Your Reflections: News from ISA members

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The first concert of “genetic music” on the basis of genetic musical tunings was held on 4 June 2015 in Vienna (Austria) in the “Festsaal” of the Vienna University of Technology on the conference IS4IS. Bio-mathematical basis of these tunings has been developed in the Russian Academy of Sciences in course of studying the genetic coding of living matter by means of DNA molecules.


The video presents fragments of the concert of genetic music here.




From International Symmetry Association’s member Veryan Weston.



Artlandia symmetry-related resources (free) and symmetry-related software (commercial):

Artlandia glossary of pattern design
Pattern Central
Tutorial: “The Counterchange Symmetries for the Mathematically Inclined”
Artlandia SymmetryWorks (Adobe Illustrator plug-in)

Dick Termes is in the news again!

This time for his newest creation, an instructional DVD, Basic Elements of Drawing. South Dakota Public Broadcasting’s Charles Michael Ray interviewed Dick about the who’s, what’s and why’s that motivated this new, non-globular creation. Listen in as Dick explains why we all need to learn to draw and just exactly how to do just that. Listen to it here!

Tom Johnson: Other Harmony

Beyond Tonal and Atonal. Editions 75 & Two-Eighteen Press; Second Printing edition, 2014.

Kostov, R. I. 2014. Crystallography of the polyhedron, enantiomorphism and a five-fold symmetry code in Durer’s “Melencolia I”

Vth National Crystallographic Symposium, NCS-2014, 25-27 September 2014, Sofia, Bulgaria, Program and Abstracts, 62.

Kostov, R. I. 2014. Pentagon-dodecahedral and icosahedral artifacts in antiquity: 3D five-fold symmetry applied to cultural heritage

Annual of the University of Mining and Geology “St. Ivan Rilski”, Vol. 57, Part IV, Humanitarian and Economic Sciences, 23-27.

Artworks by Jérémie Brunet

This video is a panorama of the Mandelbox parameter space made by Jérémie Brunet, a French fractal artist. The Mandelbox is a 3 dimensional fractal object discovered in 2010 by Tom Lowe and named after the father of fractal geometry Benoit Mandebrot. What we see here is actually a fixed cut in the middle of the Mandelbox, which has a cubic shape in general. This object exhibits the natural symmetries of a cube, but the iterated function that is used to generate it also uses the concept of symmetries intensely, most notably via the usage of a “folding” function that basically mirrors a point through different folding planes before going to the next iteration. This is translated graphically in the animation by the kaleidoscopic effects that can be seen around the 4 corners. For more details on the Mandelbox formula, please visit Tom Lowe’s website.

Your Reflections – News from International Symmetry Association’s members

Contact Us! Send your news and information on your symmetry-related activities to

From Sergey Petoukhov: In 2012, the Moscow State Conservatory by P.I. Tchaikovsky (at the initiative of the members of the International Symmetry Association) has created a Center for Interdisciplinary Studies of Musical Creativity. Prominent place in actions of this Center is devoted to the study of the role of symmetries in the theory of musical harmony and musical creativity, as well as in the neighboring areas of physiology and psychophysics of perception based on the genetic characteristics of living matter. One of interesting topics is so called “genetic music”, bases of which have been developed in Russia due to the study of symmetric features of the genetic code. In coordination with the ISA, the Center holds annual international conferences “Music. Mathematics. Science.”, the first of which took place in 2013, and the second – in 2014. In the Conservatory the Center conducts monthly scientific and creative seminars in which in addition to the problems of musicology a great attention is focused to problems of symmetrology. Representatives of the Centre actively participated in the Symmetry Festival 2013, where they have organized a specialized international symposium “Symmetry and Music” (Delft, The Netherlands, August 2013). Perhaps our new article about genetic fractals in connection with matrix analysis will be interesting for you: 

Ivan V. Stepanyan, Sergey V. Petoukhov: The matrix method of representation, analysis and classification of long genetic sequences

