Doris Schattschneider • Michele Emmer (Editors)

M.C. Escher's Legacy A Centennial Celebration

Collection of articles coming from the M.e. Escher Centennial Conference, Rome 1998

~ Springer

Editors:

Doris Schattschneider Moravian College Department of Mathematics 1200 Main Street Bethlehem, PA 18018-6650, USA e-mail: schattdo@moravian.edu

Michele Emmer University of Rome La Sapienza 5, Piazzale Aldo Moro 00139 Rome, Italy e-mail: emmer@mat.uniromal.it

The first printing of this book appeared as hardcover edition,

1st edition 2003, 2nd printing 2005

Library of Congress Control Number: 2005928381

All M.e. Escher's works @ 2002 Gordon Art B.V., Baarn, The Netherlands. All rights reserved.

A complete list of Escher's works reproduced in this volume is given on pp. 456-458.

Additional material to this book can be downloaded from http://extras.springer.com.

ISBN 978-3-540-20100-7 ISBN 978-3-540-28849-7 (eBook) DOl 10.1007/978-3-540-28849-7

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Celebrating Escher

Doris Schattschneider

The year 1998 saw many centennial celebrations of the Dutch graphic artist M.C. Escher (1898-1972). One of these, an international congress held in June of that year in Rome and Ravello, brought together a wide array of of people who not only appreciate Escher's work, but give testimony to his lasting legacy in art, science, and education.

Shortly before the congress, a review by a New York Times art critic had pro­claimed Escher "Just a nonartist in the art world." I find the "art world" a funny place - it often seems that if an artist's work is popular with the public, then it must follow that the work is "nonart." The 1998 exhibition "M.e. Escher: A Cen­tennial Tribute" held at the National Gallery of Art in Washington, D.e. drew record crowds - 364,000 people visited the exhibit, more than for any other print show. Perhaps for the "art world," Escher's art is an acquired taste. In retrospect, the official critics may come to see and understand the wonderful qualities in his work that have made it endure. e.V.S. Roosevelt, an avid admirer and collector of Escher's work once remarked, "When an art critic petulantly stamps his foot and remarks he quite despises Escher, one is reminded of the cartoon caption: 'There they go! I must hurry after them, for I am their leader' ."

What draws people to Escher's work? I can only hazard a personal and very incomplete answer to that question. I believe the qualities that make Escher's work so appealing are also the ones that inspire and challenge others. Escher was an acute observer, a thinker, a meticulous craftsman, whose prints evoke admira­tion and wonderment. "Cool!" (rather than "Beautiful !") is an oft-heard remark at Escher exhibitions.

The constant challenge of the artist is to create artifice. Escher created some highly original artifices that tease and enchant. In trying to place him in the spectrum of 20th century art, his work defies categorization. Roosevelt observed:

Regardless of what the world thought of him, Escher imperturbably always went his own way. He reminds us of a modern alchemist inge­niously and fanatically experimenting with his magic balls and mirrors, animals and books, his magic spells and magic concepts. A wonderfully

VI D. Schattschneider

obstinate figure, now artist, now thinker, philosopher, and shaman, Escher insisted, "All my works are games, serious games."*

Escher loved to challenge our eyes and understanding by tweaking the cer­tainties of the "laws" that we expect to be obeyed. By working in the plane, he could confound our perception of what is two-dimensional and what is three­dimensional. Not only does he make us wonder at what point does one dimension transform into the next, but he has us ask "what is figure? what is ground?" His device of using interlocking shapes, each shape recognizable on its own, yet each interchangeable in the role of figure or ground, is one of his trademarks. Few artists have been as fascinated by tessellation as Escher was. For him, "regular division" was not an end in itself, but rather a device to express the idea of duality (contrasting opposites), and metamorphosis.

