Islamic Geometric Patterns
A computational construction of star patterns from the Islamic tradition: translational units, motifs, rosettes, and the rosette dual, implemented in Python with NumPy.
A handout reproducing the construction of Islamic star patterns set out in Islamic Geometric Patterns (Bonner). The PDF works through tilings and patches, periodic tilings and translational units, the regular and Archimedean tilings, axis-based construction, motif drawing with contact angles, two-point patterns, rosettes, and the rosette-dual transformation, then implements the entire pipeline in Python (NumPy + Matplotlib) for two ten-fold systems and an eight-fold system.
The result is a working translational unit you can stamp across the plane to produce the kind of decagonal and octagonal star tilings that decorate the walls of the Alhambra and the Imam mosque in Isfahan.