  Topological insulators and topological superconductors are distinguished by
their bulk phase transitions and gapless states at a sharp boundary with the
vacuum. Quasicrystals have recently been found to be topologically nontrivial.
In quasicrystals, the bulk phase transitions occur in the same manner as
standard topological materials, but their boundary phenomena are more subtle.
In this Letter we directly observe bulk phase transitions, using photonic
quasicrystals, by constructing a smooth boundary between topologically distinct
one-dimensional quasicrystals. Moreover, we use the same method to
experimentally confirm the topological equivalence between the Harper and
Fibonacci quasicrystals.
