  Fermi-LAT observations provide continuous and regularly-sampled measurements
of gamma-ray photon flux for hundreds of blazars. Many of these light curves,
spanning almost 15 years, have been thoroughly examined for periodicity in
multiple studies. However, the possibility that blazars may exhibit irregularly
repeating flaring patterns in their gamma-ray light curves has not been
systematically explored. In this study, we aim to find repeating episodes of
flaring activity in the 100 brightest blazars using Fermi-LAT light curves with
various integration times. We use a Bayesian Blocks representation to convert
the time series into strings of symbols and search for repeating sub-strings
using a fuzzy search algorithm. As a result, we identify 27 repeated episodes
in the gamma-ray light curves of 10 blazars. We find that the patterns are most
likely produced in structured jets composed of a fast spine and a slower
sheath. When individual emission features propagate in the spine, they scatter
seed photons produced in the non-uniform sheath through the inverse Compton
mechanism, resulting in a set of gamma-ray flares with a similar profile every
such passage. Additionally, we explore the theoretically-predicted possibility
that the spine-sheath structure facilitates the production of high-energy
neutrinos in blazar jets. Using the catalogue of track-like events detected by
the IceCube neutrino telescope, we find evidence supporting this hypothesis at
a $2.8\sigma$ significance level.
