Note, Julia can already be run on the web:
and since iOS has a web browser, that should mean that demo should also work there. I’m not sure if or how limited it is (its old Julia and could be refreshed to newer), except that the binary is large and thus has some startup cost.
Julia apps are famously large since its runtime that you bundle with is. But it can be made smaller.
You had in mind how to run Julia, or Julia apps? It doesn’t matter really, since you can do either, e.g. this demo:
Apps can be much smaller, because of e.g.:
See WebAssemblyCompiler.jl that has fewer restrictions than other static compilers, since it e.g. has GC support.
See also a Masters thesis on this from this year:
Use cases for WebAssembly can be divided into two categories: web and non-web. […] This would also expand support to platforms like iOS, Android, and ChromeOS that do not have native Julia support.
If you think you need an internet connection, then usually for the web, you can also surf from local files, but I’m not sure how that works or if on iOS and Android. But since this isn’t just for the web, can be run somehow locally on mobile.