A Model of Islamic Rectilinear
Fig.1. An 8-Lattice with some EE Figures.
PERIODIC and APERIODIC LATTICES
The set of distances that define the lattice with the order N, can be periodic or not. The first option is the most
usual, because periodic repetition of distances allows periodic repetition of forms. But aperiodic lattices are also
possible, as the 5-lattice of Penrose which never repeats a distance pattern. Periodic lattices are suitable for plane
covering, while the aperiodic are better used in single forms (however the former can also cover planes, as the
Penrose's). See in Fig 1 and 2 for respective
examples of both kinds of lattice: in Fig.1, the 8-lattice uses two regular distance sequences, used in an alternate
way according to the angle of the series (let Square Root 2 be called D):
...-1-D-1-D-1-D-1-D-... and ...-1-1-D-1-1-D-1-1-D-..
Fig.2. A 10-Lattice with some EE Figures.
meanwhile in Fig.2. the sequences are (let Phi ' be 1 - Phi =.618..):
Phi'-... and ...- Phi'-1-1-
are no longer periodic. But these are arbitrary examples, other lattices could be used for both orders with
different periodic character.
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