1. A method for increasing the gray scale resolution of a graphic generated by an ink jet printing system, said ink jet printing system including ink jet printing means and means for controlling and operating said ink jet printing means to apply or not apply substantially equal sized dots of one color to a plurality of pixel areas located sequentially along a line scanned by said printing means and within each of which pixel areas, potential dot positions form an array identical for all pixel areas, said method comprising the steps of: producing a sequential series of image density signals each substantially representative of the gray scale color intensity level associated with a respective one of said pixel areas; converting said gray scale color intensity level value to an equivalent dot level value for each of said pixel areas; comparing the dot level value associated with each of said pixel areas to a plurality of sets of dot level values, at least one set comprising integer dot level values and another set including dot level values other than integer values, each of said integer values corresponding to one of N integral color intensity values that may be represented by printing dots in said pixel dot position array; identifying adjacent side-by-side pixel areas having dot level values corresponding to values in said another set wherein said identified pixel areas have dot level values falling between the same two successive integer values; alternately adding one and another of a predetermined dot level value to the dot level value associated with those identified adjacent side-by-side pixel areas having dot level values between two successive integers so that the dot level value of one of the two adjacent pixel areas is increased by said one predetermined dot level value and the other is decreased by said another predetermined dot level value; rounding off each of the increased and decreased pixel dot level values to the nearest integer value so that the resulting dot level value of one of the two pixels is one dot level value more than the dot level value of the other pixel, and printing each of said two pixels in accordance with the resulting dot level value determined such that the average of the sum of the dot level values of the two printed pixels more nearly approximates the gray scale value corresponding to the associated image density signal.