Local Information in One-Dimensional Cellular Automata

Helvik, Torbjørn; Lindgren, Kristian; Nordahl, Mats G.

doi:10.1007/978-3-540-30479-1_13

Cited by 20 publications

(22 citation statements)

References 24 publications

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“…At such points, we observe high transfer entropy in the direction of movement because the information source (as part of the intruding domain) adds much information about the next state of the destination that was not in the destination's past or the rest of the CA neighborhood. This highlighting of the domain walls is somewhat similar to that produced by other filtering techniques, although an important distinction to [6,22,28] is that this technique highlights the domain wall areas as only being a single cell wide: as described above, a single cell width is all that is required to explain the meeting of two domains of rule 18 from a temporal perspective.…”

Section: Domain Walls As Dominant Information Transfer Agentsmentioning

confidence: 60%

“…We note the alternative perturbation-based candidate information flow for quantifying information transfer from the perspective of causality rather than prediction; we intend to compare transfer entropy to this measure in future work. Furthermore, a separate notion of information flow in CAs was introduced in [28] (connected to the local information though not used for filtering). There are several fundamental problems with this formulation however: it is only applicable to reversible CAs, only has meaning as information flow for deterministic mechanics, and is not able to distinguish information flow any more finely than information from the left and the right.…”

Section: A Transfer Entropymentioning

confidence: 99%

“…This method of forming a local information-theoretic measure by extracting the log term from a globally averaged measure is used less explicitly for the local excess entropy [36], the local statistical complexity [23,36], and the local information [28]. It is applicable to any such informationtheoretic metric: we form the local (time-lagged) mutual information between the source and destination variables from Eq.…”

Section: B Local Transfer Entropymentioning

confidence: 99%

“…Finally, several methods already exist for filtering the important structural elements in CAs [6,22,23,28], which provide another important basis for comparison of our spatiotemporal local information transfer profiles (which can also be viewed as a method of filtering). These methods include: finite state transducers to recognize the regular spatial language of the CA [22,25]; local information (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…These methods include: finite state transducers to recognize the regular spatial language of the CA [22,25]; local information (i.e. local spatial entropy rate) [28]; displaying executing rules with the most frequently occurring rules filtered out [6]; and local statistical complexity and local sensitivity [23]. All of these successfully highlight particles.…”

Section: Introductionmentioning

confidence: 99%

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Local information transfer as a spatiotemporal filter for complex systems

2008

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We present a measure of local information transfer, derived from an existing averaged informationtheoretical measure, namely transfer entropy. Local transfer entropy is used to produce profiles of the information transfer into each spatiotemporal point in a complex system. These spatiotemporal profiles are useful not only as an analytical tool, but also allow explicit investigation of different parameter settings and forms of the transfer entropy metric itself. As an example, local transfer entropy is applied to cellular automata, where it is demonstrated to be a novel method of filtering for coherent structure. More importantly, local transfer entropy provides the first quantitative evidence for the long-held conjecture that the emergent traveling coherent structures known as particles (both gliders and domain walls, which have analogues in many physical processes) are the dominant information transfer agents in cellular automata.

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Section: Domain Walls As Dominant Information Transfer Agentsmentioning

confidence: 60%

Section: A Transfer Entropymentioning

confidence: 99%

Section: B Local Transfer Entropymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Local information transfer as a spatiotemporal filter for complex systems

2008

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Analysing Emergent Dynamics of Evolving Computation in 2D Cellular Automata

McCaskill

Packard

2019

Lecture Notes in Computer Science

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Conway's Game of Life (GoL), a famous 2D cellular automaton (CA), is extended to allow evolution by associating genetic information with individual live cells, that specifies variant local CA rules. Genomes are formed by copying (potentially with mutation) or movement from one of the live neighbour cells and are destroyed at death. Just as biological evolution discovers innovations in the space of chemical and physical functionalities, we explore how the addition of genetic information enables an evolutionary process that can coordinate robust complex dynamics by exploring spatially inhomogeneous local modifications to the non-robust GoL rules.We discovered a large family of deterministic rules which avoid stochastic choices of ancestor for genetic inheritance. Systematic genetic variations near to the game of life rule are investigated and found to produce signs of computational complexity with an abundance of spaceship and glider gun structures. We investigated evolution for four successively more differentiated symmetry cases in the nearest neighbour rules: semi-totalistic, corner-edge totalistic, 8-rotation symmetric, and physical 2D symmetric (4-rotations and 4-reflections).The genetic evolution is analysed by fast ongoing genealogy construction and population weighted activity statistics. The spatial structure is captured using hash encoded quadtrees of the connected components, which are also mapped through time for novelty and with activity statistics. This together with a novel genetic tracking of the dynamical displacement ancestry of live genes allows an efficient recognition of regular dynamical structures such as spaceships which transport information while changing shape, solving an open problem in finding efficient alternatives to e-machines for 2D automata.

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Information Transfer by Particles in Cellular Automata

Lizier

Prokopenko

Zomaya

Progress in Artificial Life

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Local Information in One-Dimensional Cellular Automata

Cited by 20 publications

References 24 publications

Local information transfer as a spatiotemporal filter for complex systems

Local information transfer as a spatiotemporal filter for complex systems

Analysing Emergent Dynamics of Evolving Computation in 2D Cellular Automata

Information Transfer by Particles in Cellular Automata

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