Five Sessions

The following is the original scope of the sessions shown in the first circular of the symposium. They are not necessarily realized as originally intended. The discrepancies may look bigger than the reality, since the proceedings contain only the selected papers. In the items of chair­persons here, all the persons are contained: both of those who joined the planning and those who chaired at the sessions.

Session 1. Science on Form.

Chairpersons:

Keywords:

Michael Burt, Takeshi Koshizuka, Ryuji Takaki, Eiji Tokunaga, Denis Weaire, Ami Korren.

tessellation, pattern formation, scientific art, sCience education, sCience play.

Let us discuss problems concerned to scientific aspects of forms, science education and science plays. This session includes both scientific presentations and entertainments motivated by in­terest in forms. Even in scientific discussions, open-mindness is considered the most important factor. Therefore, this session accepts any participants, irrespective of the present occupation or status, who wants to present a scientific paper, a toy, a demonstration setup, a puzzle, an idea of science education or a cultural aspect of science.

Session 2. Geometrical Arts and Morphology.

Chairpersons: Haruo Hosoya, Koji Miyazaki, Gisaku Nakamura, Tibor Tarnai, Ture Wester.

Keywords: geometry, morphology, multi-dimension, graphics, origami.

The session covers the themes on geometrical forms and symmetry seen in arts and NATURE. The particular field of interest is the application of classical and contemporary geometry to the solution of morphological problems arising in arts, science, and technology. The exam­ples of the theme are: Mathematical games and puzzles, Geometrical figures, Space-fillings by polygons and polyhedra, Spatial morphology, Architectural design, Multi-dimensional art, Hypergraphics, Origami, and so on.

399

400

Session 3. Invisible - Visible / Viewing Invisible Images by Comparing them to Visible Forms.

Chairpersons:

Keywords:

Christophe Charles, Takashi Masunari, Shunsuke Mitamura.

invisible, modeling, image, virtual, explanation.

People often "view" invisible images (or concepts) by comparing them to visible forms: to ge­ometric forms (the triangle, the circle and so on), for example. The former are then modeled by the latter.

As to the form cited in such comparisons, you can find a certain liking of people, which reflects their cultural backgrounds and their style of thinking.

In this session, participants will reflects will report on how and why this and that is the case, and discuss the creative roles of scientists and artists in this regard.

Session 4. Sensing Order. Chairpersons: William Huff, Shutaro Mukai, Akiko Tsukamoto.

Keywords: articulation, formulation, dynamism, Gestalt, pattern.

This session considers the various processes and the dynamism involved in the formation of Gestalt and how we perceive them. A human being has a double existence in the sense that he is living in Nature and is formed by Nature while at the same time he forms and re-forms his own cultural world. We sense order and at the same time we constantly give new meanings to it. Our sensitivity for orders and patterns varies with culture and environment and changes as our sense of beauty changes

Session 5. Symmetry, Dissymmetry, Broken Symmetry in Art and Science: Dialogue of East and West (Dedicated to the Memory of Professor Hitoshi Igarashi).

Chairpersons:

Keywords:

Gyorgy Darvas, Tsutomu Kaneko, Denes Nagy, Itsuo Sakane, Akira Yanabu.

symmetry, dissymmetry, symmetry breaking, art-science relationships, East­West dialogue.

According to Pierre Curie, "the dissymmetry makes the phenomenon". Indeed, there is no perfect symmetry in nature and art, but rather some symmetry violations make the phenom­ena or events more exciting or more useful for the researcher and the artist (practical and aesthetical values). The idea of broken symmetry plays a crucial role in the oriental, espe­cially Japanese arts. On the other hand, the Western science, and later arts, also discovered the advantage of looking for and after broken symmetry. This session would like to discuss these aspects in both interdisciplinary and intercultural contexts. We also would like to pay tribute to the late Professor Igarashi (University of Tsukuba) who significantly contributed to the dialogue between East and West in the fields of philosophy and aesthetics.

Program of the Symposium

21 (Mon) November, 1994

Opening Session (Chairpersons: MIURA Koryo and DARVAS Gyorgy)

Opening Address ,HUSIMI Kodi: Symmetry in Mon and Mon-yo: Artisans and Artificers Preceded Mathemati­cians and Scientists. Keynote Lecture 'OGAWA Tohru: Katachi and Symmetry: Towards Interdisciplinary and Intercultural Coopera­tion. A Comment 'NAGY Denes: From Morphology to Formology and the Interdisciplinary Study of Symmetry: The Japanese katachi and the Western Symmetry Shake Hand.

Plenary Session (Chairpersons: MASUNARI Takashi and WEAIRE Denis)

Main Guest Lecture ,MACKAY Alan L.: Growth and Form. Main Guest Lecture ,SUGIURA Kohei: The Sun, The Moon, and The Eyeball- A Cosmic Correspondence. Introduction to Sessions by Chairpersons (Chairpersons: OGAWA Tohru and NAGY Denes)

'Session 1: Science on Form 'Session 2: Geometrical Arts and Morphology

'Session 3: Invisible - Visible / Invisible Images by Comparing them to Visible Form

'Session 4: Sensing Order .Session 5: Symmetry, Dissymmetry, Broken Symmetry in Art and Science: Dialogue of East and West Reception

22 (Tue) November, 1994

Plenary Session (Chairpersons: MACKAY Alan L., MASUNARI Takashi, and KOSHIZUKA Takeshi)

,YANABU Akira : Katachi Versus Form: From the Viewpoint of Language. ,DARVAS Gyorgy: Dichotomies and Trichotomies in the Eastern and Western Cultures . • TAKAKI Ryuji: How to Promote the Morphological Sciences.

