Pattern formation is a fundamental process in embryogenesis and development. In his seminal paper half a century ago, Turing proposed a mechanism for spontaneous pattern formation in biological systems that involve the diffusion of two types of morphogens (“activator” and “inhibitor”) whose interaction stimulates their own synthesis. Starting from random initial perturbations, the Turing model typically generates patterns via the development of finite-wavelength dynamical instabilities in confined geometries.Recently, a collaboration led by Terry Hwa at UCSD and Jiandong Huang at HKU conducted experiments of pattern formation in open geometry through control of the synthetic chemotactic circuit of bacteria[1]. The growth process can be modeled quantitatively via Fisher-Kolmogorov type equations that exhibit traveling wave solutions.A key feature of the current model is a concentration-dependent diffusivity of the active species which can be tuned in the experiment through control of gene expression.Theoretical analysis of the traveling wave solution reveals key parameters that span the phase diagram of the system[2]. Linear stability analysis of the traveling wave yields a localized mode which undergoes a Hopf bifurcation at the onset of the striped phase. The autonomous diffusion control together with the open, expanding geometries offered by growing biological systems, give rise to novel strategies to generate well-defined patterns in space and time.