Project 24: JFourier3

Steffen Weber, March 1999

[Get FTL-SE]

Fourier transform (FT) of quasiperiodic point sets. The vertices of a quasiperiodic rhombic tiling are used as point scatterers for the FT. Since each tile has four "atoms" at its corners many of them actually overlap since several tiles share their vertex positions. Before calculating the FT those overlapped "atoms" are identified so that only one per vertex is used in the calculation. Several parameters, such as local rotational symmetry (5-fold to 20-fold), magnification factor and shift parameter can be specified. Random colouring is used for the tiling. For more details on tilings see also Project 4. Just in case anyone is wondering: the 6-fold tiling is of course periodic and not quasiperiodic.

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scale tiling Zooms tiling, results in a different number of points. This does not affect the scaling of the Fourier space.
draw tiling Button for drawing, redrawing the tiling of chosen symmetry
intensity ~F / FF Use intensity proportional to amplitude or square of amplitude
loop order 1,2,3 Loop order for generating the tiling. 2 should always be fine. The larger the value the more tiles are generated and the longer it takes.
shift 1/n, ..., ... Some shifting parameters for the dual grids, that actually produce the tiling. The result is a different arrangement of the tiles.
100 x 100 FT,.... Calculate discrete Fourier transforms at 100x100, 200x200 or 300x300 pixel resolution. A 100x100 image might not show the expected symmetry. Then you should select 200 or 300. However, the calculation time will be 4- or 9- times longer then.
use color code Generate a color- or gray-scale image.
intensity * factor Additional intensity factor to make weak peaks visible. A factor of 10 gives good results.
scale FT * factor Scaling factor (zooming) for the Fourier space. Results in different number of peaks being visible in the image. A value of 2 gives good results.
Fourier transform Calculate / update Fourier transform