Show HN: Elliptica – Make Art with Elliptic Boundary Value Problems (opens in new tab)

During my PhD in theoretical physics I spent quite a bit of time working on elliptic boundary value problems. I realized they are powerful generators of satisfying spatial patterns from relatively low dimensional input (boundary shapes and conditions). Combined with that I came across line integral convolution (LIC) which can produce incredibly beautiful visualizations of vector fields with lots of microstructure.

I’ve found that combining LIC and elliptic partial differential equations gives a very rich set of primitives for making 2d visual arts. So over the last several months I've had Opus 4.5 grind with me to make a full fledged drawing program. Currently I only support the Poisson equation and the biharmonic equation, although I’m planning to add various other physics models that give rise to interesting patterns (such as Ginzburg-Landau superconductor equations).

Elliptica is still in alpha, but it is under active development, and it should be possible to use.