Global Symmetries, Local Symmetries and Groupoids

Local symmetries are primarily defined in the case of spacetime, but several authors have defined them outside this context, sometimes with the help of groupoids. We show that, in many cases, local symmetries can be defined as global symmetries. We also show that groups can be used, rather than groupoids, to handle local symmetries. Examples are given for graphs and networks, color symmetry and tilings. The definition of local symmetry in physics is also discussed.

Designing Color Symmetry in Stigmergic Art

Color symmetry is an extension of the symmetry imposed by isometric transformations and indicates that the colors of geometrical objects are assigned according to the symmetry properties of these objects. A color symmetry permutes the coloring of the objects consistently with their symmetry group. We apply this concept to bio-inspired generative art. Therefore, the geometrical objects are interpreted as motifs that may repeat themselves with a symmetry-consistent coloring. The motifs are obtained by design principles from stigmergy. We discuss the design procedure and present visual results.

Conceptual Systems: The Dances, Music, and Drawings of Laura Dean

Laura Dean's creative output in minimalist art spans interconnected work in dance, music, and drawing. Throughout the early 1970s, Dean represented her compositional structures as works on paper, which present an expanded visualization of her artistic experimentation with color, symmetry, repetition, and form. Dean rejects the reconstruction of her performance works, instead she advances a notion of dances as impermanent. Situating Dean in the context of serial and conceptual art in which the material art object is deemphasized in favor of communicating compositional logic, I argue that Dean presents a choreographic legacy premised on the intentional disappearance of her work in favor of perpetuating ideation and concept.

Local and global color symmetries of a symmetrical pattern

This study addresses the problem of arriving at transitive perfect colorings of a symmetrical pattern {\cal P} consisting of disjoint congruent symmetric motifs. The pattern {\cal P} has local symmetries that are not necessarily contained in its global symmetry group G. The usual approach in color symmetry theory is to arrive at perfect colorings of {\cal P} ignoring local symmetries and considering only elements of G. A framework is presented to systematically arrive at what Roth [Geom. Dedicata (1984), 17, 99–108] defined as a coordinated coloring of {\cal P}, a coloring that is perfect and transitive under G, satisfying the condition that the coloring of a given motif is also perfect and transitive under its symmetry group. Moreover, in the coloring of {\cal P}, the symmetry of {\cal P} that is both a global and local symmetry, effects the same permutation of the colors used to color {\cal P} and the corresponding motif, respectively.

Crystallographic patterns in Philippine indigenous textiles

The aim of this study was to analyze a representative sample of Philippine indigenous textiles in order to capture the range of symmetries and color symmetries present. This paper examines the existence of symmetries in finite designs, and classifies the plane-group and frieze-group symmetry types of the repeated patterns in woven textiles. The tendency of a particular symmetry to be more or less common than another can indicate relationships between the symmetries and the weaving technique or the culture that produced them. This paper will also examine designs and patterns with color symmetry found in these textiles. The sample consisted of 588 repeated patterns and finite designs in textiles (389 plane, 166 frieze and 33 finite) culled from well known museums in the Philippines, personal collections of scholars, existing literature on Philippine textiles and field visits.

Mass limits for the chiral color symmetry G′-boson from LHC dijet data

The contributions of [Formula: see text]-boson predicted by the chiral color symmetry of quarks to the differential dijet cross-sections in pp-collisions at the large hadron collider (LHC) are calculated and analyzed in dependence on two free parameters of the model, the [Formula: see text] mass [Formula: see text] and mixing angle [Formula: see text]. The exclusion and consistency [Formula: see text] regions imposed by the ATLAS and CMS data on dijet cross-sections are found. Using the CT10 (MSTW2008) parton distribution function (PDF) set we show that the [Formula: see text]-boson for [Formula: see text], i.e. the axigluon, with the masses [Formula: see text] TeV and [Formula: see text] TeV is excluded at the probability level of 95% by the ATLAS and CMS dijet data, respectively. For the other values of [Formula: see text] the exclusion limits are more stringent. The [Formula: see text] regions consistent with these data at CL = 68% and CL = 90% are also found.