Pixel shaders are covered in parts 8 and 9 of the blog series I linked to.

What aspect of shadertoy disagrees with what I wrote?

All of it that shows rendering beyond what GPUs "only know".

I said "rasterisation", not "rendering".

Rasterisation is one specific step of the rendering process (+). GPUs rasterise triangles. If you're writing a software renderer you can include algorithms to directly rasterise other shapes such as circles, which is what started this whole thread. But if you're rendering with a GPU and relying on its built in rasterisation then triangles is where you start, even if circles is what you ultimately want.

(+) It's also possible to render without the rasterisation step at all - for example, a pure ray tracing based renderer doesn't have an explicit rasterisation step as it's normally thought of in graphics terms.

Ah, so you meant the only rasterisation they know is triangles. OK, got you.