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.
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.