A catalog piece, especially if one is writing it for one’s own catalog, allows too much freedom for the author. In many cases, the text is a formulation of thoughts that only serve to underline messages already communicated by the exhibition or the works once more, and needlessly. I would like to avoid that mistake and so I only make use of this opportunity in order to realize two distinct objectives.
The first one is to document, as far as possible, the development of the Spidron as innovation, as it pertains to names, to persons. The second is to settle a long-standing debt by finally defining what I/we understand the Spidron to be. I attempted to complete the first task in the text and images of the thirty-two pages of this brochure.
I shall attempt the second one below.
The real source of the Spidron is an old family name that has been changed, the name ‘Spitzer’. I have not revealed this before and instead offered the words ‘spider’ and ‘spiral’ as an explanation. The ‘-on’ at the end of the word follows Greek nouns, where a many-sided plain figure and a geometric body are called a polygon and a polyhedron.
Is the Spidron a polygon? As I often say, a Spidron arm is a spiraling formation constructed from a sequence of two kinds of triangles (usually isosceles ones). It is not possible to specify the number of its vertices or sides. Its area and circumference can be determined in the limit, but no matter how large or small a piece of it we take, it can always be extended by additional triangles. As professor of quantum logic Gyula Fáy put it, the Spidron is a process. It is a procedure in which, like the tower of Babel, the building of Spidrons can be continued as long as we want. The starting point can be set arbitrarily. The ratios of angles and lengths are the crucial aspects. Those ratios are constant and ever-present in the Spidron formations. The Spidron-arm cannot be finished, but it can be given a starting point with a clever trick: I can pick one triangle and declare that it will be the first and largest one. In order to prevent the addition of an even larger one, I can reflect the entire spiral formation across the base of that triangle. If it is a central reflection, I get the form we initially called the Spidron. If it is a mirror reflection, we get a figure like a pair of horns, which we have called the Hornflake. Various versions of those two figures fill the world of Spidrons. Those Spidron arms can be used to construct extraordinary shapes in the plane and in space. Our research ranges from plane tilings and regular and semi-regular solids through saddle surfaces and to the investigation of special, aperiodic tilings and quasi-crystals.
But the process induced by the subject of our shared thinking—which happens to be the Spidron, this time—in various human communities is at least as interesting. It generates action groups, provokes arguments and often results in striking scientific and aesthetic qualities.
It was particularly astonishing for many people that it can be used to create structures with an entirely novel kind of movement.
The Spidron has defined a position. I hope that sooner or later, through processes of their own, others will also be able to occupy that position.
At last, others may also achieve their rightful positions.