When are cellular automata random?

Coe, J. B.; Ahnert, Sebastian E.; Fink, Thomas

doi:10.1209/0295-5075/84/50005

Cited by 2 publications

(2 citation statements)

References 35 publications

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“…This observation is in agreement with with the fact that while Wolfram highlighted some rule sets that produce randomness, most of his automata rules sets do not produce complex pseudo-random patterns [55]. Coe et al [68] analytically studied the question of when automata produce 'random' and complex dynamics, and also found that relatively few are random.…”

Section: Discussionsupporting

confidence: 79%

Exploring Simplicity Bias in 1D Dynamical Systems

Dingle,

Alaskandarani,

Hamzi

et al. 2024

Entropy

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Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input–output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability–complexity relationships may be a useful tool when studying patterns in dynamical systems.

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Section: Discussionsupporting

confidence: 79%

Exploring Simplicity Bias in 1D Dynamical Systems

Dingle,

Alaskandarani,

Hamzi

et al. 2024

Entropy

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“…, 254, 257; compare also Coe et al . ). This yields a probability for LE‐like growth that is equal to the (non‐trivial) proportion of R taken up by points that, when evolved forward by means of the (deterministic) dynamics concerning evolution through

scriptS

, yield LE‐like growth.…”

Section: Derivation Of Probabilistic Approximations To Deterministic mentioning

confidence: 97%

Ceteris ParibusLaws andMinutis RectisLaws

Fenton-Glynn

2016

Philos Phenomenol Research

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Special science generalizations admit of exceptions. Among the class of non-exceptionless special science generalizations, I distinguish (what I will call) minutis rectis (mr) generalizations from the more familiar category of ceteris paribus (cp) generalizations. I argue that the challenges involved in showing that mr generalizations can play the law role are underappreciated, and quite different from those involved in showing that cp generalizations can do so. I outline a strategy for meeting the challenges posed by mr generalizations.

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When are cellular automata random?

Cited by 2 publications

References 35 publications

Exploring Simplicity Bias in 1D Dynamical Systems

Exploring Simplicity Bias in 1D Dynamical Systems

Ceteris ParibusLaws andMinutis RectisLaws

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