  Recent experimental investigations into Hydra regeneration revealed a
remarkable phenomenon: the morphological transformation of a tissue fragment
from the incipient spherical configuration to a tube-like structure - the
hallmark of a mature Hydra - has the dynamical characteristics of a first-order
phase-transition, with calcium field fluctuations within the tissue playing an
essential role. This morphological transition was shown to be generated by
activation over an energy barrier within an effective potential that underlies
morphogenesis. Inspired by this intriguing insight, we propose a novel
mechanism where stochastic fluctuations drive the emergence of morphological
patterns. Thus, the inherent fluctuations determine the nature of the dynamics
and are not incidental noise in the background of the otherwise deterministic
dynamics. Instead, they play an important role as a driving force that defines
the attributes of the pattern formation dynamics and the nature of the
transition itself. Here, we present a simple model that captures the essence of
this novel mechanism for morphological pattern formation. Specifically, we
consider a one-dimensional tissue arranged as a closed contour embedded in a
two-dimensional space, where the local curvature of the contour is coupled to a
non-negative scalar field. An effective temperature parameter regulates the
strength of the fluctuations in the system. The tissue exhibits fluctuations
near a circular shape at sufficiently low coupling strengths, but as the
coupling strength exceeds some critical value, the circular state becomes
unstable. The nature of the transition, namely whether it is a first or a
second-order-like transition, depends on the temperature and the effective
cutoff on the wavelength of the spatial variations in the system. It is also
found that entropic barriers separate the various metastable states of the
system.
