states from 29 to 8. In the end, Christopher Langton succeeded in further simplifying his design by consciously renouncing the universality - which is not present in biological systems anyway - and limiting himself to the ability to self-replicate. His loops are based on one of the simplest elements in Codds automata, the so-called Periodic Emitter ( Periodic Pulser at von Neumann) - the organ essentially responsible for replication.

description

The cellular automaton designed by Langton is two-dimensional with Von Neumann neighborhoods and 8 cell states. The initial configuration consists of 86 cells (only those with a 0different initial state are counted , see picture). There are several hundred rules that determine the changes in state of each cell during the transition from one generation to the next.

A long tone loop as a schematic graphic. The strand bent to a small “d” shows the protective cover on the outside, cells of different colors can be seen on the inside.
Long tone loop - initial configuration

Initial structure

The envelope is formed from cells with condition 2, it encloses the ring-shaped cell cord with the branching arm of cells from condition 1. The genome is encoded as a sequence of instructions on this ring. An instruction in each case consists of a cell in one of the states 4, 5, 6or 7followed by a cell of the state 0. This gene sequence rotates counterclockwise in the ring-shaped envelope.

Replication and development

If an instruction arrives at the junction of the arm, it is replicated: the original continues to circulate through the ring, the copy enters the arm. (In the example on the right, the instruction has reached 07the junction and would be replicated next.) At the end of the arm, the instructions encoded by the gene sequence control the protuberance of the pseudopodium, the growth and kinking of the arm, the formation of the daughter loop and its separation from the Parent loop. This creates new organisms with an identical genome through a process similar to budding .

In analogy to gene expression , Langton compared the replication at the branch of the arm with the transcription , the implementation of the instructions at the end of the arm with the translation .

Colony formation

A pseudopodium cannot enter the space occupied by an existing loop. This has the consequence that organisms that are surrounded on several sides by other organisms cannot reproduce any further; they die off and form with the neighboring dead organisms - similar to a coral stick - a colony made up of a framework of inactive loops with a thin shell of living organisms that continue to reproduce.

Unless unlimited habitat is available, the size of such a colony is limited, it approaches the value asymptotically , with the size of the habitat in cells indicating.

swell

  1. ^ John von Neumann, The theory of self reproducing automata , AW Burks (ED.), Univ. of Illinois Press, Illinois (1966)
  2. ^ Edgar Frank Codd, Cellular Automata , Academic Press, New York (1968)
  3. ↑ Christopher G. Langton, Self-reproduction in cellular automata , Physica D No. 10 (1984), pp. 135-144

Web links

Commons : Langton Loop  - Collection of Images