I’ve seen this discussion pop up from time to time in social media and on podcasts, and it’s an interesting thought experiment to consider whether or not we’re living in a simulation; but I fervently believe that we do not.
Nature is fractal yes, but we tend not to be. If we assume or postulate that the universe is a simulation, then that seems akin to conceding that nature is designed by an invisible hand or higher order; much like theology does insofar as they believe in a “Prime Mover” or generic sentient being.
There is also the meta-question of free will, or why humans, highly-evolved primates with a frontal lobe, would seek to explore our way out of a simulation rather than try to verify if such a simulation exists in the first place. This comes down to scientific modelling vs. scientific experiment, and I think the latter has been sorely abandoned by those who suggest that the existence of a simulation might be real.
The line of thinking I’ve come across in support of simulation theory boils down to this: we describe the world and it’s boundaries only with the tools that we have, and in the dimensions that we can inhabit. We have invented the tools themselves with which to explore the universe and reality, from the cosmic level to the quantum level, and beyond each of these limits exists both complexity and unknowns that suggest a thinning of the veil.
I think such an argument for simulation theory again alludes to a larger superintelligence (if such a conjecture is extrapolated), and belies something almost eschatonic in nature (having a finite, true end). In my humble opinion, such a fated, procedural, and linear system is at odds with the concept of free will.
To believe reality is a simulation would mean conceding that all externalities and unknowns are "glitches in the Matrix" or otherwise imprints from outside of the simulation. Emergent properties? Glitch. Creativity? Glitch.
We are not machines, and this is not a reality that can joined at the hip to a singular dimension in order to prove that a simulation is in progress (the dimension being time, in the linear sense).
I think while not improbable, it is more importantly indefensible inasmuch as it is an affront to our intelligence to suggest that our historical record, our morals, our very choices themselves are predetermined or parameterized in any given way.
It might be fun for science fiction (I’m reminded of Marvel Comic’s The Beyonders), but in my opinion it’s bordering on misanthropy to think that a simulation is in charge of all of us, let alone that the creators of such a simulation have a hand in shaping the Universe, and life itself.