A British bacteriologist working in Agra, Hankin watched Indian craftsmen and studied the monuments, and proposed that many Islamic star patterns were drawn by a single procedure: cover the surface with a network of polygons in contact, then draw lines crossing the midpoint of every edge at a fixed angle.
Hankin’s method is simple enough to be done with a ruler and compasses and powerful enough to generate a large share of the historical patterns. Take a tiling of polygons: octagons and squares, say. From the midpoint of each edge draw two lines into the polygon, each making the same angle with the edge (the contact angle), and continue each line until it meets another. Erase the tiling, and the lines that remain are the pattern. Changing the tiling changes the symmetry; changing the angle changes the character, from blunt crosses to sharp stars.
He published the idea in 1905 and developed it in a memoir for the Archaeological Survey of India in 1925, illustrated from buildings in Agra, Fatehpur Sikri and elsewhere. Later scholarship has shown that historical craftsmen used several methods, and that the Topkapı Scroll records others, but the polygons-in-contact procedure remains the clearest way to see how a pattern and its grid belong together. It is the procedure used by this book’s girih generator.
The book, part by part
I The polygons-in-contact method
Tilings of polygons; lines at a constant angle through the midpoints of their edges; the effect of changing tiling and angle.
Rules: Patterns from polygons in contact · The contact angle sets the character