A Model of Islamic Rectilinear Interlaced Lattices

Fig.4 Mevlüt, a Mosque Door.

Fig.4. "Mevlüt", a Mosque Door.


The vast majority of RIGE forms present regular symmetries which focus the attention in their centres and axes (see some aesthetic conclusions of this in Musical Relationship, below). We consider two main kinds of these symmetries, central and axial. The first constitute 'natural' centres, as the order of this symmetry becomes greater; the maximum value of it is N, the lattice order. Secondary centres are those with divisor symmetry, that is, with symmetry order a submultiple of N: in 10-lattice, the main centre has 10 order symmetry, and 5-order the secondary ones (Fig.10-11, Puertas). There is only one case left, the 2-order central symmetry, not to be confused with the axial one. See this last case in the form Mevlüt, Fig. 4, above.

The axial symmetries are easier to find, since they impose fewer conditions of similarity between parts of the form. In fact, there is a tendency to consider this symmetry as a must for every RIGE, at least in the EE, as we have seen. The symmetry facilitates not only the comprehension of a form, but also its definition and construction, as we shall now show. Only a single part needs to be defined, since the other can be found by symmetrical repetition. This leads us to search for the minimal part of a RIGE that can generate the rest in this way. If it can be found, we will call it the Generative Element (GE) of this particular RIGE.

There is also a third type of symmetry in riges, a faked spatial (3-dimensional) one: when interlace is adopted (see the page that follows) the axial symmetry presents an alternative up and down (above/below) frame crossing which can be seen and understood as a spatial axial symmetry. The ideal procedure would then be to gyrate the GE round its symmetry axes, not in the plane, but rather in the space, as a door which emerges from the plane, and return to it after a 180 degree turn. This spatial procedure agrees with the psychological impression which interlace suggests: the RIGE escapes from the plane to which it belongs and adquires depth, relief, spatial existence.

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