  A new type of self-similar potential is used to study a multibarrier system
made of graphene. Such potential is based on the traditional middle third
Cantor set rule combined with a scaling of the barriers height. The resulting
transmission coefficient for charge carriers, obtained using the quantum
relativistic Dirac equation, shows a surprising self-similar structure. The
same potential does not lead to a self-similar transmission when applied to the
typical semiconductors described by the non-relativistic Schr\"odinger
equation. The proposed system is one of the few examples in which a
self-similar structure produces the same pattern in a physical property. The
resulting scaling properties are investigated as a function of three
parameters: the height of the main barrier, the total length of the system and
the generation number of the potential. These scaling properties are first
identified individually and then combined to find general analytic scaling
expressions.
