Birkhoff Revisited: Beauty as a Function of Effect and Means

Local versus global minima in visual pattern completion

“…The experiments related to the judged complexity of patterns (Leeuwenberg, 1969(Leeuwenberg, , 1971, subjective contours (Van Tuijl & Leeuwenberg, 1979, the perception of motion (Restle, 1979), embeddedness (Van Tuijl, 1980), the effect of context on the perception ofform (Collard & Leeuwenberg, 1981), assimilation and contrast (Leeuwenberg, 1982), the perception of foreground and background (Boselie & Leeuwenberg, 1986;Leeuwenberg & Buffart, 1984), and the perceptual attractivity of patterns (Boselie & Leeuwenberg, 1985). On the whole, the results of these experiments fit in with the ordering of interpretations according to perceptual simplicity, as inferred from the system of coding rules.…”

“…'s (1981)coding procedure, which represent interpretations Band C. Both mterpretations can be represented by codes with the same amount of information (l = 7). The codes are written in the notational form used in the most recent publications by Leeuwenberg (Boselie & Leeuwenberg, 1985, 1986Leeuwenberg & Boffart, 1984). of their own set of coding rules.…”

“…Because his coding system has been presented in detail in several recent publications (Boselie & Leeuwenberg, 1985;Buffart et al, 1981;Leeuwenberg & Buffart, 1984), it will be outlined here only briefly. In Leeuwenberg's system, an interpretation of a visual pattern is represented by a series of symbols, or a primitive code.…”

Toward Measuring Network Aesthetics Based on Symmetry

“…Important examples are semiotics and computational linguistics, where the aesthetics of languages has been studied extensively [1][2][3][4]. A particularly influential approach to quantitative measurement of aesthetics was developed by Birkhoff [5,6]. Birkhoff's theory is based on the analysis of material objects such as vases whose features can represented as polygons, thus allowing for the assignment of numerical values to the features [5].…”

“…Birkhoff's theory is based on the analysis of material objects such as vases whose features can represented as polygons, thus allowing for the assignment of numerical values to the features [5]. According to the theory, perception of an object depends on the following two general features [5,6]:…”