Escher used geometry masterfully in his works. His early scenes of Italian villages clinging to steep mountainsides with valleys sweeping out below seem carefully sculpted from geometric forms. His later works celebrate polyhedra, spheres, knots, and Mobius bands. Geometry works magic in his prints - classi­cal Euclidean geometry, spherical geometry, projective geometry, transformation geometry, hyperbolic geometry, and self-similarity all are skillfully employed to achieve intricate and surprising visual effects. Not only was he a master of the craft of graphic art, he was also (despite his denials) an original researcher in the realm of science and mathematics.

Escher has left us a rich legacy in his work.

This book and CD Rom continue the 1998 celebration of Escher's legacy. The section "Escher's World" contains essays that give deeply personal reflections on Escher's work and stories of those who have literally walked some of the paths trodden by Escher.

It is often said that Escher belonged to no "school" of art and founded no "movement," and so it is assumed that there are no contemporary artists who continue to explore and express in manners directly inspired by his work. In the section "Escher's Artistic Legacy," the large number of artists who speak here and display their work show that assumption is clearly false. Escher's work planted seeds in the minds of these artists, seeds that have borne fruit that is inge­nious and original, some employing his careful graphic techniques, others using more modern media, including digital art. They, like Escher, play with illusion, with perspective and projections, with constructions (both real and impossible), with mirrors, with symmetry and division of the plane, and with metamorphosis. They, too, use geometry masterfully, inspired by Escher, yet are guided by ideas that are wholly their own.

Scientists and educators have drawn inspiration from Escher-his works have provided visual metaphors for their theories, raised new questions about

* From the catalog of the exhibition "A Mathematician Views Escher", Moravian College, April 1987.

Celebrating Escher VII

their assumptions, suggested new problems to investigate, and provided en­joyable explorations for students of all ages. The section "Escher's Scientific and Educational Legacy" contains a variety of essays by scientists (of many disciplines) and educators, a testimony to the enduring influence of Escher's work.

The CD Rom is an extension of the book. It contains color versions of many of the art works that are shown in the book in black and white, as well as additional work by the artists. It gives vignettes of the conference and the breath­taking beauty of the Ravello setting. It also affords a medium beyond print: there are animations, short videos, and interactive puzzles.

Editing this book has been a pleasurable challenge. The authors come from eleven different countries, with many languages and with a myriad of different computer programs that encode word and picture. Yet I have received wonderful cooperation from all, and thanks to email, zip disks, and CD Roms, they were able to quickly respond to the many requests to put this all together. I want to thank Moravian College for its support of my editorial work, making available to me the necessary technology and technological help. Michele Emmer and I are grateful for the encouragement and cooperation of Springer-Verlag, Heidelberg, in making this book and CD Rom a reality.

Bethlehem, August 2001

Escher, in Rome, Again

Michele Emmer

Why a conference and an exhibition dedicated to the works of Mau­rits Cornelis Escher? Escher had a very strange destiny. His works are probably among the best known in the world. But perhaps his great success and the dispersion of his work all over the world are reasons why his work as a graphic artist is not investigated seriously and not well­considered by historians of art. This is one of the reasons why the idea of organizing a conference and an exhibition of Escher's work was taken up by a Mathematics Department, the Mathematics Department of the University of Rome "La Sapienza."

Among the most popular ideas of our time are multimedia presenta­tions and interdisciplinarity, including the relationships between art and science. Escher, for a great part of his artistic life, was an "attractor" and produced connections among mathematicians, physicists, crystallo­graphers, and experts in visual perception. It is well known that his first important exhibition was mounted during the International Congress of Mathematicians in Amsterdam in 1954.

So here is a conference designed for many to discuss symmetry, visual perception, computer graphics, architecture, history of art, mathematics, and psychology, always having Escher as a starting point. The fact that so many people from different countries and from different disciplines wish to participate in this conference is the main reason for its organization.

