  Fibonacci anyon, an exotic quasi-particle excitation, plays a pivotal role in
realization of a quantum computer. Starting from a $SU(2)_4$ topological phase,
in this paper we demonstrate a way to construct a Fibonacci topological phase
which has only one non-trivial excitation described by the Fibonacci anyon. We
show that arrays of anyonic chains created by excitations of the $SU(2)_4$
phase leads to the Fibonacci phase. We further demonstrate that our theoretical
propositions can be extended to other topological phases.
