  Although the search for azimutal patterns in cosmological surveys is useful
to characterise some effects depending exclusively on an angular distance
within the standard model, they are considered as a key distinguishing feature
of some exotic scenarios, such as bubble collisions or conformal cyclic
cosmology (CCC). In particular, the CCC is a non-stardard framework which
predicts circular patterns on the CMB intensity fluctuations. Motivated by some
previous works which explore the presence of radial gradients, we apply a
methodology based on the radial derivatives to the latest release of
\textit{Planck} data. The new approach allows exhaustive studies to be
performed at all sky directions at a HEALPix resolution of $N_{\mathrm{side}} =
1024$. Specifically, two different analyses are performed focusing on weight
functions in both small (up to a $5$-degree radius) and large scales. We
present a comparison between our results and those shown by An et al. (2017),
and An et al. (2018). In addition, a possible polarization counterpart of these
circular patterns is also analysed for the most promising case. Taking into
account the limitations to characterize the significance of the results,
including the possibility of suffering a look-elsewhere effect, no strong
evidence of the kind of circular patterns expected from CCC is found in the
\textit{Planck} data for either the small or the large scales.
