A Model of Islamic Rectilinear Interlaced Lattices

Fig.1 An 8 Lattice with some EE figures

Fig.1. An 8-Lattice with some EE Figures.


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

Fig.2. A 10-Lattice with some EE Figures.
meanwhile in Fig.2. the sequences are (let Phi ' be 1 - Phi =.618..):

 ... -Phi-1-Phi'-1-Phi-1-
 Phi'-... and ...- Phi'-1-1- 
Phi'-1-Phi-1- Phi'-...
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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