The above paragraphs are not my opening to the Escher Centennial congress held in Rome in 1998, but rather they are taken from the introduction I wrote for the catalog of the exhibition of Escher's work held at the Dutch Institute in Rome in March 1985. That exhibition took place during the last international confer­ence on Escher, with lectures in the same "Aula Magna" at the University of Rome "La Sapienza" 14 years ago. The title of that conference was M. C. Escher: Art and Science [1]. The 6000 copies of the catalog ofthe exhibition [2] sold out in three weeks.

I can use the same words to write this introduction to the proceedings of the 1998 congress because now the fascination with the work of Escher is perhaps even greater than 14 years ago, even though much of the world has completely changed. In 1985 there was the Soviet Union and the wall in Berlin. I was very sorry that professor Vladimir Koptsik from Moscow State University, who was an invited speaker for the 1998 congress, at the last moment was not able to attend. I remember very well (and perhaps others who were at the previous con­ference will also remember), that during the conference in 1985 the Red Brigades killed a professor from our university, professor Tarantelli. The world is really different now, but interest in Escher is still alive and unchanged.

x M. Emmer

This special congress to celebrate the centennial of Escher's birth was also organized in Rome This is fitting since Escher was in Italy and lived in Rome for many years; for the same reason a session of the congress was organized in Ravello, on the Amalfi coast. And a last, but not least reason: my family name Emmer is originally Dutch and very similar to "Escher."

The 1998 congress differed from the 1985 one in several respects. There were many new faces, including several contemporary artists, as well as some familiar participants. Some participants at the previous conference were not able to attend this one, in particular, my co-editors of the 1985 Proceedings: H.S.M. (Donald) Coxeter, Marianne Teuber, and Sir Roger Penrose [1]. Another difference is that in 1985, Johannes Offerhaus, the energetic and enthusiastic director the Dutch Institute, arranged for the Escher exhibition to be held there and The Queen of Holland came to open the exhibition. Unfortunately, Offerhaus died a few years ago. This time the Dutch Embassy and the Dutch Institute in Rome had no in­terest in supporting an exhibition. (Ironically, the cultural attache of the Dutch Embassy, answering my letter of 1996 asking if there would be interest in spon­soring a new exhibition, answered that an exhibition was held in 1985 - of course he did not know I was the organizer.)

This time the M.e. Escher Foundation gave us wonderful support for the art exhibitions in Rome and in Ravello. I want to thank them for their encour­agement and cooperation in every aspect of the congress, and their enthusiastic attendance at the sessions. In 1998 we had a private three-day exhibition at the Museo Laboratorio di Arte Contemporanea of the University of Rome "La Sapienza," held during the congress. Here, along with many of Escher's prints, the work of contemporary artists from many countries was shown, in an Homage to Escher [3]. (The exhibit was held despite many difficulties of importing the works of art for the show, thanks to the rules of the Italian and other European Customs). The exhibit in Ravello featured almost exclusively the little-known prints of Escher's beloved Italian scenes. Its opening reception was a special part of the congress session in Ravello, and was open to the public for an extended period. Two different catalogs were printed; one for each exhibition in Rome and in Ravello [4].

I want to thank many people who helped with the hundreds of details of organization of this congress:

First of all Doris Schattschneider. She first presented the results of her study on the symmetry notebooks of Escher at the previous congress; a few years later she published the book Visions of Symmetry [5]. Without her handling the per­sonal contacts with all the speakers, exhibitors, and participants, it would have been impossible to organize the congress.

My colleagues Valentina Barucci and Stefania Gabelli for organizing the Rome exhibition and its catalog. Alessandra Seghini, the director of the com­puter science lab of my department, Alessandro Franchi the computer technician, and Angelo Bardelloni of our library: they solved many seemingly impossible technical problems. The electricians of the Aula Magna, the private cops, the staff of Latour catering. Michele dell' Aquila for the congress web site, Matteo

Escher, in Rome, Again XI

Emmer for the congress logo, animated on the web site, and shown at the be­ginning of this preface (yes, he is my son and an architect). Maria Pia Cavaliere and Orietta Pedemonte of the University of Genova, Laura Tedeschini Lalli, of the University of Rome III, who helped with local arrangements and registration. Mr. Bruno, for the Apple computers and the technical help.

