From the megalithic temples of Malta to indulgent study of symmetric proportions by the likes of Vitruvius and Da Vinci to the current study of hemispheres of the brain by neuroscientists, our fascination and emotional pleasure from symmetric structures and ordered geometric shapes is undeniable.

This fascination is reflected in architectures around the world spanning millennia. One such example is Jali (from Jala in Sanskrit, Jalaka in Hindi) described in ancient Indian architecture texts and popularised through the Mugal architecture. While originally carved in stone with much diligence, drawing them on paper with the ruler and protractors is a much satisfying endeavor, maybe similar to the therapeutic use of Mandala art today (I haven’t tried one myself yet!), but maybe more exciting if you love geometry.

After spending an hour drawing the neatly stacked nonagon on paper, I decided to program it. After all, it is an iterative process of moving from one point in space to another with a fixed set of rules.

Turtle graphics on Python seemed the right tool. (Fun Fact: Turtle was part of the original Logo programming language developed by Wally Feurzeig, Seymour Papert, and Cynthia Solomon in 1967.)

What I needed to replicate the pattern from paper was a combination of 9-sided regular polygon and 6-sided regular polygon. Some iterations until the Jala was perfected:

4-sided regular polygon

Stacked 9-sided regular polygon

And Finally:

Mosaic, of 9-sided regular polygon and 6-sided regular polygon

Wandering further into the edges of symmetry, it is fascinating how pentagonal (5-sided) and decagonal (10-sided) Girih-tile pattern (an aperiodic tilling similar to famous Penrose tiling ) is found in Darb-i Imam shrine, Iran, built-in 1453 C.E. Seems the architects found it in aesthetics before mathematicians formulated it!