  We develop a new method to locally cluster curves and discover functional
motifs, i.e.~typical ``shapes'' that may recur several times along and across
the curves capturing important local characteristics. In order to identify
these shared curve portions, our method leverages ideas from functional data
analysis (joint clustering and alignment of curves), bioinformatics (local
alignment through the extension of high similarity seeds) and fuzzy clustering
(curves belonging to more than one cluster, if they contain more than one
typical ``shape''). It can employ various dissimilarity measures and
incorporate derivatives in the discovery process, thus exploiting complex
facets of shapes. We demonstrate the performance of our method with an
extensive simulation study, and show how it generalizes other clustering
methods for functional data. Finally, we provide real data applications to
Berkeley growth data, Italian Covid-19 death curves and ``Omics'' data related
to mutagenesis.
