CHAPTER 2
TESSELLATIONS
In origami, tessellation is a technique used to create an endless variety of motifs from a sheet of paper without the need for cutting or pasting. Its foundations were laid in the research of Shuzo Fujimoto (1922–2000), with concurrent contributions by another Japanese scholar, Yoshihide Momotani. Since then, many other authors have appeared on the scene—Chris Palmer, Alexander Beber, Alex Bateman, Ben Parker, Eric Gjerde, Joel Cooper, and later Polly Verity and Robin Scholtz—and come up with a wide variety of designs. In 2017, Robert J. Lang published Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami, a 776-page volume that organizes and systematizes information on the subject.
In this chapter, we present spirals created from double-twist folds (through original works by Tomoko Fuse) and models that combine multiple motifs. (TF)
WHIRLPOOL + SQUARE 1 STANDARD
10.8 x 17.5 inches (275 x 445 mm)
PAPER Washi/Hamada, Kochi
The technique of tessellation seems to have originated over 6,000 years ago with mosaics and Sumerian majolica. The idea was further developed in Islamic and Moorish designs, as in the still visible decorations of the Alhambra in Granada, Spain. Inspired by these in the twentieth century, Maurits Escher designed tiles out of complex, closed (non-repetitive) motifs in which figures of birds, fish, or other animals gradually morph into a decorative surface. In origami, too, one can create two-dimensional patterns by individually folding modular tiles, attaching them to a base sheet, or linking them together with pockets and tabs, as is usually done in modular origami. Nowadays, however, tessellated origami, which has been immensely popular for the last twenty years, usually consists of (repetitive) two-dimensional motifs created by folding a single sheet of paper in such a manner that it finally assumes the appearance of distinct tiles. The creation of a tessellated pattern requires a great deal of preliminary work. The origami artist must first prepare a grid based on rigorous geometric criteria. Since such designs require large sheets of paper, some artists prefer using mechanical tools to speed up the process and thus resort to laser cutters that eliminate the possibility of human error and allow them to skip particularly tedious preliminary steps.
The result of executing a series of parallel folds that intersect at 90 or 60 degrees is a surplus of paper at the points of intersection that can be modeled into polygonal tiles. These layers can be opened, reworked, and flattened so that the tiles can be juxtaposed with extreme precision, or arranged into the form of a star or polygon. Origami tessellation becomes even more mesmerizing when a light source from behind makes more designs visible, as we shall see in the chapter on lamps. Various flat and reshaped layers end up generating new shapes and areas of shade, surprisingly different from those visible in the unilluminated structure. Note how Tomoko plays with material, as if she were drawing and painting with paper. Look at the colorful paper with its tessellations, and compare the regular, repeating patterns to those that gradually change across the surface. (DB)
WHIRLPOOL + SQUARE 2 STANDARD
15 x 10.2 inches (380 x 260 mm)
PAPER Washi/Hamada, Kochi
WHIRLPOOL + SQUARE 2 TWIST THE INTERSECTION
10.6 x 15.6 inches (270 x 395 mm)
PAPER Washi/Hamada, Kochi
WHIRLPOOL + TILT SQUARE 1 TWIST THE INTERSECTION
11.8 x 16.1 inches (300 x 410 mm)
PAPER Washi/Hamada, Kochi
TILT SQUARE + SQUARE
11.6 x 17.1 inches (295 x 435 mm)
PAPER Washi/Hamada, Kochi
WHIRLPOOL DOUBLE
14.1 x 10.4 inches (360 x 265 mm)
PAPER Washi/Hamada, Kochi
INFINITE WHIRLPOOL
9.4 x 12.6 inches (240 x 320 mm)
PAPER Washi/Hamada, Kochi
TWO FLOWERS
16.9 x 12 inches (430 x 305 mm)
PAPER Washi/Hamada, Kochi
RIPPLE WAVE 1 CRIMP TECHNIQUE
9.8 x 14 inches (250 x 355 mm)
PAPER Washi
RIPPLE WAVE 2 CRIMP TECHNIQUE
5.9 x 11.8 inches (150 x 300 mm)
PAPER Washi
HYDRANGEA MIXING TECHNIQUE
13 x 35.4 inches (330 x 900 mm)
PAPER Washi/Koide, Niigata
AROMA IN THE FOREST MIXING TECHNIQUE
17.7 x 43.1 inches (450 x 1095 mm)
PAPER Washi/Paper Nao, Tokyo
WIND OF SPRING PARK MIXING TECHNIQUE
14 x 40.2 inches (355 x 1020 mm)
PAPER Washi/Kochi (Tesuki Washi Berlin/Osaka) Hand dyeing
AFTER THE RAIN MIXING TECHNIQUE
43.3 x 14.2 inches (1100 x 360 mm)
PAPER Washi/Paper Nao, Tokyo
ORANGE MIXING TECHNIQUE
14.2 x 37.2 inches (360 x 945 mm)
PAPER Washi/Kochi (Tesuki Washi Berlin/Osaka) Hand dyeing
EARLY SPRING PARK MIXING TECHNIQUE
13.8 x 39 inches (350 x 990 mm)
PAPER Washi/Kochi (Tesuki Washi Berlin/Osaka) Hand dyeing
PURPLE PARK MIXING TECHNIQUE
46.5 x 28 inches (1180 x 710 mm)
PAPER Washi/Hamada, Kochi
CITY MIXING TECHNIQUE
41 x 24.8 inches (1040 x 630 mm)
PAPER Washi/Hamada, Kochi
GOLDEN AUTUMN MIXING TECHNIQUE
24.6 x 42.1 inches (625 x 1070 mm)
PAPER Washi/Hamada, Kochi
RAINBOW
Tunagu Exhibition in Kokusai Pulp & Paper Co. Ltd, Tokyo, Japan (Frame) 43.3 x 43.3 inches (1100 x 1100 mm)
PAPER Washi/Hamada, Kochi
AERIAL CLOUD
Tunagu Exhibition in Kokusai Pulp & Paper Co. Ltd, Tokyo, Japan (Frame) 43.3 x 43.3 inches (1100 x 1100 mm)
PAPER Washi/Hamada, Kochi
