The two dimensional plane can be filled with rhombuses, so as to generate non-periodic tilings with 4, 6, 8, 10 and 12-fold symmetries. Some representative tilings constructed using the rule of inflation are shown. The numerically computed diffraction patterns for the corresponding tilings are also shown to facilitate a comparison with possible X-ray or electron diffraction pictures.

The diffraction patterns from Fibonacci quasilattices have been calculated. Finite-size effects are evaluated for weak and strong peaks. For a smaller number of scatterers (<100) there are fluctuations in the intensities of weak and strong peaks. The fluctuations in weak peaks are greater than that in strong peaks. The fluctuations in intensities of weak and strong peaks near the origin are larger than in the corresponding cases of weak and strong peaks far away from the origin. Small shifts in peak-positions are unexpectedly found, the shifts being proportional toN^−3/2 for a large number of scatterers. The diffraction pattern of a one-dimensional crystal and random structure is compared with that of the Fibonacci quasilattice. The strong peaks observed in the diffraction pattern of 1-d crystal show negligible peak-shifts, they being comparable with computational errors even when the number of scatterers is as small as 5. The implications for analysing the experiments are briefly indicated.

A method for generating aperiodic tilings with five fold symmetry is discussed here. Basic patterns formed within decagons can be used to fill two dimensional space, by matching such suitable patterns. It appears to be possible to generate perfect tilings without retracing already established coordinates imposing conditions at the initial stages of generating them. Various possible ways to generate tilings, when perfectness is not required, are discussed. The calculated diffraction patterns for some representative finite size tilings are shown. There are subtle differences in the intensities of peaks in the diffraction patterns corresponding to different finite size tilings constructed using intersecting decagons. These effects persist for a larger number of scatterers in weak peaks than in strong peaks. They are unaffected by an introduction of systematic disorder. These effects could be termed as the finite size boundary effects. There are also small shifts in the peak positions owing to the finite size effects. The possibility of formation of large approximate square cells in large tilings is shown.

Spiral space filling geometrical constructions using rhombuses in two dimensions are considered as plausible mechanisms for quasicrystal growth. These models will show staircase-like features which may be observed experimentally.