Supplement to "Asymptotic Estimates of Large Gaps Between Directions in Certain Planar Quasicrystals",
by Gustav Hammarhjelm, Andreas Strömbergsson and Shucheng Yu
The programs below should be downloaded into a directory which should be equipped with two subdirectories called "data" and "sectors".
Maple program for "exact" computation of the constant a_P in certain cases:
explicit_aP.mpl
Python program for collecting gap statistics or data for plot of patch for the Ammann-Beenker tiling:
gapstat_AB.py
Python program for collecting gap statistics for the Ammann-Beenker tiling, treating 4 radii
simultaneously, and using a splitting of the disc into sectors so as to reduce the memory requirement:
gapstat_AB_sectors.py
(The sector data must then be collected using the program gapstat_collect.py below.)
Python program for collecting gap statistics or data for plot of patch for the Gähler Shield tiling:
gapstat_GH.py
Python program for collecting gap statistics for the Gähler Shield tiling, treating 4 radii
simultaneously, and using a splitting of the disc into sectors so as to reduce the memory requirement:
gapstat_GH_sectors.py
(The sector data must then be collected using the program gapstat_collect.py below.)
Python program for collecting gap statistics or data for plot of patch for the Tübingen Triangle tiling:
gapstat_TTT.py
Python program for collecting gap statistics for the Tübingen Triangle tiling, treating 4 radii
simultaneously, and using a splitting of the disc into sectors so as to reduce the memory requirement:
gapstat_TTT_sectors.py
(The sector data must then be collected using the program gapstat_collect.py below.)
Python program for collecting the data from sector files into a single data file:
collect_sectors.py
Python program for extracting information about the asymptotics, from a gap statistics data file generated by
gapstat_AB.py or gapstat_GH.py or gapstat_TTT.py or collect_sectors.py:
collect_asympt_data.py
Maple program for drawing a patch of a tiling, using data generated by
gapstat_AB.py or gapstat_GH.py or gapstat_TTT.py:
patch_plot.mw
Maple program for drawing histogram, using data generated by
gapstat_AB.py or gapstat_GH.py or gapstat_TTT.py or collect_sectors.py:
draw_histogram.mw