Five Parallel Sessions

I Session 11 SCIENCE ON FORM (Chairpersons: WEAIRE Denis and TAKAKI Ryuji)

.BU RT Michael and KORREN Ami: Periodic Hyperbolic Surfaces and Subdivision of 3-Space . • TANEMURA Masaharu: On the Beauty of Random Packing. ,ISHIHARA Shozo : Origami-Model of Crystal Structure, 1. Rutile, Marcasite, and Cubic Close Packing Structures. ,KAINO Keimei and CHIBA Norishige : Origami Modeling Method of Digitate Leaves for Im­age Generation . ,KOSE Katsumi. HASHIMOTO Takeyuki. and INOUYE Tamon: 3D NMR Imaging of Foam Structures . • SANO Osamu: Numerical Simulation of a planar Labyrinthian Structure of a Ferrofluid in the Presence of Randomly Distributed Obstacles.

401

402

.MATSUURA Shu and TEJIMA Shoko: Fungal Colony Landscapes . • SHIMIZU Hideo and SUDA Koichi: Three-Dimensional Structure of Hepatic Sinusoids: Topo­logical Analysis and Its Application to Histopathological Diagnosis . • TOKUNAGA Eiji : Fractality of Drainage Basin Forms . • KODAMA Sachiko: The Relationship between Cycles of Complementary Colors.

I Session 21 GEOMETRICAL ARTS AND MORPHOLOGY (Chairpersons: NAKAMURA Gisaku, TARNAI Tibor, and MIYAZAKI Koji)

.RIGBY John: Precise and Perfect Colourings of Tilings . • HIGASHI Iwami, KOBAYASHI Masayoshi, and KOBAYASHI Kimiko: Icosahedral B12 Crystals

.HIZUME Akio: Star Cage . • KOSTOV Ruslan I.: Crystal Symmetry of the Gem Minerals and Their Cultural Shape . • ATAKE Katuhito: Diagonal & Variable Frame Structures: N (Aleph) - Structures or Instant Structures . • HOSOYA Haruo: Multi-Layered Cyclic Fence Graphs: Discovery of New Series of Graphs with Exceedingly High Symmetry . • ISHII Motonaga and MIYAZAKI Koji: Regular Multiprisms . • MIYAZAKI Koji, SHIOZAKI Manabu: Pentagonal Regular Figures in Four-Space . • BETSUMIYA Toshiaki and NAKAMURA Gisaku: A Solid Model for Penrose Tiling . • FUKUDA Hiroshi, NISHIYAMA Shizuka, and NAKAMURA Gisaku: pg Tiling of Polyomino . • ITOH Yoshiaki: Random Walk on Crystal Groups and Statistical Distribution of Symmetry.

I Session 311NVISIBLE - VISIBLE /Invisible Images by Comparing Them to Visible Form (Chairpersons: MITAMURA Shunsuke, CHARLES Christophe, and MASUNARI Takashi)

.CHARLES Christophe: Images and Urban Spaces: Art and Environment in Japan . • HOZUMI Takeshige: A Method for Creating New Shapes on the Basis of Already-Established Shapes . • ADACHI Ryoko and TEJIMA Shoko: Muon-Scapes . • ISHIGAKI Setsuko: Metaphysical Basket . • MASUNARI Takashi: Katachi of Thinking.

I Session 41 SENSING ORDER (Chairpersons: TSUKAMOTO Akiko and HUFF William)

.HUFF William 5.: The Landscape Handscroll and the Parquet Deformation . • KOMACHIYA Asao: Reversible Perspective with Color Spectacles Eyes . • BAN DO Toshihiro: Texture Plays an Important Role in Visual Perception of Natural Pat­terns . • IRWIN Thomas: Form in Fiction of Thomas Hardy . • KAMIO Akio: Invisible Territory in Language . • HANAOKA-KAWAMURA Eiko: The Relation Between "Knowledge of Form" and "Form of Knowledge" as Understood Through the Philosophy of Whitehead and Nishida.

I Session 51 SYMMETRY, DISSYMMETRY, BROKEN SYMMETRY IN ART AND SCIENCE (Chairpersons: KANEKO Tsutomu, DARVAS Gyorgy, NAGY Denes, and YANABU Akira)

.ARAKAWA Hiroshi: A Symmetrical View of Japanese Cosmology and Architecture . • IGUCHI Toshino: Symmetry-Asymmetry in Constructivist Art:Case Study ofL. Moholy-NAGY . • SHAYESTEH Farrokh : In Search of Paradise between the Orient and the Occident . • BCZI Szaniszl6: Connected Organizational Levels in the Evolution of Matter . • KANEKO Tsutomu : The Spiral Recognition in the East and West . • KRESLING Biruta : Nature's Dissymmetry: The Ta.o of Failure . • IGARASHI Masako: From Kata to Katachi . • SAITO Takao: Spectral Katachi of Music; Pa.rt 1, Natural and Artificial.

