A pattern of micro-wires in a layer over which ink is to be coated to form micro-wires includes a substrate with first, second, and third regions. A plurality of connected first micro-channels, second micro-channels, and third micro-channels are formed in the first, second, and third regions having first, second, and third micro-channel densities, respectively. The first density is greater than the second density and the second density is greater than the third density. Thus, the density of the layer monotonically decreases from the first region to the second region and from the second region to the third region so that the ink coated over the layer is more effectively distributed.