Meeting Alhambra
ISAMA BRIDGES The International Society of the Mathematical Connections Arts, Mathematics, and Architecture in Art, Music, and Science
UNIVERSITI OF GRANADA FACULTI OF SCIENCES
Meeting Alhambra ISAMA-BRIDGES 2003
Organizers
Javier Barrallo Jose Martinez Aroza Registration and Reservation Space Management School of Architecture Faculty of Sciences University of the Basque Country University of Granada 20018 San Sebastian, Spain 18071 Granada, Spain
Nathaniel Friedman Reza Sarhangi Art Exhibit Conference Proceedings Department of Mathematics Mathematics Department University At Albany Towson University 1400 Washington Avenue 8000 York Road Albany, NY 12222 Towson, MD 21252
Juan Antonio Maldonado Carlo Sequin Space Management Poster Session Faculty of Sciences EECS, Computer Science Division University of Granada Soda Hall # 1776 18071 Granada, Spain University of California Berkeley, CA 94720-1776 Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings, 2003.
Editors:
Javier Barrallo Jose Martfnez-Aroza School of Architecture Faculty of Sciences University of the Basque Country University of Granada San Sebastian, Spain Granada, Spain
Nathaniel Friedman Reza Sarhangi Department of Mathematics Mathematics Department University At Albany Towson University Albany, New York, USA Towson, Maryland, USA
Juan Antonio Maldonado Carlo Sequin Faculty of Sciences EECS, Computer Science Division University of Granada University of California Granada, Spain Berkeley, California, USA
ISBN:
Price: $40.00
Distributed by MATHARTFUN.COM (http://mathartfun.com)
Front cover design: Polynomiograph of a Physicists' polynomial by Bahman Kalantari.
Back cover design: The step 2-octogonal tiling projected onto a dome and used as the basis for a zellij created by Jean-Marc Castera.
Cover layout and border designs: Chris Palmer.
© Meeting Alhambra, ISAMA-Bridges 2003 Conference. (http://www.sckans.edu/~bridges/). All rights reserved. General permission is granted to the public for non-commercial reproduction, in limited quantities, of individual articles, provided authorization is obtained from individual authors, and a complete reference is given for the source. All © rights and responsibilities for individual articles in the 2003 Conference Proceedings remain under the control of the original authors. Contents
Preface xiii
Three Traditions of Self-Similarity in Fourteenth and Fifteenth Century 1 Islamic Geometric Ornament Jay Bonner
Volution's Evolution 13 Carlo H. Sequin
Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines 25 Godfried Toussaint
Hidden Inscriptions in the Laurentian Library 37 Paul L. Rosin and Ralph R. Martin
Computers, Mathematics and Conceptual Art 45 Michael Mahan
Mathematical Sculpture Classification 53 Ricardo Zalaya and Javier Barrallo
Constructing and Classifying Designs of al-Andalus . 61 B. Lynn Bodner
Nodal Lines and Quasi-Space Filling Curves . 69 Tiziana Giorgi and Caryn Werner
On the Perception of Tone 77 Richard J. Krantz, Jack Douthett, and Richard Plotkin
Computational Aesthetics Based on Gaze Patterns 85 Gary R. Greenfield
Seashell Architectures 93 Kamon Jirapong and Robert 1. Krawczyk
Composable Art: Objects That Can Be Arranged in Many Ways 101 Marc van Kreveld
Mathematics in Literature 109 Lorna B. Hanes vi Dimension of Time in Strange Attractors 119 Robert 1. Krawczyk
Geometric Mosaic Tiling on Hyperbolic Sculptures 127 Irene Rousseau
The Mathematics of Color-Reversing Decorative Friezes: Fa~ades of Pirgi, Greece 135 David A. James, Loukas N. Kalisperis, and Alice V. James
Computer-Aided Aesthetic Evaluation of Visual Patterns 143 Tomas Staudek
Frieze-Generation Using Artificial Life 151 Dirk Fischer, Eric Goles, and Mario Markus
A Unified Theory of Proportion 161 Jay Kapprafj and Gary W. Adamson
The Art in Polynomiography of Special Polynomials 173 Bahman Kalantari
Arraying Alternative Housing Archetypes: An Online Resource 181 Jin-HoPark
Play with Infinity 189 Jean-Marc Castera
Two Perspectives on Inversion 197 John Sharp
Finding the Dual of the Tetrahedral-Octahedral Space Filler 205 Eva Knoll and Simon Morgan
Square Decompositions with Hyperbolic Consequences in Art, 213 Chemical Physics and Mathematics Robert G. Smits
Polyhedral Designs of Detection Systems for Nuclear Physics Studies 219 N. G. Nicolis
Leonardo's da Vinci's Bar Grids 229 Rinus Roelofs
Fractal Geometry and Self-Similarity in Architecture: 235 An Overview Across the Centuries Nicoletta Sala
Tangramoids 245 Samuel Verbiese vii The Sundial, Beyond Form and Time ... 253 Andrzej Zarzycki
The Poincare Surprises 257 Claude-Paul Bruter
Quilt Designs Using Non-Edge-to-Edge Tilings by Squares 265 Gwen L Fisher
An Extended Mural for a House of Mathematics 273 Anna Campbell Bliss
Hidden Geometry in Music of Bach and Schoenberg: 283 Reflection, Rotation, Proportion Jonathan Saggau
An Introduction to the Tiling Properties of Precious Triangles 291 Stanley Spencer
NEC Polygonal Groups and Tessellations 299 Domingo Gamez. Miguel Pasatias, Rafael Perez. and Ceferino Ruiz
Mathematics & Esthetics - Science and Art in the Bay Area 307 Benjamin Wells
Sculpture from Symmetrically Arranged Planar Components 315 George W. Hart
Easy Digitalization and Representation of Three-Dimensional Maps 323 Javier Bilbao Landatxe and Jorge Lazaro Dominguez
Dynamical Systems: A Golden Gate from Auditory Physiology 331 to Musical Aesthetics? Julyan H. E. Cartwright, Diego L Gonzalez. Oreste Piro, and Domenico Stanzial
Introducing Simple Arithmetic and Geometric Series 339 in Complex Parametric Modeling Jane Burry and Mark Burry
Abraham as Bridge and Mediator: A Metaphoric Reflection on the Alhambra 347 Ozayr Saloojee
M6bius Concepts in Architecture 353 Jolly Thulaseedas and Robert J. Krawczyk
On the Shapes of Water Fountains and Times Tables 361 Stephen Eberhart viii Lengthening, Expansion and Torsion: 367 Three Geometric Operations for Aesthetics Creation Delgado Olmos, A., Marquez Garda, L.
