Girih tiles of Islam (from X to XV centuries.)
Remember in the Renaissance in the fourteenth and fifteenth centuries Borromini, Bernini, Brunelleschi, crowned with domes clerestories, spherical triangles which are then painted with figurative motifs of human, saints and orchards.
Islam forbade the human figure, animal or any other figurative subject, so that believers would not fall in idolatry. Hence it is difficult to find religious figurative representations within the Muslim culture. This led, in turn, to a large development of geometric and plant motifs with increasing degree of abstraction, defining ornamentation in Islamic art. All this representation of geometric purity was about as great as unknown were the origin of its bases..
The curved surfaces of the intrados of the arch or the interior of the scallops or vaults, should be systemized geometrically modulated in response to the curved shape to be coated as a periodic pattern.
This materialized with no equal pieces responding to glazed ceramic tiles called nonrecurring Girih (of Islam) designs.
The morphological quasi periodicity is an intrinsic property of the (Girih tiles) for non figurative covering Islam as vaulted spaces and endings of each of its architectural corners where these ceramic modules, synchronous and non-recurring adapted to the infinite and rich curvatures of dematerialization of walls, domes and arches.
(The aforementioned morphologies maintains a correlate with patterns of the quasi atomic diffraction of crystals (Al Cu Fe). )