English: This picture shows the modulus ${\displaystyle |\phi (q)|}$ on the complex plane, inside the unit circle ${\displaystyle |q|\leq 1}$, where

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

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

general resemblance to colorings of the interior of the Mandelbrot set.