One of the puzzling aspects of high temperature superconductors is the prevalence of magnetism in the normal state and the persistence of superconductivity in very high magnetic fields. Generally, superconductivity and magnetism are not compatible. But recent neutron scattering results indicate that antiferromagnetism can appear deep in the superconducting state in an applied magnetic field. Magnetic fields penetrate a superconductor in the form of quantized flux lines each one representing a vortex of supercurrents. Superconductivity is suppressed in the core of the vortex and it has been suggested that antiferromagnetism might develop there. To address this question it is important to perform electronic structural studies with spatial resolution. Here we report on implementation of a high field NMR imaging experiment that allows spatial resolution of the electronic behavior both inside and outside the vortex cores. Outside we find strong antiferromagnetic fluctuations, and localized inside there are electronic states rather different from those found in conventional superconductors.