Origami Tessellations. Awe-Inspiring Geometric Designs.pdf
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Open-Back Square Twist .................................
21
Open-Back Hexagon Twist ...................... ..... ...
22
BEGINNER PROJECiS
Five-and-Four .......................................... .....
24
Spread Hexagons.......... .. ............. ........ ... .... .
28
Tiled Hexagons ............................................
32
Star Puff. ................ ........................... ...........
36
3.6.3.6 ................. ... .. ................ ... ...... ...........
4()
Pinwheel ............ .... .... ...................................
43
Open-Back Hexagon Twist.. ........................
47
Basket Weave ... ...... .... .................................
50
Water Bomb ...... ...... ....................................
54
Square Weave ...... ...................................... ..
51
INTERMEDIATE PROJECTS
Contents
Chateau-Chinon ..........................................
6()
Rhombus Weave .............. ..................... .. ....
64
Preface ..................... ..... .. ................... .. ....... ........
\fI
Roman Church Floor Tiling .... ............ .........
70
Overview ........ .. ............... .. .... ...............................
2
Daisy Chains ................ ..... .......... ............... ...
73
Double Triangle Sawtooth ............ .... .........
76
Stacked Triangles ........................................
SO
Bird Base .......... ........ ........... .... ....... ............. .
84
Propellerheads ....................... .. ...................
88
Techniques .. .. ......................... ...............................
5
Precreasing ..................................... ................. ..
5
Sq~are
Grid .. ........... ........ ..... .. .... ....... ........ .......
e,
Triangle Grid .....................................................
7
r
Pleat Intersections .. .. .. ............ .. .......................
9
120-Degree Pleat Intersection ...........................
9
ADVANCED PROJECTS
------
120-Degree Inverted Pleat Intersection ............
U)
Arabesque Flourish .. .......... ................ .........
92
gO-Degree Pleat Intersection ............................
11
Field of Stars ...............................................
96
60-Degree Pleat Intersection ...........................
12
Negative Space Stars ................... .. .............
99
Rabbit-Ear Triangle Sink ...................................
14
3.4.6.4 .........................................................
1()3
Twists ....... ..................................... ....... ... .........
16
Aztec Twist ................................................
106
Triangle Twist ..................................................
1(,
Arms of Sh iva .............................................
110
Square Twist ............... .. .......... ...... .... .. ............
17
Gallery ..............................................................
114
Hexagon Twist .......... .. ....................................
18
Acknowledgments... .... .. ... ... .. ... ......... ... ... ........
12()
Rhombus Twist........ .......................................
20
About the Author .... .... ..... ... ... .. ........ ...............
120
Open-Back Triangle Twist ................................
21
Index ..... .............................................. ...............
121
Star Twist.................. .................... ...... .... .....
e,7
..,hen
I was five, my parents asked me what I wanted
n
to be when I grew up. "A paperologist," I replied
enthusiastically.
Throughout my early childhood and teen years,
I enjoyed paper crafts and origami. I found imagining
a thing and then creating it from materials at hand very
satisfying. Friends and family frequently gave me stacks
of papers and rolls of tape as birthday gifts.
Paperology wasn't a major at my college of choice,
however. So, after preparing for a technology career,
I found I still needed an artistic outlet. I turned back to
my childhood love of paper and origami .
How was I drawn to the geometric art of origami
tessellations, specifically? It started with a fish .
I was folding an origami koi designed by Robert
J.
Lang . The fish-scale design was folded from repeated
patterns called tessellations . I practiced a bit on some scraps
of paper, and, just like a fish, I was hooked on tessella-
tions . I folded sheet after sheet of paper, experimenting
with different shapes and variations . My excitement led
to deeper exploration and the creation of new tessellation
designs . I never looked back; in fact, I never did complete
that fish!
Since then I have folded hundreds of origami tessella-
t ions . Tessellations are geometric patterns that can repeat
forever. When captured in paper, beautiful pieces of art are
created in intricate pleats and folds .
For this book, I have taken 25 of my favorite tessel-
lations and turned them into projects for newcomers and
experienced origamists alike . With step-by-step instructions,
illustrated crease patterns, and how-to photos, you'll learn
to create these wonderful designs yourself-hopefully,
more easily than I did!
