Sufism in particular is closely linked to the practice of geometry, above all in the form of symmetries, as a way of giving physical expression to mystical thought. Source: Saudi Aramco World : The Tiles of Infinity

Robert Irwin writes in his study of Islamic art, such patterns may have been viewed “as exteriorized representations of abstract, even mystical, thought”—aiming to inspire contemplation or to make a statement about the imponderable harmonies of a divinely ordered universe. Source: Saudi Aramco World : The Tiles of Infinity

Source: AnimSun2k – Penrose tiling – Wikipedia, the free encyclopedia

Source: Evolution of Islamic geometric patterns

Source: Islamic Art and Geometric Design: Activities for Learning – Islamic_Art_and_Geometric_Design.pdf

Patterns made with nothing more than a compass and a straight edge Source: Ancient Islamic architects created perfect quasicrystals – physicsworld.com