We develop a method for the simultaneous restoration and halftoning of fingerprints using the ``M-lattice'', a new non-linear dynamical system. This system is rooted in the reaction-diffusion model, first proposed by Turing to explain morphogenesis (the formation of patterns in nature). But in contrast with the general reaction-diffusion, the state variables of the M-lattice are guaranteed to be bounded. The ML is closely related to the analog Hopfield network and the CNN, but has more flexibility in how its variables interact. These properties make it better suited than reaction-diffusion for several new engineering applications. The proposed method for enhancing fingerprints explores the ability of the M-lattice to form oriented spatial patterns (like reaction-diffusion), while producing binary outputs (like feedback neural networks). The fingerprints synthesized by the M-lattice retain and emphasize more of the relevant detail than do those obtained by adaptive thresholding, a common halftoning method employed in traditional fingerprint classification systems.