  Fracton topological phases host fractionalized topological quasiparticles
with restricted mobility, with promising applications to fault-tolerant quantum
computation. While a variety of exactly solvable fracton models have been
proposed, there is a need for platforms to realize them experimentally. We show
that a rich set of fracton phases emerges in interacting Majorana band models
whose building blocks are within experimental reach. Specifically, our Majorana
constructions overcome a principal obstacle, namely the implementation of the
complicated spin cluster interactions underlying fracton stabilizer codes. The
basic building blocks of the proposed constructions include Coulomb blockaded
Majorana islands and weak inter-island Majorana hybridizations. This setting
produces a wide variety of fracton states and promises numerous opportunities
for probing and controlling fracton phases experimentally. Our approach also
reveals the relation between fracton phases and Majorana fermion codes and
further generates a hierarchy of fracton spin liquids.
