 Ramanujan's Butterfly Digital Print 2019

The cover art is inspired by the article in this issue by Dresden et al. Let $r_1$, $r_2$, and $r_3$ be the roots of the Ramanujan simple cubic $f_B(x) = x^3 - \left(\frac{3+B}{2}\right) x^2 - \left(\frac{3-B}{2}\right) x + 1$, then the function $n(x) = \frac{1}{1-x}$ permutes the roots: $n(r_1) = r_2$, $n(r_2) = r_3$, and $n(r_3) = r_1$. For a particular $B$ value, consider the triangle with vertices that are the ordered pairs of roots $\{(r_1,r_2), (r_2, r_3), \text{and} (r_3, r_1)\}$; its vertices lie along the graph of $n(x)$. The artwork is a visualization of these triangles for $B$ values in the set $\{0, \pm 4, \pm 8, \pm 12, \pm 16, \pm 20, \text{and} \pm24\}$.

### Background and Inspiration

A version of this work was originally done for use as cover art for the December 2019 issue of Mathematics Magazine. This is one of 25 original artworks I created for the journal Mathematics Magazine during 2015–2019.

### Publication History

• 2020 Joint Mathematical Meetings Exhibition of Mathematical Art, p. 77, Edited by Robert Fathauer and Nathan Selikoff, ISBN: 978-1-938664-33-5, Tessellations Publishing, 2020.
• Mathematics Magazine, Cover Art, Vol. 92, No. 5, December 2019.

• Dresden