HYPERSYMMETRICS by JENS W. BEYRICH
Expect the Unexpected
The exhibition presents artwork as a result of a seemingly inexperienced synergy: collecting
art and antiques with the passion of developing complex equation systems – mathematics
being the universal base of science and philosophy.
Visiting hundreds of museums, exhibitions and fairs over several decades gave me an
overview and insight in which geometric systems for decoration have been used by the
earliest cultures until modern times.
Quite complex geometric decoration can be found on stoneware and ceramics from the site of
Uruk in Mesopotamia, 3000 B.C., coinciding with the dawn of the Pharaonic Empire. The
most sophisticated designs have been developed in the Arabic world for the decoration of
mosques, before 1000 A.D.. Nonetheless, I have not found a graphical artwork of regular,
symmetric and repetitive geometries with components that are all individually different and
dissymmetric in their colour arrangement.
Modern art lets think first of M. C. Escher, who developed the famous „Metamorphosis“ in
the 1930’s. The continuous surfaces are two-colour arrangements showing a continuous shift
of regular surfaces into different shapes (fish, birds, etc.). M. C. Escher and I have in common
that we both developed bank note designs.
Victor Vasarely developed a vast range of geometric paintings but symmetries are mainly the
result of the underlying patterns (visuals of spheres and cubes for instance) showing inherent
axes of symmetry. The colour arrangements are a matter of pure taste or continuous,
following different grid structures and being therefore visually “easy” to understand. The very
first signed lithography in my art collection was a classic sphere of Vasarely.
Max Bill, Swiss architect and artist, made use of some mathematical formulas to create
sculptures, as for example the set of „hemispheres“ in front of the Institute for Mathematics at
the University of Karlsruhe. These sculptures play with aspects of symmetry, but as a mere
result of the mathematical equations applied, and are quite evident to visualise. We share
interest in architecture and design and are Swiss born.
The fractals of Mandelbrot, developed in the late 1970’s, are visually the most impressive
generated by applying mathematics and incomparable to any former graphical presentations.
The underlying formula(s), though “recursive”, show one degree of freedom. Any application
of the formulas leads to exactly one determined result.
My graphical artwork basically consists of hexagonal (star shaped) symmetric structures
(„stars“) that differ by their colour arrangement. With three colours unevenly applied (3
points show one colour, 2 points a second colour and 1 point a third colour), just ten possible
solutions (permutations) can be obtained. Since the colour arrangement is dissymmetric (3-2-
1, not 2-2-2), each colour of each solution can be exchanged against another and generates an
individual colour arrangement, in which there are 60 different solutions.
Given any field sized X times Y = 60, for example 5x12 or 6x10, the first star can be placed
on any of the 60 positions, once the first is set, the next has 59 options free etc.), and each
star, as being a hexagonal symmetric structure, can be rotated at any field in six different
positions. Such that there are not one but 60 x 6 = 360 degrees of freedom
The total possibilities to arrange these 60 stars therefore are 60! x 6^60, around 10^126 – a
one followed by 126 zeros! The number of Avogadro, the number of atoms in the known
universe, is approx. 10^78 – we have billions of billions of billions more different solutions
for the graphical arrangements than atoms in the universe. Staggering.
Once certain rules are set how the stars need to be placed on any given field of 60, the - more
than astronomic - quantity of solutions gets reduced at an equally fantastic pace. For instance,
as for the graphic „spiral flower“, only ONE solution is possible, which, by the way, can be
perpetuated to the centre or infinity. As for the graphic „tower“, more than fifty (!) rules are
generating the particular design.
Needless to say, the most sophisticated of all are the spheres and the icosahedrons. Rules of
placement for the stars are not only to be met locally on the surface, but qualify for complex
symmetries over the poles – truly tricky.
Circumstances seemingly unprecedented, since October 2012 some of my graphics are
exhibited at my business school INSEAD on campus.
One sphere I am in discussion with the Dean, Dipak C. Jain, and his staff to donate to the
school. I believe no other work of art may reflect the philosophy of the school better – bring
together equally high level distinct individuality of its participants, develop structures
generating a complex network and new perspectives to its graduates.
I let the visitors of the exhibition discover the rules generating the beauty and harmony of the
graphics and sculptures; some rules are easy to find, others hidden and reveal only to whom is
committed to meditate in order to discover a new choreography based on individuality.
Jens W. Beyrich, Dipl.-Ing. s.c.l., MBA
January 2013
Venue: The Gallery in Cork Street
28 Cork Street, Mayfair, London W1S 3NG
Vernissage: Monday 17th June 2013
Exposition from 17th June till 22nd June
Opening hours to be communicated later
Contact: jens.beyrich@alumni.insead.edu
www.galleryincorkstreet.com