  We report on critical phenomena in the gravitational collapse of the
electromagnetic field in axisymmetry using cylindrical coordinates. We perform
detailed numerical simulations of four families of dipole and quadrupole
initial data fine-tuned to the onset of black hole formation. It has been
previously observed that families which bifurcate into two on-axis critical
solutions exhibit distinct growth characteristics from those which collapse at
the centre of symmetry. In contrast, our results indicate similar growth
characteristics and periodicity across all families of initial data, including
those examined in earlier works. More precisely, for all families investigated,
we observe power-law scaling for the maximum of the electromagnetic field
invariant ($\mathrm{max}|F_{\mu\nu}F^{\mu\nu}| \sim |p-p^{\star}|^{-2\gamma}$)
with $\gamma \approx 0.149(9)$. We find evidence of approximate discrete
self-similarity in near-critical time evolutions with a log-scale echoing
period of $\Delta \approx 0.62(8)$ across all families of initial data. Our
methodology, while reproducing the results of prior studies up to a point,
provides new insights into the later stages of critical searches and we propose
a mechanism to explain the observed differences between our work and the
previous calculations.
