  We consider a model of interacting Bose-Einstein condensates on small
Sierpinski gaskets. We study eigenstates which are characterised by cyclic
supercurrents per each triangular plaquette ("loop" states). For noninteracting
systems we find at least three classes of loop eigenmodes: standard; chaotic
and periodic. Standard modes are those inherited from the basic three-site ring
of condensates with phase differences locked to $2\pi/3$. Standard modes become
unstable in the interacting system but only when interaction exceeds a certain
critical value $u_c$. Chaotic modes are characterised by very different
circular currents per plaquette, so that the usual symmetry of loop currents is
broken. Circular supercurrents associated with chaotic modes become chaotic for
any finite interaction, signalling the loss of coherence between the
condensates. Periodic modes are described by alternating populations and two
different phase differences. The modes are self-similar and are present in all
generations of Sierpinskii gasket. When interaction is included, circular
current of such a mode becomes periodic in time with the amplitude growing
linearly with interaction. Above a critical interaction the amplitude saturates
signalling a transition to a macroscopic self-trapping state originally known
from a usual Bose Josephson junction. We perform a systematic analysis of this
novel and rich physics.