23 (Wed) November, 1994

Plenary Session

403

(Chairpersons: TAKAKI Ryuji, TARNAI Tibor, and HUSIMI Kodi)

.WEAIRE Denis: Sorp and Serendipity: Cellular Structures in Two and Three Dimensions . • H ECKER Zvi: The Serpent, the Spiral, and the Sunflower . • Prince MIKASA Takahito: Development and Modification of the "Holy Symmetrical Design": East and West of the 'Silk Road'

Five Parallel Sessions

I Session 11 SCIENCE ON FORM (Chairpersons: BURT Michael, KOSHIZUKA Takeshi, and TOKUNAGA Eiji)

.GEVAY Gabor: Changes of Shape and Symmetry in the Construction of Perfect Polytope . • HUZITA Humiaki and FORCHER Peterpaul: On a Single Tile Element That Has Infinite Pos­sible Patterns . • MAEDA John and HARADA Akira: The Design of Forms which Design Form . • ICHIKAWA So, KAWAMURA Hiroshi, and TANI Akinori: Automatic Formation of Rigid Frames by Genetic Rules: An Application of Artificial Life . • MORIKAWA Ryota and SAITO Yukio: Monte Carlo Simulation of Vesicles with Intercalated Molecules . • TAINAKA Keiichi and ITOH Yoshiaki: Critical Population Size for Extinction . • HONDA Hisao and YOSHIZATO Katsutoshi: A Computer Simulation of Vascularization from Blood Islands . • KOGA Tatsuzo and TSUTSUI Tatsuo: Isometric Membrane Valve Conceived from a Morpho­logical Study of Aortic Valve.

I Session 21 GEOMETRICAL ARTS AND MORPHOLOGY (Chairpersons: HOSOYA Haruo, WESTER Ture, and MIYAZAKI Koji)

.SZOBOSZLAI Mihaly: Construction of Helical Surfaces . • MATSUO Mitsunobu: Ovalogy . • SEKIGUCHI Jiro: Quasi-Zalgaller Polyhedra Constructed by an Algebraic Method . • TARNAI Tibor: Symmetry of Golf Balls . • NAKATA Hiroaki: Four-Dimensional Mathematical Design for Architecture . • WESTER Ture: The Fabulous Paraboloid: Dual Transformation as a Design Method . • SUEHIRO Naoki: Hyper Regular Polyhedron in 16 Dimensional Euclid Space . • TAKADA Ichiro: On Rotations and Projections for Visualization of Lattices and Polytopes in n-Dimensional Euclidean Space . • WADA Kazuhiro: Super-Ellipsoids in Japanese Remains Toro . • SASAKI Mutsuko K. and SASAKI Tateaki: Mathematical Functions Can Generate Interesting and Attractive Patterns . • TESHIMA Yoshinori, WATANABE Yoshinori, and OGAWA Tohru: The Periodic Six-axes struc­tures in Rod System.

I Session 31 INVISIBLE - VISIBLE / Invisible Images by Comparing Them to Visible Form (Chairpersons: MITAMURA Shunsuke, CHARLES Christophe, and MASUNARI Takashi)

.SCHWABE Caspar: New Kinetic Models as an Analogue to Manifold Space . • MINAMI Shigeyuki, SASAKI Tohru, and SAITO Takao: Spectral Katachi of Music; Part 2, East and West . • NAKAGAWA Motoko: Images of Book in Modern Art . • TRIVEDI Kirti: From Formless to Form: A Methodology for Making Manifest the Unmanifest according to Hindu Iconography. ,MITAMURA Shunsuke: Virtual-Real Imaging.

404

I Session 41 SENSING ORDER (Chairpersons: TSUKAMOTO Akiko and HUFF William)

.OGAWA T ohru: Puzzle, Science, Culture: Taking Rod Constructions as an Example . • TSUKAMOTO Akiko : Does Thinking Have Style? .ILGEN Fre: The Synchronizing Self: A Seach for Harmony = ProcessofSymmetryBreaking . • KIMURA Harumi : Forms of Body Movements: Dance Notation . • COGSWELL Jim: An Anthropomorphic Alphabet . • KATO Etsuko: The Tea Ceremony: A Sacred Dance with Utensils.

I Session 51 SYMMETRY, DISSYMMETRY, BROKEN SYMMETRY IN ART AND SCIENCE (Chairpersons: KANEKO Tsutomu, DARVAS Gyorgy, NAGY Denes, and YANABU Akira)

.CAGLIOTI Giuseppe: From Perception to Thought via Symmetry Breaking . • ISHIDA Yoshiteru and SIMON Herbert A. : Symmetry for AI: Symmetries for Reasoning about Physical Laws . • HOLBA Agnes and LUKAcs Bela: Hominid Chilarity as Spontaneous Symmetry Breaking . • MATSUNO Koichiro: A Frozen Symmetry Emerging from Broken Symmetries . • PIMENTA Emanuel D.: KATACHI U SYMMETRY: A Question of Symmetry in Nature . • WATANABE Yasunari, IKEGAMI Yuji, and TAKAHASHI Kiyoji: Quasi-Periodic Dogs . • FAN Xu dong: Visualization of Broken Symmetries of Super Structure . • KOPTSIK Vladimir A. : Creative Power of Dissymmetry in Science and Art and the Principle of Restoration of Broken Symmetry: Information-Synergetic Aspects of Visual Thinking.

24 (Thu) November, 1994

Special Session WASAN lOjiJ (Japanese Old Mathematics) (Chairpersons: MATSUOKA Motohisa, NAKAYAMA Shigeru, and MACKAY Alan L.)

.NAGY Denes: Wasan and Discrete Geometry: From Ethnomathematics and Aesthetics to Ed­ucation and Research . • MICHIWAKI Yoshimasa: On the Symmetry in Transformation with Preserving: Area Figures in the Geometrical Figures . • DARVAS Gyorgy and NAGY Denes: Wasan Versus Western Mathematics: Asymmetry of the Brain and Education . • OKUMURA Hiroshi: A Symmetric Technique in the Japanese Geometry.

Plenary Session (Chairpersons: WESTER Ture, MIYAZAKI Koji, and MASUNARI Takashi)

.LYONS Phyllis: Women's Narratives and Antinarratives: Re-reading Japanese Traditions . • MIURA Koryo: From Metamorphoses to Adaptive Structures.