Mathematical Bridges to Philosophy and Theology 375 Douglas Norton
Whirled White Web: Art and Math in Snow 383 Brent Collins, Steve Reinmuth, Dan Schwalbe, Carlo Sequin, and Stan Wagon
Quilts Inspired by Mathematics 393 Mary C. Williams
Geometric Designs in Architecture and Textiles Revisited 401 and Reconstructed Through Layered Planar Geometry Benigna Chilla
Fractal Geometry Describes the Beauty of Infinity in Nature 407 Maria Antonia Castro and Maria Jose Perez-Luque
Number Theory and Art 415 Vera W. de Spinadel
Magic Geometry: Mosaics in the Alhambra 423 Miroslav Lovric
Graphs and Circulation in Rural Housing 433 MB Francisca Blanco and Miriam Pisonero
Diversifying the Curriculum: The Tessellations Case 441 Reza Sarhangi, Gabriele Meiselwitz, and Goran Trajkovski
The "Mathematics and Culture" Project 449 Michele Emmer
Islamic Constructions: The Geometry Needed by Craftsmen 459 Raymond Tennant
Developmental Morphology: X, Y, & Z Coordination 465 as a Dynamic and Generative Cellular Process Manuel A. Bdez
A Study on the North Dome of Masjid-I-Jami Isfahan 473 Marjan Ghannad
Crossing the Equal Sign 485 Marion D. Cohen
Great Kiva Design in Chaco Canyon: An Archaeology of Geometry 493 Chris Hardaker ix
Petrie Polygons 503 Paul Gailiunas
The Mathematics of Quilting: A QUilter's Tacit Knowledge 511 of Symmetry, Tiling, and Group Theory Katrina Hebb
Hyperbolic Spirals and Spiral Patterns 521 Douglas Dunham
Optimal Geometry as Art 529 John M. Sullivan
Folding Polyhedra and Painting Mosaics 533 Chris K. Palmer
Abstracts
A Patterned Life 541 Jennifer Angus
Origami: A Good Way to Communicate Mathematics 544 Ann Hanson
Goldbach THings 545 SharolNau
Conceptual Art and Algorithms 547 Susan Happersett
Symmetry and Trigonometry 549 Steve Whealton
Digital Monoprints: Mining Conchoid Nets 551 Stephen Luecking
Cayley Tables as Quilt Designs 553 Gwen L. Fisher and Elsa Medina
Duality: A Common Thread in Math, Science, Literature, and Art? 555 Michael de Villiers
An Interdisciplinary Study of an Archetype: Across Cultures and Disciplines 557 Ann Hanson, Paula Frohele, Carol Haliday-McQueen, and Renee Hansen
Space Blanket 558 Lorella Di Cintio x
On Mathematics in Art 559 Clifford Singer
The Relationship among Proportions, Ottoman-Turkish Music and Architecture 561 Guney Kurdak
Polyhedra in "Polyart" Style 562 Ulrich Mikloweit
An Evaluation Approach fot Circulation in Buildings 563 Mohamed Nada and Khaled M. Nassar
Discrete-Event Activity Simulation for Predicting 564 Occupants' Movements in Buildings Khaled M. Nassar and Mohamed Nada
Why Do Penrose THings Diffract? 565 Robert V. Moody
My Use of Number Sequence and Geometry in Art 567 Kathleen Hyndman
New Pentatonic Scale Relationships with Visual Parallels 569 Veryan Weston
Hexa-Twistor Triangular Section 571 AkioHizume
Some Mathematical Patterns in the Analysis of 573 Selection and Deletion in Modem Short Stories Masoudd Norouzian and Shadman Shokravi
Golomb Rep-Tiles and Fractals 575 lmameddin Amiraslanov
Two Geometric Sculptures with Distant Ontogenies 577 Benjamin Wells
The Collapse Series 578 Andrzej Zarzycki
Connecting Writing and Contextual Development 579 with Mathematics in Introductory College Math Courses Stan T. Yoshinobu
Geometry in Dali' s Painting 580 F. Blanco, E. Reyes, and C. Santamarina