In this blog post I want to talk about the research and development results for a library that I started working on more than a year ago - TensorFrost. Under the hood it’s a static optimizing tensor compiler with a focus on being able to do more “shader-like” things while still keeping the ability to do high level linear algebra for ML in Numpy-like syntax with automatic differentiation support. (Click on the example GIF’s for more details!)

When thinking about renders of things like warp drives and black holes we usually just expect to see a simple approximation or an artist rendition, assuming the math required to pull off something accurate would require someone with at least a PhD in Mathematical Physics. Which I won’t tell that its completely untrue, but in this blog post I’ll try to explain a way to do quite accurate visualizations within a 100 or so lines of code, for basically any kind of space-time for which you can write its metric as code. Although, the detailed mathematical derivation of this approach might be somewhat math heavy.

In this blog post I’ll explain this advection algorithm and how to use it to make advanced fluid simulations like the ones I made, including Paint streams and Everflow. Before starting, I should give a big thanks to my friend Wyatt for giving useful suggestions on building this algorithm.