Performance Session Chairperson: TSUKAMOTO Akiko

.KOZU Yoshiyuki and The ROKKASEN GROUP: Rokkasen Concert . • ZENCHIKU Juro: Kyogen with a Lecture.

25 (Fri) November, 1994

Plenary Session Panel Discussion: What are Discussed in Five Parallel Sessions Chairpersons: MIURA Koryo, NAGY Denes, and OGAWA Tohru) Panelist: Chairpersons of five parallel Sessions Closing Session Future of KATACHI U SYMMETRY (Chairpersons: TMIURA Koryo, MASUNARI Takash, and TAKAKI Ryuji Farewell Party

Coinciding Exhibition: The Catalogue of the Exhibits

1 Setsuko Ishigaki: Metaphysical Basket (I)rv(IV). 2 Mitsunobu Matsuo: (1) CM no Capsule, (2) Arc, (3) Kaze

no Mai, (4) Column. 3 Keiko Kimoto: (1) Phase #01, (2) Phase #02, (3)

Phase #03. 4 Ryoko Adachi + Shoko Tejima: (1) Trace of Discharges, (2) Trace of

Molds. 5 Yasunari Watanabe: Quasiperiodic Dogs (1)rv(3). 6 Kenji Kohiyama: Alphabet Tiling "ARS+". 7 Sanpei Seki: Maze de Sampe. (1) No. 81 Steps be-

tween Hell and Heaven, (2) No. 158 The Opposite World, (3) No. 588 II' David's Star of Fraudulent Dimen-sion, (4) No. 640 The Stairs-Garden, (5) No. 685 Cut-out Work.

8 Takeshi Maeda: Reactive Color. 9 Toshiaki Betsumiya: (1) Penrose Dodecahedron, (2) Pen-

rose Dodecahedron, (3) Flower Do-decahedron T3 with Flower Dodeca-hedra, (4) A Pentagonal Piramid by Penrose Pattern.

10 Mutsuko Sasaki: Mandarian Ducks. 11 Mari Kubo: Proliterate. 12 John Rigby: Seven Hyperbolic Tiling Patterns. 13 Biruta Kresling: Nature's Dissymmetry - The Tao of

Faqilure. 14 Hiroshi Tomura: Moving Dimension (1) 3·4 dotsr = ~,

(2) 5 dots r = ~. 15 Akio Hizume: Star Cage. 16 Shunsuke Mitamura: Holograms (1) and (2). 17 Takeshige Hozumi: Kinetic Light Art E-24-I1. 18 Sachiko Kodama: (1). 19 Yaghan. Mohammad Ali: (1) Mugarnas half dome, (2) Mqarnas

Islamic Colum Capital, (3) Mugarnas III.

405

KATACHI U SYMMETRY Symposium Organization

Honorary Chairman: General Chairman: Program Committee Chairman:

HUSIMI, Kodi

OGAWA, Tohru

MIURA, Koryo

MASUNARI, Takashi

Exhibition Committee Chairman: MITAMURA, Shunsuke

Local Committee: KOSHlZUKA, Takeshi HIRATA, Takayuki

Art Designer: MORISAKI, Tadashi HARA, Tadanobu

Secretary: SASAKI, Setsuko

Proceedings Committee

OGAWA, Tohru MIURA, Koryo MASUN ARI, Takashi NAGY, D'enes

Organizing Committee

KANEKO, Tsutomu

KOSHIZUKA, Takeshi

MASUNARI, Takashi

MITAMURA, Shunsuke

Advisory Committee

MIURA, Koryo

MIYAZAKI, Koji

OGAWA, Tohru

SAKANE, Itsuo

SAWACHIKA, Tokuichi

TAKAKI, Ryuji

TSUKAMOTO, Akiko

YOSHIMOTO, Naoki

ARLANDI, Gian Franco (Italy)

CORBALLIS, Michael (New Zeeland)

DARVAS, Gyorgy (Hungary) GARDNER, Martin (U.S.A.) GERDES, Paulus (Mozambique)

HUZITA, Hurniaki (Italy)

MALDONADO, Tomas (Italy)

MUKAI, Shutarou (Japan)

NAGY, Denes (Fiji, Hungary, Japan) PENROSE, Roger (U.K.) TARNAI, Tibor (Hungary)

TODA, Morikazu (Japan)

KOPTSIK, V. A. (Russia) TRIVEDI, Kirti (India)

LOEB, Arthur L. (U.S.A) TU, Shiran (China)

MACKAY, Alan L. (U.K.) WEAIRE, Denis (Ireland)

Chairpersons

BURT, Michael MASUNARI, Takashi OGAWA, Tohru

CHARLES, Christophe MATSUOKA, Motohisa SAKANE, Itsuo

DARVAS, Gyorgy MITAMURA, Shunsuke TAKAKI, Ryuji

HOSOYA,Haruo MIURA, Koryo TARNAI, Tibor

HUFF, William MIYAZAKI, Koji TOKUNAGA, Eiji

HUSIMI, Kodi MUKAI, Shutaro TSUKAMOTO, Akiko

KANEKO, Tsutomu NAGY, Denes WEAIRE, Denis

KORREN, Ami NAKAMURA, Gisaku WESTER, Ture

KOSHIZUKA, Takeshi NAKAYAMA, Shigeru YAN ABU, Akira

MACKAY, Alan L.

