Why is FRACTRAN turing complete?

I've tried to google for explanation but most links only say things like "FRACTRAN is turing complete. As an example, let's look at multiplication." I remember seeing an xkcd forum post say that FRACTRAN helped the poster understand Turing Completeness. I am looking for an intuitive explanation as to why this esolang is Turing complete, as it's not very obvious looking at the language mechanics.

Mar 3, 2025 - 02:06
 0
Why is FRACTRAN turing complete?

I've tried to google for explanation but most links only say things like "FRACTRAN is turing complete. As an example, let's look at multiplication."

I remember seeing an xkcd forum post say that FRACTRAN helped the poster understand Turing Completeness. I am looking for an intuitive explanation as to why this esolang is Turing complete, as it's not very obvious looking at the language mechanics.