Q-Eulero

${\displaystyle |\phi (q)|}$

${\displaystyle |q|\leq 1}$

${\displaystyle \phi (q)=\prod _{k=1}^{\infty }(1-q^{k})}$

is Euler's q-series for the Partition of an integer. The fractal self-similarity of this function is that of the modular group; note that this function is closely related to a modular form, the modular discriminant. Every modular function will have this general kind of self-similarity.

It is colored with a rainbow of colors, with black representing values near zero, and red values near four. Note the Modular group symmetry, and the