03/198 – Fractals

2003.02.03

The design wich is abstract, appeals to us, although at this time it is without any evident application : its convergence towards five squares with four right angled isosceles triangles that form an irregular octagon and refers to several symbolic or esoteric drawings such as for example the italian Tarot or the indian Mandala.

Subsequent drawings of fractals of the other regular polygons were made in 1991, likewise without any obvious concrete application.

Fractals were later developped, in 1992, in various ways with respect to spheres.

Two of these seem to us particularly interesting :
– the fractal of the square on the sphere of wich the large circle surrounds the original square, because the sum of the surfaces of the triangles of each interaction is constant and equal to the surface of the original square.
– the fractal of the hexagon on the sphere, the circle surrounding the hexagon being a small circle of the sphere. This latter fractal is particularly interesting because it produces a sub-division of the sphere based on identical spherical triangles and can be used as a regulatory pattern for a ” lattice dome “.

This pattern is all the more interesting because the fractal of the hexagon on the plan only produces a repetitive and regular paving of equilateral triangles. The result is to be compared with ” the isobar and isonode domes ” which we presented at the Second International Conference on Space Structures at Guilford (UK) in 1975.

Before continuing these studies (for example their development on surfaces with negative Gaussian curvature such as hyperbolic paraboloïds) and in order to better grasp the subject matter, we are now in the process of drawing the fractals of the regular polyhedras which will hold for us, we hope, some pleasant surprises.

• Philippe Samyn, ” Principes de Construction, ébauche “, Institut Supérieur d’Architecture Saint-Luc, Bruxelles, collection Référence n°XVI, February 1993, 64p. ; (Belgium).
  – SPACE DESIGN, Tokyo, n°346, July 1993, pp.69-96 ; (Japan).