The true pattern (i.e. the many-particle wavefunction) is smooth. The issue is that the pattern depends on the positions of every electron in the atom. The variational principle gives us a measure of the goodness of the wavefunction, but it doesn't give us a way to find consistent sets of positions. We have to rely on numerical methods to find self-consistent solutions for the set of differential equations, but it's ludicrously expensive to try to sample the solution space given the dimensionality of that space.

It's really difficult to solve large systems of coupled differential equations. You run into different issues depending on how you attempt to solve them. For most machine-learning type approaches, those issues manifest themselves via the curse of dimensionality.