Fluctuations and The Onset of Chaos

Crutchfield, James P.; Huberman, Bernardo A.

doi:10.1201/9780203734636-30

Cited by 15 publications

(27 citation statements)

References 2 publications

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“…We hypothesize that such a condition is sufficient for x to be complex. This hypothesis agrees with the work of Crutchfield and Young in [6] and Simon's famous paper on the architecture of complexity [18]. According to [6], "The idea is that a data set is complex if it is the composite of many symmetries."…”

Section: Process Cruditysupporting

confidence: 77%

“…This hypothesis agrees with the work of Crutchfield and Young in [6] and Simon's famous paper on the architecture of complexity [18]. According to [6], "The idea is that a data set is complex if it is the composite of many symmetries." According to [18], in complex systems there are often many levels of organization that can be thought of as forming a hierarchy of systems and sub-systems.…”

Section: Process Cruditysupporting

confidence: 77%

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On Natural Representations of Objects

Chedid¹

EPiC Series in Computing

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We give explanations on the differences between a number of representations that have been proposed in the literature to measure the structural complexity of an object. In particular, we propose the notion of process complexity, the notion of sophistication from a given perspective, the notion of sophisticated depth, and the notion of self-dissimilarity. We also propose the notion of an approximate process for an object and argue that for all practical purposes, an approximate process is as good as an exact process.

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Section: Process Cruditysupporting

confidence: 77%

Section: Process Cruditysupporting

confidence: 77%

On Natural Representations of Objects

Chedid¹

EPiC Series in Computing

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“…The kneading sequence of the infinite limit of the Feigenbaum perioddoubling cascade may be obtained by infinitely repeated application of the homomorphism h = (R → RL, L → RR) to the single letter R. It was the only known context-sensitive language in the unimodal maps in the beginning of 1990s, first proved to be a non-context-free language [14], in which the language consists of the set of all substrings of the kneading sequence only. Now the class of context-sensitive language has split into layers as shown in Fig.…”

Section: Grammatical Complexity Of Unimodal Mapsmentioning

confidence: 99%

Factorizable Language: From Dynamics to Biology

Hao

Xie²

2008

Reviews of Nonlinear Dynamics and Complexity

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“…Information storage involves lowering entropy, while transmission involves raising it. For maximal computing capacity, the system must be both, and this optimal state is near the transition point [8,41]. Actually, many complex systems appear to stay in the vicinity of this threshold analogical to systems on a successful adaptive cycle of resilient systems.…”

Section: Dynamic Cellular States and Entropymentioning

confidence: 99%

An Urban Cellular Automata Model for Simulating Dynamic States on a Local Scale

Partanen

2016

Entropy

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Abstract:In complex systems, flexibility and adaptability to changes are crucial to the systems' dynamic stability and evolution. Such resilience requires that the system is able to respond to disturbances by self-organizing, which implies a certain level of entropy within the system. Dynamic states (static, cyclical/periodic, complex, and chaotic) reflect this generative capacity, and correlate with the level of entropy. For planning complex cities, we need to develop methods to guide such autonomous progress in an optimal manner. A classical apparatus, cellular automaton (CA), provides such a tool. Applications of CA help us to study temporal dynamics in self-organizing urban systems. By exploring the dynamic states of the model's dynamics resulting from different border conditions it is possible to discover favorable set(s) of rules conductive to the self-organizing dynamics and enable the system's recovery at the time of crises. Level of entropy is a relevant measurement for evaluation of these dynamic states. The 2-D urban cellular automaton model studied here is based on the microeconomic principle that similar urban activities are attracted to each other, especially in certain self-organizing areas, and that the local dynamics of these enclaves affect the dynamics of the urban region by channeling flows of information, goods and people. The results of the modeling experiment indicate that the border conditions have a major impact on the model's dynamics generating various dynamic states of the system. Most importantly, it seemed that the model could simulate a favorable, complex dynamic state with medium entropy level which may refer to the continuous self-organization of the system. The model provides a tool for exploring and understanding the effects of boundary conditions in the planning process as various scenarios are tested: resulting dynamics of the system can be explored with such "planning rules" prior to decisions, helping to identify planning guidelines that will support the future evolution of these areas.

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Fluctuations and The Onset of Chaos

Cited by 15 publications

References 2 publications

On Natural Representations of Objects

On Natural Representations of Objects

Factorizable Language: From Dynamics to Biology

An Urban Cellular Automata Model for Simulating Dynamic States on a Local Scale

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