An Escher aware pattern analysis: symmetry beyond symmetry groups

Adanova, Venera
Ornaments constructed by repeating a base motif, timeless and ubiquitous, link culture, art, science and mathematics. To this date, the mathematical study of the ornaments has been the study of discrete symmetry groups and permutations. As such, the study merely focuses on the mechanical side of repetition, ignoring the artistic aspects (symmetry breaking strategies via intriguing choices of form and color permutations) that make ornaments such bewildering objects. Taking our inspiration from Escher's art, we study all aspects of ornamental patterns not only considering the usual mathematical properties but also other idiosyncratic features that are often more important in perception, aesthetics, art and design and as well as in appreciating cultural heritage. Our novelty is to replace the structure extraction problem with a content attenuation or suppression problem. When content is suppressed, clues to the repetition structure emerge. We show that based on content-suppressed images, unit cells and fundamental regions of planar ornaments can be robustly extracted even for ornaments with peculiar color permutations. Moreover, using tools of deep learning, we perform key validation tests showing that our coding via content-suppression makes it possible to construct content-dependent, subjective and more importantly continuous characterizations of the underlying symmetry behavior.


Beyond symmetry groups: A grouping study on Escher's Euclidean ornaments
Adanova, V.; Tarı, Zehra Sibel (2016-01-01)
© 2015 Elsevier Inc.From art to science, ornaments constructed by repeating a base motif (tiling) have been a part of human culture. These ornaments exhibit various kinds of symmetries depending on the construction process as well as the symmetries of the base motif. The scientific study of the ornaments is the study of symmetry, i.e., the repetition structure. There is, however, an artistic side of the problem too: intriguing color permutations, clever choices of asymmetric interlocking forms, several symm...
Symmetry analysis from human perspective
Çengel, Furkan; Tarı, Zehra Sibel; Department of Computer Engineering (2019)
Ornaments are repetitive patterns. They are created by repeating a base unit using four primitive geometric operations: translation, reflection, glide reflection and rotation. Using combinations of these primitive operations one can fill the plane in 17 different ways, which are known as 17 Wallpaper groups. In recent studies, an automated method is presented which can detect the symmetry group of given ornament. While automated methods aim to capture theoretical representation of the symmetry, they lack th...
Crystal Formations and Symmetry in the Search of Patterns in Architecture
Kruşa Yemişcioğlu, Müge; Sorguç, Arzu (2018-09-21)
Nature is always full of patterns inspiring all the disciplines and especially architecture in many ways. Currently, with the advances in technology and growing interest towards nature-driven studies, retrieving information from nature has a new connotation in scales and dimensions including both living and non-living beings. In this study, it is aimed to explore the scales of nature from Nano to Macro and a holistic approach is embraced to cope with the complexity of nature and architecture. To understand ...
Analysis of Planar Ornament Patterns via Motif Asymmetry Assumption and Local Connections
Adanova, Venera; Tarı, Zehra Sibel (2019-03-01)
Planar ornaments, a.k.a. wallpapers, are regular repetitive patterns which exhibit translational symmetry in two independent directions. There are exactly 17 distinct planar symmetry groups. We present a fully automatic method for complete analysis of planar ornaments in 13 of these groups, specifically, the groups called p6, p6m, p4g, p4m, p4, p31m, p3m, p3, cmm, pgg, pg, p2 and p1. Given the image of an ornament fragment, we present a method to simultaneously classify the input into one of the 13 groups a...
A Data Driven Modeling of Ornaments
Adanova, Venera; Tarı, Zehra Sibel (Springer, 2019)
Ornaments are created by repeating a base motif via combination of four primitive geometric repetition operations: translation, rotation, reflection, and glide reflection. The way the operations are combined defines symmetry groups. Thus, the classical study of ornaments is based on group theory. However, the discrete and inflexible nature of symmetry groups fail to capture relations among ornaments when artistic freedom is used to break symmetry via intriguing choices of base motifs and color permutations....
Citation Formats
V. Adanova, “An Escher aware pattern analysis: symmetry beyond symmetry groups,” Ph.D. - Doctoral Program, Middle East Technical University, 2015.