I've played around with shaders in the past to build particle simulations with millions of points, and it's always really tickled my mind. You basically write functions that operate against a big 2d grid of colors. But because colors are represented by a 4x1 vector [r,g,b,a], you can repurpose this pattern to do general purpose computation (e.g. you can represent a point in a 3D coordinate space as a [r,g,b] color).

You can see this in the codepen in this post. It's literally creating "materials" and "render targets" that are actually just intermediate computation steps in the fluid simulation.

  class Fluid {
      constructor(context) {
          this.context = context;
          this.speed = 4;
          this.forceInitMaterial = this.createShaderMaterial(forceInitFrag);
          this.divergenceMaterial = this.createShaderMaterial(divergenceFrag);
          ...
          this.divergence = this.createRenderTarget();
          this.advection = this.createRenderTarget();
          ...