Dynamic generation of quasicrystals is breakthrough method for creating throse objects, primarily because it can be realized in a physical processes, unlike the high-dimensional projection methods. Under gracious support by Dr. Jiri Patera at CRM, I have implemented a Matlab program realizing this approach.
Moody, R. V., Patera, J. Dynamical generation of quasicrystals, Letters in Mathematical Physics, Volume 36, Number 3 / March, 1996
The software might not work - I don't use Matlab anymore.
The algorithm takes O(n) to add a new vertex – this can be improved to O(log n) by doing more smart testing for previously created vertices