  Fractals -- objects with non-integer dimensions -- occur in manifold settings
and length scales in nature, ranging from snowflakes and lightning strikes to
natural coastlines. Much effort has been expended to generate fractals for use
in many-body physics. Here, we identify an emergent dynamical fractal in a
disorder-free, stoichiometric three-dimensional magnetic crystal in
thermodynamic equilibrium. The phenomenon is born from constraints on the
dynamics of the magnetic monopole excitations in spin ice, which restrict them
to move on the fractal. This observation explains the anomalous exponent found
in magnetic noise experiments in the spin ice compound Dy$_2$Ti$_2$O$_7$, and
it resolves a long standing puzzle about its rapidly diverging relaxation time.
The capacity of spin ice to exhibit such striking phenomena holds promise of
further surprising discoveries in the cooperative dynamics of even simple
topological many-body systems.
