1. In a bit mapped color display system which accommodates the display of multiple windows, an apparatus for controlling the assignment of display attribute identification values and hardware color look-up tables, comprising; a) a plurality of hardware color look-up tables: b) a mechanism for creating colormap objects, coupled to said plurality of hardware color look-up tables, said colormap objects containing a data structure comprising a colormap and a plurality of display attribute data, and said colormap objects also containing one or more program operators; c) a first control facility, coupled to the mechanism for creating colormap objects, said first control facility having devices to establish and assign a finite number of display attribute identification values, said display attribute identification values being distinct from window identification numbers, and having devices for linking windows to the colormap objects and for assigning said finite number of display attribute identification values to the colormap objects, rearranging a previous assignment of said finite number of display attribute identification values if necessary;and d) a second control facility coupled to said first control facility for assigning one of said plurality of hardware color look-up tables to a designated colormap object, said designated colormap object sharing an existing one of said finite number of display attribute identification values with other colormap objects if necessary, whereby said finite number of display attribute identification value can be assigned to multiple colormap objects which are linked to multiple windows.