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Exploring Sumba woven textile motifs through a digital technique using the Escher method
Published in Ratri Wulandari, Idhar Resmadi, Vika Haristianti, Rahmiati Aulia, Riky Taufik Afif, Gema Ari Prahara, Aulia Ibrahim Yeru, Dynamics of Industrial Revolution 4.0: Digital Technology Transformation and Cultural Evolution, 2021
Initial exploration was carried out to understand the Escher technique. The experiments applied were translation, reflection, rotation, and glide reflection. The four methods used objects found in the ornamental variety of Sumba ornament shapes. The result of the process was the motif modules. In advanced exploration, colors and more detailed elements were added into the motif modules. The use of virtual texture elements (invented texture) was done by making a square geometrical arrangement in the coloring process and providing details that aimed to imitate the actual texture inspiration (real texture) on Sumba woven textiles because of the intersection points of warp and weft. By using contrasting colors, it became more dynamic and brought up the harmony and balance patterns. The best results were presented on the table below. The translation and glide-reflection method are the most optimal form and produce the best visual from this experiment. The advanced exploration was aimed to create the tessellation formed composition from the motif modules, then it automatically seamlessly repeats.
Symmetry
Published in Michael Hann, The Grammar of Pattern, 2019
Translation is therefore a simple repetition whereby a motif is ‘translated’ from a specific location (without change in size, orientation or content) to another position (considered in one direction only with regular border patterns and in two distinct directions with regular all-over patterns). Meanwhile, glide-reflection is an action which combines translation with reflection, best imagined as the imprint made by feet walking on wet sand. With border patterns, assuming an orientation in a horizontal direction, reflections in two directions only (horizontal and vertical) are possible, glide-reflection in a horizontal direction only is possible and rotation can only be two-fold. With regular all-over patterns, the principal restriction is that rotation can only be two-fold, three-fold, four-fold and six-fold. As noted above, combinations of these four symmetry operations permit seven regular border pattern types and seventeen regular all-over pattern types.
Mathematical walks in search of symmetries: from visualization to conceptualization
Published in International Journal of Mathematical Education in Science and Technology, 2022
Umberto Dello Iacono, Eva Ferrara Dentice
As far as rotations are concerned, S8 draws three copies of the butterfly by cutting out the given image, overlapping it on the sheet and copying three times the image. Then, she cuts out also the three new copies and pastes them on a sheet, in such a way that the whole image is fixed by 90-degrees rotations. Also, S3, S17 and S18 work on rotations. They do not use the provided images, but they choose a picture that is fixed by rotations. In this way, they realize the rosette group D4. Student S4 uses the picture of the cat to realize a glide-reflection. She draws two copies of the cat by cutting out the given image, overlapping it on the sheet and copying the image, as also S8 do for the butterfly. S4 recognizes the frieze group F13 by comparing her drawing with the table of groups of Figure 4. Finally, S11 seems to be able to recognize reflections and glide-reflections. Indeed, she decides to use a heart (which is not in the set of given images). She draws her heart, realizes two copies of it by cutting, overlapping and copying, and pastes them realizing the glide-reflection. However, she does not demonstrate to be able to recognize rotations. Thus it seems that S8, S17, S18 reach the Visualization Level, and S3 and S4 consolidate it, but S11 still does not reach it.