  We investigate the dynamics and topology of metastructures with
quasiperiodically modulated local resonances. The concept is implemented on a
LEGO beam featuring an array of tunable pillar-cone resonators. The versatility
of the platform allows the experimental mapping of the beam's Hofstadter-like
resonant spectrum, which is the first reported observation for an elastic
medium. The non-trivial spectral gaps are classified by evaluating the
integrated density of states of the bulk bands, which is experimentally
verified through the observation of topological edge states localized at the
boundaries. Results also show that the spatial location of the edge states can
be varied through the selection of the phase of the resonator's modulation law.
The presented results open new pathways for the design of metastructures with
novel functionalities going beyond those encountered in periodic media by
exploiting aperiodic patterning of local resonances and suggest a simple,
viable platform for the observation of a variety of topological phenomena.
