Symmetropy, an entropy-like measure of visual symmetry

Yodogawa, Eiji

doi:10.3758/bf03206227

Cited by 39 publications

(32 citation statements)

References 20 publications

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“…We measure the initial condition (2 6 × 1) and the final pattern. The number of cells is 2 6 × 2 6 because, to measure the number of symmetries, this number of cells is the minimum needed [4]. In the present study, we can use only two kinds of initial condition, horizontal symmetry and double symmetry, because we consider 2 in the discrete Walsh function (as in Figure 3).…”

Section: Calculationsmentioning

confidence: 99%

“…Since this entropy relates to the symmetry, it is called the "symmetropy" [6]. The symmetropy can be considered as a quantitative and objective measure of symmetry.…”

Section: The Discrete Walsh Analysismentioning

confidence: 99%

“…For details of the mathematical procedures, see previous studies [3,4,6]. The Walsh function , of order and argument can be represented over the interval 0 1 as follows:…”

Section: The Discrete Walsh Analysismentioning

confidence: 99%

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Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata

Tanaka

2015

Symmetry

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Abstract:To examine the development of pattern formation from the viewpoint of symmetry, we applied a two-dimensional discrete Walsh analysis to a one-dimensional cellular automata model under two types of regular initial conditions. The amount of symmetropy of cellular automata (CA) models under regular and random initial conditions corresponds to three Wolfram's classes of CAs, identified as Classes II, III, and IV. Regular initial conditions occur in two groups. One group that makes a broken, regular pattern formation has four types of symmetry, whereas the other group that makes a higher hierarchy pattern formation has only two types. Additionally, both final pattern formations show an increased amount of symmetropy as time passes. Moreover, the final pattern formations are affected by iterations of base rules of CA models of chaos dynamical systems. The growth design formations limit possibilities: the ratio of developing final pattern formations under a regular initial condition decreases in the order of Classes III, II, and IV. This might be related to the difference in degree in reference to surrounding conditions. These findings suggest that calculations of symmetries of the structures of one-dimensional cellular automata models are useful for revealing rules of pattern generation for animal bodies.

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Section: Calculationsmentioning

confidence: 99%

“…Since this entropy relates to the symmetry, it is called the "symmetropy" [6]. The symmetropy can be considered as a quantitative and objective measure of symmetry.…”

Section: The Discrete Walsh Analysismentioning

confidence: 99%

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Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata

Tanaka

2015

Symmetry

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“…Various metrics of the detectability of symmetry in a stimulus have been proposed (see, e.g., Chipman, 1977;Dakin & Watt, 1994;Dry, 2008;Masame, 1986Masame, , 1987Yodogawa, 1982;Zimmer, 1984), and two things are pretty clear. First, a simple cross-correlation of the two symmetry halves does not seem to agree with human symmetry detection (see, e.g., Barlow & Reeves, 1979;Tapiovaara, 1990).…”

Section: Detecta T T Bility Of Regulari R R Tymentioning

confidence: 99%

Weber-Fechner behavior in symmetry perception?

Helm

2010

Attention, Perception, & Psychophysics

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“…In [287], the Walsh functions are used as basis functions for evaluating mirror-symmetry (horizontal, vertical or both) and rotational-symmetry (of order 2). The 2D basis functions (Figure 3.3a) denoted W n,m (with integer n, m values) are equally divided into four sets according to the type of symmetry they represent: vertical mirror (m-even, n-odd), horizontal mirror (m-odd, n-even), doubly mirror (m-even, n-even) and rotational-symmetry (m-odd, n-odd).…”

Section: Global Vs Local Symmetrymentioning

confidence: 99%