407

List of Participants

ADACHI, Ryoko (Japan] KANEKO, Tsutomu (Japan] OGAWA, Tohru (Japan]

ARAKAWA, Hiroshi (Japan] KATO, Etsuko (Japan] OKUMURA, Hiroshi (Japan]

ARLANDI, Gian Franco (Italy] KAWAMURA, Hiroshi (Japan OTOBE, Yuro (Japan]

ATAKE, Katsuhito (Japan] KIMOTO, Keiko (Japan] PAIREAU, Fran~oise (Japan]

BAN DO, Toshihiro (Japan] KIMURA, Harumi (Japan] PIMENTA, Emanuel D. (Portugal]

BERCZI, Szaniszl6 (Hungary] KODAMA, Sachiko (Japan] RIGBY, John (UK]

BETSUMIYA, Toshiaki (Japan] KOGA, Tatsuzo (Japan] SAITO, Takao (Japan]

BURT, Michael (I.rael] KOHIYAMA, Kenji (Japan] SAKANE, Itsuo (Japan]

CAGLIOTI, Giuseppe (Italy] KOMACHIYA, Asao (Japan] SANO, Osamu (Japan]

CHARLES, Christophe (Japan] KOPTSIK, Vladimir A. (Russia] SASAKI, Mutsuko (Japan]

COGSWELL, Jim (USA] KORREN, Ami (Israel] SCHWABE, Casper (Switzerland]

DARVAS, Gy6rgy (Hungary] KOSE, Katsumi (Japan] SEKI, Sanpei (Japan]

DOTERA, Tomonari (Japan] KOSHIZUKA, Takeshi (Japan] SEKIGUCHI, Jiro (Japan]

FAN, Xudong (Australia] KOSTOV, Ruslan I. (Bulgaria] SHAYESTEH, Farrokh (Japan]

FUKAO, Seiichi (Japan] KOZU, Yoshiyuki (Japan] SHIMIZU, Hideo (Japan]

FUKUTA, Kenji (Japan] KRESLlNG, Biruta (France] SUEHIRO, Naoki (Japan]

FUKUDA, Hiroshi (Japan] KUBO, Mari (Japan] SUGIURA, Kohei (Japan]

GFNAY, Gabor (Hungary] LUKAcs, Bela (Hungary] SZOBOSZLAI, Mihaly (Hungary]

HANAOKA, Eiko (Japan] LYONS, Phylis (USA] TAINAKA, Keiichi (Japan]

HECKER, Zvi (Israel] MACKAY, Alan L. (UK] TAKADA, Ichiro (Japan]

HIGASHI, Iwami (Japan] MAEDA, John Takeshi (Japan] TAKAKI, Ryuji (Japan]

HIRATA, Takayuki (Japan] MASUNARI, Takashi (Japan] TAKENOUCHI, Kyo (Japan]

HIZUME, Akio (Japan] MATSUNO, Koichiro (Japan] TANEMURA, Masami (Japan]

HONDA, Hisao (Japan] MATSUO, Mitsunobu (Japan] TANIZAKI, Takayuki (Japan]

HOSOYA, Haruo (Japan] MATSUOKA, Motohisa (Japan] TARNAI, Tibor (Hungary)

HOZUMI, Takeshige (Japan] MATSUURA, Shu (Japan) TESHIMA, Yoshinori (Japan]

HUFF, William S. (USA] MICHIWAKI, Yoshimasa (Japan] TOKUNAGA, Eiji (Japan]

HUSIMI, Kodi (Japan] Prince MIKASA Takahito (Japan] TOMURA, Hiroshi (Japan]

HUZITA, Humiaki (Italy] MINAMI, Sigeyuki (Japan) TRIVEDI, Kirti (India]

IGARASHI, Masako (Japan] MITAMURA, Shunsuke (Japan] TSUKAMOTO, Akiko (Japan)

IGARASHI, Michiko (Japan] MIURA, Koryo (Japan] USHIRO, Kanae (Japan)

IGUCHI, Toshino (Hungary] MIYAZAKI, Koji (Japan] WACHMAN, A (Israel]

ILGEN, Fre (The Netherlands] MORIKAWA, Ryota (Japan] WADA Kazuhiro (Japan]

INOUYE, Tamon (Japan] MORIOKA, Taeko (Japan] WATANABE, Kazuko (Japan]

IRWIN, Thomas A. M. (UK] NAGY, Denes (Japan] WATANABE, Yasunari (Japan)

ISHIDA, Yoshiteru (Japan] NAKAGAWA, Motoko (Japan] WATANABE, Yoshinori (Japan]

ISHIGAKI, Setsuko (Japan] NAKAMURA, Gisaku (Japan] WEAIRE, Denis (Ireland]

ISHIHARA, Shozo (Japan] NAKASHIMA Yoshito (Japan] WEBER, Steffen (Japan]

ISHII, Motonaga (Japan] NAKATA, Hiroaki (Japan] WESTER, Ture (Denmark]

ITO, Satsuki (Japan] NAKAYAMA, Shigeru (Japan] WHITING, Steven M. (USA]

ITOH, Yoshiaki (Japan] NANNICHI, Yasuo (Japan] YANABU, Akira (Japan)

KAINO, Keimei (Japan) NATSUME, Yuhei (Japan) YOSHIMOTO, Naoki (Japan]

KAMIO, Akio (Japan) OGAWA, Taeko (Japan] ZENCHIKU, Juro (Japan)

409

Author Index

ARAI, Yoji 143 NAGY, Denes 3,27 ARAKAWA, Hiroshi 381 NAKAMURA, Gisaku 231 ARLANDI, Gian Franco 117 NAKATA, Hiroaki 215