The helpful staff of the Museo Laboratorio di Arte Contemporanea: Maurizio Calvesi, the director, Francesca Lamanna, Maurizio Pierfranceschi, who was always at the artists' disposal; Linda Riti, Bruno di Martino for the video and film presentations.

The students and graduate students who performed many tasks: Marta Angelilli, Massimiliano Amoroso, Daniela Bassi, Alessia Sao, Monica Amore, Maria Silvia Cosma, Maria Silvia De Angelis, Andrea di Marco, Daniele Mancini.

Mr. Pedrocchi of the travel agency Touring Viaggi. And for all local arrange­ments in Ravello: Eugenia Apicella and all the staff of the Centro Universitario Europeo per i Beni Culturali. Francesco Fortunato, Antonio Gisolfi of the Uni­versity of Salerno, the organization of the concert, the public administration of the City Hall of Ravello and of the Province for their help. In particular for the beautiful weather and the sea. A particular thank you to the Mayor of the town Secondo Amalfitano and to the Soprintendente dei Beni Ambientali, Artistici e Storici di Salerno e Avellino Ruggero Martines.

A very, very special thank you to Mark and Wim F. Veldhuysen, George Escher, and all the Escher family for their unflagging enthusiasm and support.

The congress received financial support from the University of Rome "La Sapienza," the Dipartimento di Matematica "G. Castelnuovo," the National Council of Research e.N.R., the M.e. Escher Foundation, and Michele Emmer.

In the proceedings of the previous conference I wrote, "I would like to thank my son Matteo and my wife Valeria, and in particular my son Tommaso. With­out their continuing encouragement (and my friends know how true this is) the congress would never have taken place." I can now reveal that Tommaso was bat­tling leukemia during the conference in 1985; thankfully, he recovered and he is now a medical doctor. It was Valeria who was suffering from cancer during the 1998 conference. She died October 8,1998. This is why this volume is dedicated to her. I must thank Matteo, Tommaso, and Marta very, very much.

Rome, February 1999

References

[1] H.S.M. Coxeter, M. Emmer, R. Penrose, M. Teuber, eds., M.e. Escher: Art and Science, North-Holland, Amsterdam, 1986; IV edition.

[2] M. Emmer, C. van Vlaanderen, eds., M. e. Escher, catalog of the exhibition, Roma, The Dutch Institute, 1985.

XII M.Emmer

[3] V. Barucci, ed., Homage to Escher, catalog of the exhibition, Universita di Roma "La Sapienza," Diagonale ed., Roma, 1998.

[4] M. Emmer, ed., Escher 1898-1998, catalog of the exhibition, Centro Universitario Europeo of Ravello, Diagonale ed., Roma, 1998.

[5] D. Schattschneider, Visions of Symmetry, New York, WH. Freeman & Co., 1990.

Note on the CD Rom

When the icon shown above appears at the beginning of an article, it indicates there is additional material by that author on the CD Rom that accompanies this book. The CD Rom contains collections of artwork (in color) by the contributing artists, several short videos, a video-essay based on a letter ofM.C. Escher, some animations, and an interactive puzzle.

The CD Rom will run on either a PC with Windows 98 or higher or Macin­tosh with OS 8.S or higher, 200 MHz processor or higher, and 800x600 minimum screen resolution with high color setting. It uses Acrobat Reader and Quicktime, which may be installed from the CD Rom if your machine does not have them.

Contents

Preface

Doris Schattschneider Michelle Emmer

Escher's World

H.S.M. Coxeter

Celebrating Escher .............. . Escher, in Rome, Again ........... .

