  We report on the discovery of a relation between the number of star formation
(SF) peaks per unit time, $\nu_{\rm peak}$, and the size of the temporal
smoothing window function, $\Delta t$, used to define the peaks: $\nu_{\rm
peak}\propto\Delta t^{1-\phi}$ ($\phi\sim 1.618$). This relation holds over the
range of $\Delta t=10$ to $1000$Myr that can be reliably computed, using a
large sample of galaxies obtained from a state-of-the-art cosmological
hydrodynamic simulation. This means that the temporal distribution of SF peaks
in galaxies as a population is fractal with a Hausdorff fractal dimension equal
to $\phi-1$. This finding reveals, for the first time, that the superficially
chaotic process of galaxy formation is underlined by a temporal
self-organization up to at least one gigayear. It is tempting to suggest that,
given the known existence of spatial fractals (such as the power-law two-point
function of galaxies), there is a joint spatio-temporal self-organization in
galaxy formation. From an observational perspective, it will be urgent to
devise diagnostics to probe SF histories of galaxies with good temporal
resolution to facilitate a test of this prediction. If confirmed, it would
provide unambiguous evidence for a new picture of galaxy formation that is
interaction driven, cooperative and coherent in and between time and space.
Unravelling its origin may hold the key to understanding galaxy formation.