NISHIYAMA, Shizuka 231 BETUMIY A, Toshiaki 231 BURT, Michael 179 OGAWA, Tohru 3,7,239

OHASHI, Tsutomu 347 CAGLIOTI, Giuseppe 355 CHARLES,Christophe 263 RIGBY, John F. 201

DARV AS, Gyorgy 91 SAITO, Rumiko 347 SAITO, Takao 347

FUKUDA, Hiroshi 231 SAITO, Yokan 347 SASAKI, Mutsuko K. 249

HIZUME, Akio X SASAKI, Tateaki 249 HOSOYA, Haruo 195 SUGIURA, Kohei 63 HOZUMI, Takeshige 257 SZOBOSZLAI, Mihaly 185 HUFF, William S. 291,307 HUSIMI, Kodi 3, 75 TAKADA,Ichiro 215

TAKAHASHI, Kiyoji 333 ICHIKAWA, So 165 TAKAKI, Ryuji 143 IKEGAMI, Yuji 333 TANI,. Akinori 165 ILGEN, Fre 315 TARNAI, Tibor 207 ISHIHARA, Shozo 173 TESHIMA, Yoshinori 239

TRIVEDI, Kirti 283 KANEKO, Tsutomu 373 TSUKAMOTO, Akiko 291,323 KAWAMURA, Hiroshi 165 KOMACHIY A, Asao 293 UTUMI, Masaki 143 KOPTSIK, Vladimir A. 363 KORREN,Ami 179 WATANABE, Yasunari 333 KOSE, Katsumi 157 WATANABE, Yoshinori 239 KOZU, Yoshiyuki 391 WEAIRE, Denis 125

WESTER, Ture 223 LYONS, Phyllis I. 109 WHITING, Steven Moore 301

MACKAY, Alan L. 47 YANABU, Akira 101 MASUNARI, Takashi 3,279 MATSUOKA, Motohisa 341 ZENCHIKU, Juro 395 Prince MIKASA, Takahito 81 MINAMI, Sigeyuki 347 MITAMURA, Shunsuke 271 MIURA, Koryo 3, 135 MIYAZAKI, Koji 215

411

Index

The index is arranged for the convenience of finding an interesting paper and the keyword itself does not necessarily appear in it.

The number indicates the starting page of a concerning paper.

Chinese characters, ............... 3, 27, 101 A cocoon curve, .......................... 135

aesthetics, ................................ 7 - surface, ............................. 135 ambigram, ................................ 7 colour, ............................ 293, 315 ambiguous figure, ... .,.,., ......... ., ... 355 colouring, perfect -, ................... 201 analogies between art and science, ...... 315 -, precise -, .......................... 201 antinomies, .............................. 91 combination, ........................... 239 architecture, 27, 135, 185, 215, 263, 373, 381 comparing, ............................. 279 art, . ., ..... ., ..... ., .......... 263, 271, 333 composite material, ..................... 239 - and science,7, 27, 47, 75, 315, 341,333,363 computer aided design, ................. 185 - and mathematics, ..... 117,249, 333, 341 - art, ................................. 249 artificial life, ........................... 165 communication, ........................ 143 - vs. natural, ......................... 347 configuration, .......................... 239 artisans, ................................. 75 congruent spaces, ....................... 179 Asia, . ., ..... ., ..... 63,81,91,283,381,391 conservation laws, ...................... 363 asymmetry, .... ., ........... ., .... .,81,381 constructive art, ........................ 257 automaton, ............................... 7 continuous deformation, ................ 307

cosmology, ...... ., ..... ., .... ., ..... 63, 381 B creating new shapes, .................... 257

Bach, Johann Sebastian, ........... 117, 301 critical size, ............................ 239 ball, golf -, ............................ 207 cross-fertilization of the different cultures, 91 Banko, .................................. 63 crossover, .............................. 165 basic art and design, ................... 257 crystal structure, origam~model of -, .. 173 - substances, ........................... 91 crystallographic group, .................. 75 beauty, danger of -, ................... 279 crystallography, (generalized), .. 47, 239, 363 -, geometrical -, ..................... 215 cultural background of science, ............ 7 Beethoven, Ludwig van, ................ 301 culture, diversity of -, ................... ·7 body, .............................. 263, 323 -s, Eastern and western -, ....... 7, 27, 91 -, huma - in space, ................... 135 -,'history of -, ...... 3,7,75,81,101,109, brain, .................................. 293 307, 341, 373, 381, 391, 395 bubble, ................................. 157 -, split -, ........................ 3, 7,27 Buddha, ................................. 63 -, two -s, ............................ 3,7

curve, cocoon -, ....................... 135 C curved surface, four-dimensional -, ..... 215

canon in music and mathematlics, ...... 117 cyclic fence graph, ...................... 195 cellular automata, .................. 47, 165 chant in Sprawling (Ne-Ongyoku), ...... 395 D characteristic polynomial, ............... 195 danger of beauty, ....................... 279

413

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danryu bungaku (literature by men), .... 109 fourth dimension, ....................... 263 database of katachi, .................... 279 fractal domain, ......................... 333 deconstruction, ......................... 109 function method, ....................... 249 deformation, continuous -, ............. 307 descriptive geometry, ................... 185 G design, architectual -, ................. 135 garden, ............................. 27, 263 -, holy symmetry -, ................... 81 generalized symmetry principle, ......... 363 design method, ......................... 223 genetic algorithm, ...................... 165 dichotomy, .............................. 91 geometrical construction, ............... 185 discrete mathematics, .................. 239 geometry, descriptive -, ................ 185 dissymmetry, ....................... 27, 363 global environment, .................... 391 diversity of culture, ....................... 7 Goethe, J.ohann Wolfgang, ................ 3 "dog, standing and sprawling", ......... 333 golf ball, ............................... 207 dual, self -, ........................... 179 graph, cyclic fence -, .................. 195 - transformation, ...................... 223 graphite network, ....................... 195 duality, structural-, ............... 91, 223 growth, ................................. 47 Duchamp, Marcel, ...................... 263 gun, ................................... 373 dynamic spectrum, ..................... 347 - symmetry, ............................ 27 H

harmony, search for -, ................. 315 E helicoid, ................................ 185

