Creating and probing the spatial and/or magnetic confinement of particles is ubiquitous in physics, from thermonuclear fusion to ultracold atoms. Spatial confinement leads to the well known "particle-in-a-box"-like states that describe electron behavior in quantum corrals and semiconductor quantum dots (QD). Magnetic confinement leads to charged particles performing tight cyclotron motion and is responsible for the integer quantum Hall effect, a striking example of a macroscopic topological quantum state of matter. But what happens when we finely tune from spatial to magnetic confinement, and what role do electron interactions play?

In this talk I will present scanning tunneling microscopy/spectroscopy (STM/S) measurements that explore the interplay between the spatial and magnetic confinement of massless Dirac fermions in a custom 'rewritable' graphene quantum dot. I will first describe how graphene electrons can form quasi-bound QD states due to relativistic Klein scattering. As a magnetic field is applied, I will show measurements that directly visualize the intricate evolution of the atomic shell-like QD states into highly degenerate Landau levels. Here, increased electron interactions lead to the subsequent formation of a 'wedding cake' structure of compressible-incompressible electron strips, showing that custom-made QDs are a new platform for corralling quantum Hall liquids.