Do programming/computing systems have to be self-referential/meta-circular to scale?

Are fractals self referential?

By self-referential I mean a system that can inspect itself. As inspection is an active process, not sure any analogies to static descriptions make sense (a fractal can't introspect itself since it doesn't do anything)

Is C++ self-referential? Does it scale? I'm not exactly sure what you're asking, but I think the answer to most of the questions that match your text is "no". All of your terms, by reasonable/useful definitions, offer enough room for exceptions to any rule like "systems must be support self-reference to scale".

What does "scale" mean in this question?

I suppose the referential argument is that scale requires recoverability requires some degree of process management. Somehow we seem to muddle along with pretty course tools.

I suspect that programs that run for a long time and/or use memory resources near the limit of the available need reflection to work reliably. For example, observe its own memory use to use scarce resources efficiently. Or check the status of its own processes to restart after failures. If "scale" is just a question of running a single process on ever bigger datasets, or different input parameters, then the answer is no. Most HPC software is not reflective.

Sorry I should have defined what I mean by scale (ie not scaling to larger data). It seems like "amount of code/unit of functionality" seems to be quite low relative to the modern capabilities of computers.

Yes they do