I am trying to wrap my mind around the concept of exotic smoothness in (and only in) $\mathbb{R}^4$.

I have some mathematical literature, but can anyone point to a semi-intuitive, semi-visual example? How should I begin to imagine a differentiable manifold that is homeomorphic but not diffeomorphic to Euclidean space $\mathbb{R}^4$?

Of course I realize that if a mathematical structure exists only in four dimensions, I will not be able to see it intuitively/visually, but what lower dimensional analogy comes closer?