I have heard the structure of the atom called "ordered," of course they use the word "order" to actually mean "organized." But in both cases they're dead wrong.
First, everything in nature appears predictable, we created laws based on those predictions. However, nothing in nature is organized.
Atoms are not an exception, the more we study these building blocks of everything, the more we see just how chaotic they are. In fact, on the quantum level, atoms are so chaotic that the math for predictions becomes too cumbersome to do on paper.
The nucleus is often thought of as stationary, still, and in place. But this is certainly not the case, every proton and neutron are constantly shifting position and vibrating.
Often these neutrons and protons vanish for short periods of time, or are replaced by other neutrons and protons seemingly at random. Ironically, this is the reason we were ever able to split the atoms.
The electrons are even stranger, to the point of defying all logic. Electrons don't fly in a simple orbit around the nucleus, they actually move around quickly and randomly. If you looked at an atom it would look like a cloud with a very dense core, nothing like the model used to describe how they behave.
Electrons also don't stay on their "levels," as we once thought. Often they jump levels, seemingly at random.
The atom is the perfect reflection of the universe, chaotic, strange, unpredictable in many ways.