Visualizations of the internal workings of a popular pseudo-random number generator. Made to be displayed at the Seattle Universal Math Museum "For the Love of Math!" exhibition.
Parts of the inverse matrix that transforms 24 bit output of MT19937 into its internal state, super-imposed with different colours. 24 bits is chosen because it gives the most interesting patterns.
Parts of the matrix that transforms MT19937 internal state to its 32-bit output, super-imposed with different colours. The black-ness demonstrates how bad MT19937 is at diffusion, and the fact that it can be represented as a matrix shows that its also completely linear.
There's order in random number generators because computers. MT19937 in particular has maybe too much order (it isn't cryptographically-secure).
2022 note: I submitted this to be displayed in the Seattle Universal Math Museum, “For the Love of Math!” exhibition curated by Timea Tihanyi. Thank you for the opportunity to exhibit my work!