6-day AYP retreat | April 13-18, 2027 | Sweden
The classical Sri Yantra consists of four upward and five downward-facing triangles. It is thousands of years old, has spiritual meaning and applications, and is also intriguing for its mathematical properties. You can explore the 4-dimensional shape space of the sri yantra here: https://sriyantra.tystnadsklangen.se/
This is a generalisation that might increase the pleasantness when gazing at the Sri Yantra. Instead of straight lines the triangles are built from circle arcs. There are traditional curved-line Sri Yantras like this, particularly this one in the Chintamani Shiva temple. Notice that all tips of the yantra touch the circle thanks to the curvature of the triangle sides. Also the two innermost downward triangles are more laminar. The convex curvature of the arcs produces a petal-like and lens-like effect. To play with its shape select "Arcs - no rings held" in https://sriyantra.tystnadsklangen.se/.
The arcs defining the Sri Yantra can be naturally extended outside of the yantra’s circumference. These extended arcs will intersect outside the yantra to form petals. So, the two yantras you see here grow their own petals without the need to add them by hand. To make the petals look somewhat regular, both yantras have the tips of one row of the grown petals constrained to the touch a larger circle. To play with their shape select "Arcs - ring 1/2 built" in https://sriyantra.tystnadsklangen.se/.
Instead of the four up and five down facing triangles, these yantras use five up and six down facing triangles. In the coloring style used here this gives rise to a new ring of small outward-facing triangles around the original yantra. There are 64 of such extended yantras, but I found only two of them pleasant looking. Their construction also uses arcs instead of straight lines, since otherwise this extension from nine to eleven triangles is not possible.
To play with their shape select "Arcs - extended 2/3" in https://sriyantra.tystnadsklangen.se/.
The software is freely available at https://github.com/michaelkopp/sriyantra, where you also find two papers describing some mathematical properties of these arc yantras.