Journal for Geometry and Graphics, Vol. 5, No. 2, pp. 133-144 (2001)

Periodic and Aperiodic Figures on the Plane by Higher Dimensions

Emil Molnar, Tilman Schulz, Jenö Szirmai

Department of Geometry, Budapest University of Technology and
Economics, Egry Jozsef ut 1, H.22.,
H-1111 Budapest XI, Hungary

Abstract: We extend de Bruijn's idea of constructing Penrose's non-periodic tilings of the plane to higher-dimensional analogons. On the base of $d$-dimensional space groups we can draw nice aperiodic coloured plane tilings with the aid of computers, especially interesting ones if d+1 is prime. Our proposed probabilistic method seems to produce attractive pictures, in particular.

Keywords: higher-dimensional space groups, two-dimensional projection, aperiodic tiling

Classification (MSC2000): 52C22; 52C23

Full text of the article will be available in mid of 2003.

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