  Universality is a well-established central concept of equilibrium physics.
However, in systems far away from equilibrium a deeper understanding of its
underlying principles is still lacking. Up to now, a few classes have been
identified. Besides the diffusive universality class with dynamical exponent
$z=2$ another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ)
class with $z=3/2$. It appears e.g. in low-dimensional dynamical phenomena far
from thermal equilibrium which exhibit some conservation law. Here we show that
both classes are only part of an infinite discrete family of non-equilibrium
universality classes. Remarkably their dynamical exponents $z_\alpha$ are given
by ratios of neighbouring Fibonacci numbers, starting with either $z_1=3/2$ (if
a KPZ mode exist) or $z_1=2$ (if a diffusive mode is present). If neither a
diffusive nor a KPZ mode are present, all dynamical modes have the Golden Mean
$z=(1+\sqrt{5})/2$ as dynamical exponent. The universal scaling functions of
these Fibonacci modes are asymmetric L\'evy distributions which are completely
fixed by the macroscopic current-density relation and compressibility matrix of
the system and hence accessible to experimental measurement.
