|LUDWIG DANZER AND GERRIT VAN OPHUYSEN, Universität Dortmund, Facherbereich Mathematik, Lehrstuhl II, 44221 Dortmund, Germany|
|A species of planar triangular tilings with inflation factor|
Consider the set of two right triangles in with sides having squared lengths 1, , and , , respectively. These can be glued together (in only one way) to form a third right triangle with sides of squared length , , . We then consider the inflation rule infl(A):=X, . Interpreting as the inflation factor becomes which is a complex Pisot-number. The species of all global -tilings created by has a unique deflation (`` infl-1'') and hence is aperiodic. The set of all vertices can be shown to be a ``model set'' (Robert Moody), so the Fourier-transformation of the autocorrelation function is ``pure point'' with the Bragg-peaks located on the -module .
, where B and C are
congruent to A, while Y and Z are congruent to X, but all
differently coloured, and