This paper presents the M-lattice system, which is rooted in the reaction-diffusion model, first proposed by Turing in 1952 to explain the formation of animal patterns such as zebra stripes and leopard spots. The M-lattice system is related to the analog Hopfield network and the cellular neural network, but has more flexibility in how its variables interact. We demonstrate the use of this model for two different halftoning examples. The first example synthesizes a halftone of Einstein in the ``hand-drawn'' style of the Wall Street Journal portraits; it illustrates how a flexible quality metric can be used when the binary requirement is stated as an explicit constraint. The second example synthesizes halftones free of correlated artifacts; it illustrates the noise-shaping capability of the M-lattice system.
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