Simple measure for complexity

Shiner, J. S.; Davison, Matt; Landsberg, P. T.

doi:10.1103/physreve.59.1459

Cited by 290 publications

(282 citation statements)

References 19 publications

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“…We are pleased that our contribution on a "simple measure for complexity" [1] (hereafter referred to as SDL) is of sufficient interest to have generated two comments, one by Crutchfield, Feldman and Shalizi [2] (CFS) and another by Binder and Perry [3] (BP). In SDL we proposed…”

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confidence: 99%

Reply to Comments on “Simple measure for complexity”

Shiner

Davison²,

Landsberg³

2000

Phys. Rev. E

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We respond to the comment by Crutchfield, Feldman and Shalizi and that by Binder and Perry, pointing out that there may be many maximum entropies, and therefore "disorders" and "simple complexities". Which ones are appropriate depend on the questions being addressed. "Disorder" is not restricted to be the ratio of a nonequilibrium entropy to the corresponding equilibrium entropy; therefore, "simple complexity" need not vanish for all equiibrium systems, nor must it be nonvanishing for a nonequilibrium system. 05.20.-y, 05.90.+m We are pleased that our contribution on a "simple measure for complexity" [1] (hereafter referred to as SDL) is of sufficient interest to have generated two comments, one by Crutchfield, Feldman and Shalizi [2] (CFS) and another by Binder and Perry [3] (BP). In SDL we proposed∆ ≡ S/S max , Ω ≡ 1 − ∆.(2) as a "simple measure for complexity". α and β are (constant) parameters, S is the Boltzmann-Gibbs-Shannon entropy [4], and S max , the maximum entropy. ∆ was introduced earlier by one of us as a measure for disorder, and Ω is referred to as "order" [5,6]. CFS raise several points: I. Since S max is the equilibrium entropy, ∆ and Γ αβ vanish for all equilibrium systems, and neither can "distinguish between two-dimensional Ising systems at low temperature, high temperature, or the critical temperature . . .

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Shiner

Davison²,

Landsberg³

2000

Phys. Rev. E

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“…The main advantage of LMC complexity is its generality and the fact that it is operationally simple and do not require a big amount of calculations. This advantage has been worked out in different examples, such as the study of the time evolution of C for a simplified model of an isolated gas, the "tetrahedral gas" [5], the slight modification of C as an effective method by which the complexity in hydrological systems can be identified [11], the attempt of generalize C in a family of simple complexity measures [12], some statistical features of the behavior of C for DNA sequences [13] and some wavelet-…”

Section: Discussionmentioning

confidence: 99%

Shannon information, LMC complexity and Rényi entropies: a straightforward approach

López‐Ruiz

2005

Biophysical Chemistry

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The LMC complexity, an indicator of complexity based on a probabilistic description, is revisited. A straightforward approach allows us to establish the time evolution of this indicator in a near-equilibrium situation and gives us a new insight for interpreting the LMC complexity for a general non equilibrium system. Its relationship with the Rényi entropies is also explained. One of the advantages of this indicator is that its calculation does not require a considerable computational effort in many cases of physical and biological interest.

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“…At a higher level, Shiner et al (1999) characterize complexity from the perspective of order and disorder. They present three broad categories of complexity, depicted in Figure 1.…”

Section: Background: Complexity Form and Designmentioning

confidence: 99%

Measuring the Complexity of Urban Form and Design

Boeing

2017

SSRN Journal

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Complex systems have become a popular lens for conceptualizing cities, and complexity has substantial implications for urban performance and resilience. This paper develops a typology of methods and measures for assessing the complexity of the built form at the scale of urban design. It extends quantitative methods from urban planning, network science, ecosystems studies, fractal geometry, and information theory to the physical urban form and the analysis of qualitative human experience. Metrics at multiple scales are scattered throughout these bodies of literature and have useful applications in analyzing the complexity that both evolves and results from local planning and design processes. The typology developed here applies to empirical research of multiple neighborhood types and design standards and it includes temporal, visual, spatial, fractal, and network-analytic measures of the urban form.

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Simple measure for complexity

Cited by 290 publications

References 19 publications

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Reply to Comments on “Simple measure for complexity”

Shannon information, LMC complexity and Rényi entropies: a straightforward approach

Measuring the Complexity of Urban Form and Design

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