Escher's Fondness for Animals

Bruno Ernst (Hans de Rijk)

V IX

1

Selection is Distortion ................................. 5

Michele Emmer Ravello: An Escherian Place 17

Douglas R. Hofstadter Mystery, Classicism, Elegance: an Endless Chase After Magic 24

J. Taylor Hollist and Doris Schattschneider M.e. Escher and e.v.S. Roosevelt. . . . . . . . . . . . . . . . . . . . . . . . . 52

Anne Hughes Escher's Sense of Wonder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Claude Lamontagne In Search of M.C. Escher's Metaphysical Unconscious . . . . . . . . . . 69

Marjorie Senechal Parallel Worlds: Escher and Mathematics, Revisited . . . . . . . . . . . . 83

Mark Veldhuysen M.e. Escher in Italy: The Trail Back 92

XIV

Escher's Artistic Legacy

S. Jan Abas Islamic Patterns: The Spark in Escher's Genius

Victor Acevedo

Contents

100

Space Time with M.e. Escher and R. Buckminster Fuller. . . . . . . . 113

Sandro Del Prete Between Illusion and Reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

JosDe Mey Painting After M.e. Escher. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Michele Emmer M.e. Escher: Art, Math, and Cinema. . . . . . . . . . . . . . . . . . . . . . . 142

Tamas F. Farkas Organic Structures Related to M.e. Escher's Work. . . . . . . . . . . . . 150

Robert Fathauer Extending Escher's Recognizable-Motif Tilings to Multiple-Solution Tilings and Fractal Tilings

Helaman Ferguson with Claire Ferguson

154

A Circle Limit in Stone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

Kelly M. Houle Portrait of Escher: Behind the Mirror. . . . . . . . . . . . . . . . . . . . . . . 175

Eva Knoll Life After Escher: A (Young) Artist's Journey 189

MatjuSka Teja KraSek Sharing some Common Interests of M.C. Escher 199

Makoto Nakamura New Expressions in Tessellating Art: Layered Three-Dimensional Tessellations. . . . . . . . . . . . . . . . . . .. 207

Istvan Orosz The Mirrors of the Master . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

Peter Raedschelders Tilings and Other Unusual Escher-Related Prints 230

Marjorie Rice Escher-Like Patterns from Pentagonal Tilings 244

Contents xv

Rinus Roelofs Not the Tiles, but the Joints: A little Bridge Between M.e. Escher and Leonardo da Vinci 252

Claudio Seccaroni and Marco Spesso Architecture, Perspective and Scenography in the Graphic Work of M.C. Escher: From Vredeman de Vries to Luca Ronconi . . . . . .. 265

Richard A. Termes Hand with Reflective Sphere to Six-Point Perspective Sphere

Escher's Scientific and Educational Legacy

Douglas Dunham Families of Escher Patterns

H.S.M. Coxeter The Trigonometry of Escher's Woodcut Circle Limit III

Jill Britton Escher in the Classroom

Victor J. Donnay Chaotic Geodesic Motion: An Extension of M.e. Escher's Circle Limit Designs

Jane Eisenstein and Arthur L. Loeb

275

286

297

305

318

Rotations and Notations ................................ 334

George Escher Folding Rings of Eight Cubes 343

Istvan Hargittai Dethronement of the Symmetry Plane 353

Scott Kim Computer Games Based on Escher's Spatial Illusions. . . . . . . . . . . 366

Vladimir A. Koptsik Escher's World: Structure, Symmetry, Sense 379

Kevin Lee Adapting Escher's Rules for "Regular Division of the Plane" to Create TesseIMania!® ................................ 393

Jean-Fran~ois Leger M.e. Escher at the Museum: An Educator's Perspective 408

XVI Contents

John F. Rigby Escher, Napoleon, Fermat, and the Nine-point Centre. . . . . . . . . . . 420

Marjorie Senechal The Symmetry Mystique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

Valentin E. Vulihman Escher-Like Tessellations on Spherical Models 442

Solution to Scott Kim's puzzle. . . . . . . . . . . . . . . . . . . . . . . . . . 448

About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449