Constructing Penrose tiles with de Bruijn projections
In mathematics, a
If a tiling has no periods, it is said to be
In 1980, N. G. de Bruijn showed that Penrose tilings can be seen as the projection of a two-dimensional plane in five-dimensional space. In the figure below, you can click and drag to translate the viewport along the plane.
Additional resources:
de Bruijn's Algebraic theory of Penrose's non-periodic tilings of the plane
Penrose tiling (wikipedia)
Aperiodic tiling (wikipedia)
Roger Penrose (wikipedia)
Nicolaas Govert de Bruijn (wikipedia)
Martin Gardner's summary of Penrose tiles
Jason B Healy's Automatic Generation of Penrose Empires
Jeff Preshing's Penrose tiling implementation in Python
Penrose tiling implementations in Go-lang and Java
Venkkatesh Sekar programed a Penrose tiling applet from this repository
Grant Glouser programed a de Bruijn projection applet from this repository
Large image of tilings in different local isomorphism classes obtained by the cut and project method