From Emanuel Pimenta: In 1973 I started a long photo essay with portraits of artists, scientists, thinkers from different countries, as the expression par excellence of a planetary Zeitgeist. It is titled SOULS. Now, I’m releasing the forty years version of this essay (SOULS 40 Years – 1973 to 2013) with the publication of a book in four volumes and a movie at the Streaming Museum in New York – three hundred and fifty people in forty countries. The books have portraits of René Berger, Leonel Moura, William Anastasi, Dove Bradshaw, Roy Ascott, Maurizio Barbetti, Jorge Lima Barreto, John Cage, Merce Cunningham, Maria Bonomi, Daniel Charles, Ornette Coleman, Phill Collins, Phill Niblock, Joe Cocker, Alberto del Genio, Stan Getz, Marcia Grostein, Hans Joachim Koellreutter, Takehisa Kosugi, Pierre Levy, Arthur Loeb, Harald Szeemann, Pierre Restany, Mario Merz, António Cerveira Pinto, Artur Matuck, Hermeto Pascoal, Monika Weiss and many more. Especially the movie SOULS 40 Years includes thoughts of the Mahabharata, John Cage, Alvar Aalto, Theodor Adorno, Woody Allen, Guillaume Appollinaire, Louis Aragon, Hanna Arendt, Rudolf Arnheim, Jean Arp, Antonin Artaud, Gaston Bachelard, Pablo Picasso, and Joseph Beuys. In April 2014 it will be an exhibition at Baahng & Co in New York City. SOULS 40 Years is dedicated to a dear friend, whom I greatly admire and with whom I have collaborated on mutual projects since 1990, nearly twenty- five years ago: Lucrezia De Domizio Durini. The book has a preface by the genius critic, curator and art historian Pilar Parcerisas. I’ve no words to thank Pilar Parcerisas, Nina Colosi and Jennifer Baahng for their immense support in this version SOULS 40 Years. The history of this project, with its mysteries – including introductions, texts etc. – is at hereThe books – which are , as always, for sale at cost price – can be ordered at here.

From Haresh Lalvani: We are pleased to share this Pratt video link on Haresh Lalvani entitled Future of Soccer Ball Design. Here’s the text from the Pratt website: The 2014 World Cup “Brazuca” soccer ball has been touted as being the most advanced ever made after the company spent two years designing it with fewer panels of a single shape across the ball’s surface. Such “single-panel” design makes the ball smoother, rounder, and more consistent. But Pratt Institute Architecture Professor and designer Haresh Lalvani says the preferred “one-panel” design means future choices for ball designs are limited. In 2007, Lalvani disclosed one-panel soccer ball designs in a patent which included a very similar design to the 2014 World Cup soccer ball. He says that through mathematics and geometry it is possible to see where innovation in ball design may be heading.

From Jay Kapraff: Jay Kapraff’s new book “A Participatory Approach to Modern Geometry” has appeared. This book aims to make the subject of geometry and its applications easy and comfortable to understand by students majoring in mathematics or the liberal arts, architecture and design. It can be used to teach students at different levels of computational ability and there is also sufficient novel material to interest students at a higher cognitive level. While the book goes deeply into the applications of geometry, it contains much introductory material which up to now may not have been known to the student. The constructive approach using compass and straightedge engages students, not just on an intellectual level, but also at a tactile level. This may be the only rigorous book offering geometry that attempts to engage students outside of the mathematics discipline. More info: here.

From Michel Petitjean: JE SUIS CHARLIE

Obituary – Paulus Gerdes, mathematician and symmetrologist, member of International Symmetry Association

We are sorry to report the death of Paulus Gerdes, internationally renowned symmetrologist on November 10, 2014. He was a member of the Advisory Board since ISA’s foundation in 1989.

Paulus Gerdes was internationally known for his work in ethnomathematics, as he learned from ordinary people and their use of geometry to improve mathematics education.

Among his many books, all lavishly illustrated with baskets and other daily items made by Mozambicans and other Africans, and many published in English, Portuguese, and Dutch editions, are
Women, Art and Geometry in Southern Africa
(Trenton, N.J.: Africa World Press, 1998)
Otthava: Making Baskets and Doing Geometry in the Makhuwa Culture in the Northeast of Mozambique
and Supplement
Otthava: Images in Colour
(Maputo: Centre for Mozambican Studies and Ethnoscience, Universidade Pedagógica, 2010).

His books can be found at

International Symmetry Association is co-organizing International Society for Information Studies’ Summit Vienna 2015

IS4IS Summit Vienna 2015 – The Information Society at the Crossroads – Response and Responsibility of the Sciences of Information will be organized at Vienna University of Technology, June 3-7, 2015.

International Symmetry Association joins to the scientific preparations of the large event, contributes with several sessions, an art exhibit and community events, moreover provides publication forum for the congress’ symmetry-related papers.

International Symmetry Association’s members are organizing the following sessions:

  • As we may teach – ICT in education: an odd couple.
    Read the call for papers and join to the session, here!
  • Information in the exact sciences and symmetries – approaches of physics versus those of philosophy of science. Read the call for papers and join to the session, here!
  • Music, information and symmetry.
    Read the call for papers and join to the session, here!