This book covers the fundamentals of origami tessella-
tions, providing a little history and describing simple begin-
ning techniques with detailed illustrations. The techniques
then are utilized in specific projects that will help you make
impressive works of art. Finally, the book's gallery of tessel -
lation images is designed to inspire you to experiment and
innovate, trying out the tessellations of others and, eventu -
ally, creating your own patterns.
NO ClJiilNG, NO GI.lJING,
ON I: Stll: I:i
01:
I'J.\I'I: It
All you need to make origami tessellations are your two
hands and a piece of paper. Folding tessellations is not
complicated. At its core, it is the repetition of simple folding
patterns to create larger, more complex designs .
Folding tessellations is a meditative experience . While
origami is labor-intensive, it's also very relaxing . Often
when I fold something I lose track of time. Hours pass
without my knowledge. When I'm finished, the completed
piece is almost like a present.
When I teach students how to create tessellations, they
always have an "Aha!" moment. They suddenly, unexpect-
edly understand how the folded shapes repeat themselves
and how they all work together. From that point on the
students take off and start folding madly. Three words of
warning: Tessellations are addictive!
Don't worry if your first project comes out imperfectly;
your next attempt will be greatly improved . Your own
"Aha!" moment will come soon. Practice and repetition are
great teachers .
As your skill and experience increase, you 'll start to see
tessellation patterns everywhere. Tiles on the floor, cobble-
stones in the courtyard, the patterns of light falling through a
stained-glass window-you'll find inspiration all around you .
You may find discovery and creation are the most
rewarding parts of this craft, because making origami
tessellations is very much about infinite possibility. When
you draw upon your newfound recognition of patterns and
think about how they might be recreated in paper, you can
use the techniques in this book to create amazing arrange-
ments and artwork all your own.
INiIIOI)IJCiION
,\NI) il:CtINIQIJI:S
The tiles you saw likely created tessellations-repeating
patterns of specific shapes . The word "tessellation"
comes from the Latin
tessel/a,
meaning "small square ."
The Romans frequently used squares for making mosaics
and tile designs .
While the Romans and Byzantines made complex
mosaic patterns, tessellations were raised to a true art form
by artisans of the Islamic faith . Since Islam forbade repre-
sentational imagery, artists and craftsmen focused their
creativity on developing complex geometric designs. Their
geometric orientation was reflected in inspiring architec-
ture, tile work, painting, ceramics, and illustration.
The Islamic Moors in Spain built the Alhambra, a
magnificent palace decorated with some of the best tessel-
lation artwork in the world. The Dutch artist M . C. Escher
(1898-1972) made several visits to the Alhambra . The
complex tessellation patterns he studied had a formative
impact on his art. Escher said the tiling at the Alhambra
was "the richest source of inspiration I have ever tapped ."
Now Escher's own art is among the most widely
known and loved in the world. Tessellations are an impor-
tant part of many of his sketches and illustrations, which
feature fantastic animals, figures, and shapes .
Tessellating Birds
by David Bailey
Today's origami tessellations are primarily the brain-
child of Shuzo Fujimoto, a Japanese chemistry teacher who
was instrumental in exploring the possibilities of folding
repeating shapes on paper. Fujimoto's singular focus on
origami tessellations continues to inspire many folders .
Most of the basic tessellation ideas covered in this book
were discovered by Fujimoto-sensei in the 1970s.
Many people have contributed to this art form's
development, including the computer scientist Ron Resch,
prolific origami author Yoshihide Momotani, and artist
Chris Palmer. Not long after spending six months living in
the caves of Sacremonte outside of Granada, Spain, on an
artistic journey to study the tilings of the Alhambra, Palmer
was exposed to the tessellations of Fujimoto.
Building on Fujimoto's work, Palmer has pushed the art
of origami tessellations upward and outward. He is one of
the greatest tessellation folders today, and many tessella-
tion artists count Palmer among their primary influences.
OIIlGj.\MI il:SSI:I.I.j.\iIONS
Origami tessellations are geometric designs folded from
a single sheet of paper, creating a repeating pattern of
shapes from folded pleats and twists. Tessellated origami
pieces range from simple square tilings to extremely intri-
cate, complex pieces inspired by Islamic art. Tessellated
shapes can form everything from twisted architectural
flourishes to realistic faces .
",tU\i IS' il:SSI:I.IJ.\iION7
tl
ave you ever looked at the patterns on a tile floor?
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