East and West, ................ 7, 27, 81, 91, high symmetry, ......................... 195 143, 347, 391, 395 Hirata Morizo, ............................ 3

elementary periodic region, ............. 179 history, of culture, .... 3, 7, 75, 81, 101, 109, endless, ................................ 117 307, 341, 373, 381, 391, 395 environment, ........................... 263 -, of science, ........ 3,7,47,143,341,373 -, global -, ........................ 7, 391 holy symmetrical design (H. S. D.), ...... 81 extended self, .......................... 315 Hojoki, .............................. 7, 125 exhaustive search, ...................... 179 holography, ............................ 271 extension of science, ...................... 7 hyperbolic plane, ....................... 201 eyeballs, ................................. 63 -, periodic - surfaces, ................ 179

hypercube, ............................. 215 F Hyperspace, ............................... 3

family crest, ............................. 75 - Science, Japan Institute of - -, ...... 3 figure, ambiguous -, ................... 355 foam, .............................. 125, 157 I form, .................... 3,27,47,101,143 iconography, .................... 63, 81, 283 - and Culture Society, .................. , 3 Igarashi Hitoshi, ....................... V, 7 -, Society for Science on -, Japan, ...... 3 image, ................................. 263 - creation methodology, ............... 283 imaging, ........................... 157, 271 - visualisation, ........................ 283 information, ............................. 47 Forma, ................................... 3 instability, ............................. 355 formology, ............................... 27 Institute, Japan - of Hyperspace Science, 3 four-dimensional curved surface, ........ 215 interdisciplinary bridges, ................. 27 - regular polytope, .................... 215 international standards, ................... 7

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ISIS-Symmetry .""""""""""" 3, 27 "mobil perpentuum", ................... 117 model, origami - of crystal structure, .. 173

J -, solid -, ............................ 231 jory'U b'Ungak'U (literature by women), ... 109 module system, .......................... 293 Japan Institute of Hyperspace Science, .... 3 mon (family crest), ..... " ..... ".27, 75,91 -, opening up of, ........................ 7 monohedral tiling, ...................... 307 -, science in -, ...................... 7,27 mon-yo (pattern), .................. " ... 75 Japanese automaton (karak'Uri), ........... 7 monotheism-polytheism, .................. 7 - constitution, ........................... 7 moon, .............................. 63, 395 - culture, ." ........... 7,27, 75, 109, 125, morphological science, .............. 27, 143

""""""""" .341,373,381,391,395 morphology, ." .. " ..... "." ............ 27 - language, ............................ 101 -, structural-, ....................... 223 - literature, ........................... 109 morphogenesis, ......................... 143 - mathematics, .................... 27,341 Mobius strip, ." ..... " .... " ........... 117 - music, ... " .... "." .. "." .. ".391,395 MRI (magnetic resonance imaging), ..... 157 - writing, ....... " ........... " .. ,,27, 101 music, """""""".7,117,301,347,391

- instruments, ....... " ..... " .... " ... 391 K -, Japanese -, ................... 347,391

karak'Uri ningyo (Japanese automaton), .... 7 -, natural -, ......................... 347 katachi, " ..... " ..... " .... 3,7,27,47,101 -, western -, ............ : ....... 347,391 -, database of -, ..................... 279 -, visualization of -, ............. 117,347 K - no B'Unka-Shi, .. " .... " .... " ..... " 3 myth, ................................... 63 kaleidoscope, ........................... 231 kei(~), ................................ 101 N Kyogen, ................................ 395 Nakaya Ukichiro, ......................... 3

natural-artificial, ." ..... ".""" .... " 347 L -, picture of -, ...................... 7,91

language, ............................... 101 Ne-Ongyok'U (Chant in Sprawling), ...... 395 landscape handscroll, ................... 307 network(s), " .. " .. " ... "." ...... 263, 315 Leonardo da Vinci, ....................... 3 -, graphite -, ........................ 195 literature, .............................. 109 NMR (nuclear magnetic resonance) imaging, logo mark, ..................... cover, IX, 3 ...................................... 157

No, .................................... 395 M - masks, .............................. 395

mandala, ................................ 63 nonverbal thinking process, ............... 7 mapping, ... " ........... "." .......... 249 nuclear power, ............................ 7 masks No -, ........ " .. " ............. 395 matching rule, " .... " ..... " ..... " .... 333 o mathematical pattern, .................. 249 Oe, Kenzaburo, ........................... 7 media, ................................. 263 on-k'Un readings, .............. " .... " .. 101 meditation, .............................. 63 optimal principle, ......................... 7 methodology, form creation -, ......... 283 origami-model of crystal structure, ...... 173 mind, .................................. 323 mind's eye, ............................... 7 p minimal surface, " ... " ...... " ..... 47,125 packing problem, ....................... 239

