  The last decades witnessed the emergence of the field of correlated
disordered media, a great challenge offering a large panel of new perspectives
for applications in theoretical modelling and material fabrication. The
efficient design of structures with a controlled level of spatial correlation
is a central challenge in this field, in a context where existing techniques
generally rely on gradient descent on non-convex functions and on the use of
stochastic methods to explore vast design spaces more efficiently. In this
work, we propose a new generative technique based on Alan Turing's
morphogenesis theory for designing correlated disordered materials. Inspired by
the structuring of living organisms, this technique relies on the definition of
simple local interactions guiding the self-organization of a generated medium.
The decentralization of design constraints and the elimination of cost function
minimization make this approach natively scalable to the design of large
domains with controlled levels of disorder. As a validation, the morphogenetic
generation of stealthy hyperuniform disordered structures is exploited to
reproduce an experiment of isotropic electromagnetic bandgap synthesis in the
microwave range using a low refractive index contrast.
