My understanding is that what we consider as particles can be described as waves of smaller particles.
For example, atoms are fluctuating electrons, neutrons and protons, all of which are fluctuating subatomic particles and so on. And what we describe as particles are essentially the maxima of these fluctuations.
Not really. Electrons are as far as we know not composed of smaller particles, and there's good reason to think they are elementary. Basically because smashing them with things reveals no smaller structure. Whereas when you smash things into a proton it is very clear that there are smaller localized objects inside it (there is a great blog post with pictures of what a proton looks like at different energies that I can't seem to find now...)
For example, atoms are fluctuating electrons, neutrons and protons, all of which are fluctuating subatomic particles and so on. And what we describe as particles are essentially the maxima of these fluctuations.