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packing, spherical circle -, ............. 207 rigidity, ................................ 223 paraboloid, ............................. 223 rods, ................................... 239 paradigm, .............................. 279 rutile structure, ........................ 173 parquet deformation, ................... 307 pattern, ................................. 75 S - formation, ........................... 143 science, .............................. 7, 143 -, mathematical -, ................... 249 -, extension of -, ....................... 7 Penrose tiling, ................ 231, 239, 333 -, history of -, ..... 3,7,47,143,341,373 perception, ........................ 293, 355 -, morphological -, ............... 27, 143 perfect colouring, ....................... 201 S- on Form, Society for -, .............. 3 performance, .................. 263,391,395 scientific interplanation of the world, ..... 91 perspective, ............................ 293 - revolution, .......................... 373 periodic, ............................... 239 - standards, ............................. 7 - hyperbolic surfaces, .................. 179 scissor( s), ............................... 75 "philomorph", ......................... 3, 7 screw, .................................. 373 plane, hyperbolic -, ................... 201 selection, ............................... 165 - tiling, ............................... 231 self, extended -, ....................... 315 plant transmission wave, ................ 391 - -dual, ............................... 179 polyhedra, ........... 125, 157, 173, 215, 223 - -similar, ............................. 333 -, regular -, ..................... 143, 207 semiotics, ................ 117, 279, 323, 363 polyhedral skeletons, ................... 173 serch for harmony, ...................... 315 - structures, .......................... 223 shape, ............................... 3, 143 polynomial, characteristic, .............. 195 shin-josei (new women), ................ 109 polyomino, ............................. 231 Silk Road, ........................ 7, 81, 391 polytope, four-dimensional regular -, ... 215 similar, self -, ......................... 333 polytheism-monotheism, .................. 7 skill, ................................... 239 possible, ............................... 263 Smith, Cyril Stanley, .............. 3, 7, 125 precise colouring, ....................... 201 snow crystal, ........................... 3, 7 preference, ............................. 279 Society, Form and Culture -, ............. 3 processing original shapes, .............. 257 -, International- for Interdiscplinary Study pump, .................................. 373 for Symmetry, ........................ 3,27 puzzle, ................................. 239 - for Science on Form, Japan, ....... 3, 143

solid model, ............................ 231 Q sophistication, ............................ 7

quantum mechanics, .................... 355 space, congruent -, .................... 179 quasiperiodic, .......................... 239 - extensions, .......................... 263 quasiperiodic tiling, .................... 333 -, human body in -, .................. 135

- lattice, .............................. 179 R - -Time, .............................. 263

real, ................................... 271 -, work -, ............................ 135 regular polyhedra, ...................... 207 spectrum, dynamic -, .................. 347 - polytope, four-dimensional-, ....... 215 spherical circle packing, ................. 207 - tiling, ............................... 201 standards, international -, ............... 7 renunciation of war, ...................... 7 -, scientific -, .......................... 7 reverse, ................................ 293 "Star Cage", ................... cover, X, 7

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star rhombic dodecahedra, .............. 231 thinking, way of -, .................... 279 stereology, .............................. 143 Thompson, D' Arcy, ................... 3, 47 structure, .............................. 239 thought, ............................... 323 - , foam -, ...................... 125, 157 three dimension (3D), .................. 157 - of the material reality, ................ 91 tiling, monohedral-, .................. 307 structural duality, ...................... 223 -, Penrose -, .................... 231, 239 - morphology, ......................... 223 -, plane -, ........................... 231 styles, .................................. 323 -, quasiperiodic -, .................... 333 sumi-nagashi, ............................. 7 -, regular -, .......................... 201 sun, ................................ 63, 395 tomoe (whirl), ............... 27, 75,91, 239 surface, cocoon -, ..................... 135 torus, .................................. 195 -, four-dimensional curved -, ......... 215 tradition, ............................... 109 -, minimal-, ..................... 47,125 transformation, ......................... 257 -, periodic hyperbolic -, .............. 179 translationability between different cultures, symbolic images, ....................... 283 7, 27, 101 symmemetrical design, holy - -, ........ 81 trichotomy, .............................. 91 symmetry, ......... 3, 7, 27, 75, 81, 239, 381 twist, .................................. 239 - breaking, .................. 315, 355, 315 two-color eyeglasses, .................... 293 - -dissymmetry relations in science, 27, 363 - cultures, ............................ 3, 7 - -dissymmetry relations in art, .... 27, 363 -, generalized - principle, ............. 363 V - group, ..................... 179,207,363 variable geometry truss, ................ 135 -, high -, ............................ 195 variation form, ......................... 301 -, the holy - design, ................... 81 vertual, ................................ 271 -, in Asia, .......... 27,63,81,91,283,391 vibrating drop, ......................... 143 -, in Japan, .......... 7, 27, 47, 75, 91, 101, virtual, ................................. 263

341,363,373,381,391 395 visual thinking, ......................... 355 - in music, ............................ 301 visualisation, form -, .................. 283 -, International Society for Interdisciplinary - of music, ....................... 117, 347 Study of -, .............................. 3 vocalization, ............................ 395 S-: Culture and Science, ............. 3, 27 -, twofold and threefold, ................ 91 W synchronization, ........................ 315 war, renunciation of -, ................... 7 synergetics, ............................ 355 wasan, .............................. 27,341

way of thinking, ........................ 279 T whirl relation, ................... 75, 91, 239

tacit knowing, ....................... 7, 239 Whyte, Lancelot Law, ................. 3,27 teaching material, ...................... 173 work space, ............................ 135 technology, ............................. 263 temporal visual art, .................... 307 Terada, Torahiko, ...................... 3, 7 y

tessellation, ............................ 125 Yin-Yang, ................... 27, 63, 91, 395

thesaurus, .............................. 143 thinking, ............................... 323 -, visual-, ........................... 355