  In strongly correlated systems the strength of Coulomb interactions between
electrons, relative to their kinetic energy, plays a central role in
determining their emergent quantum mechanical phases. We perform resonant x-ray
scattering on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, a prototypical cuprate
superconductor, to probe electronic correlations within the CuO$_2$ plane. We
discover a dynamic quasi-circular pattern in the $x$-$y$ scattering plane with
a radius that matches the wave vector magnitude of the well-known static charge
order. Along with doping- and temperature-dependent measurements, our
experiments reveal a picture of charge order competing with superconductivity
where short-range domains along $x$ and $y$ can dynamically rotate into any
other in-plane direction. This quasi-circular spectrum, a hallmark of
Brazovskii-type fluctuations, has immediate consequences to our understanding
of rotational and translational symmetry breaking in the cuprates. We discuss
how the combination of short- and long-range Coulomb interactions results in an
effective non-monotonic potential that may determine the quasi-circular
pattern.
