in addition to the insights underlying the present invention as stated at the beginning of the earlier “ summary ” section , philosophically the invention takes a novel approach to the solution . earlier masking such as summarized in cleveland &# 39 ; s discussions was completely determinative . more - recent masking innovations have swung toward an opposite approach of controlled degrees of both internal and external randomization . the present invention returns to a determinative or systematic strategy , but only with respect to what is external to the individual masks . the invention reveals that the repetitive effects of printmask and dither - mask interaction can be deferred by very greatly extending the periodicity of their interaction — systematically , with no need for randomness . in comparison with the prior - art interfitting of two masks shown in fig2 the present invention provides masks that are of slightly different dimensions — or are modified during printing to perform as if they were of slightly different dimensions . thus the width 201 ( fig3 ) of the new printmask 202 no longer fits integrally across the width 203 of the new dither mask 204 ; in fact , for the illustrated example the printmask 202 is now some 25 % wider than the dither mask 204 . ( for readier comparison of this example with that given for the prior art in fig2 the dither mask here is the same size — and the printmask the same height — as in the prior - art illustration .) the result , for widths , is that — in the particular example illustrated — five horizontal cycles 221 ( fig4 ) of the dither mask 204 are required to catch up to four horizontal cycles 222 of the printmask 202 . patterning across a simulated midtonal printout ( fig5 ) is accordingly very greatly diminished . this technique does not abandon the operational advantages of binary - sized data blocks . the width differential 207 between the two masks is , in the example illustrated , one - quarter of the dither - mask width 203 ; hence the width 201 in pixels across the new printmask 202 is still a multiple ( though not a power ) of two . for instance , for a new dither - mask width 203 of two hundred fifty - six ( 2 8 ) pixels , written “ 10000000 ” in binary notation , the new printmask width 201 exceeds that dither - mask width by one - quarter , which amounts to a distance 207 that is sixty - four ( 2 6 ) pixels . thus the width of the new printmask is three hundred two ( 2 8 - 2 6 ) pixels , written in binary “ 10100000 ”. data blocks of this size are perhaps not as convenient as the prior - art block of binary “ 10000000 ” pixels , but still readily tractable . a comparable advantage can be gained by applying the same technique in the vertical direction . for the vertical relationships in the illustrated example , however , a different facet of the invention has been applied . here the height 205 of the new dither mask 204 still does fit an integral number of times ( namely twice ) down the height 206 of the new printmask 202 . to overcome this , however , the printmask is indexed by a horizontal offset 208 . in other words , the internal pattern of the printmask is moved toward the left by a certain band 208 of pixels , so that the mask outline itself appears in the illustration to be shifted toward the right . to understand that the internal pattern is shifted leftward , it may be noted that : in the top row 211 of printmask tiles , what appears at the left margin of the entire illustrated interaction cell 209 is the left margin 212 ( fig3 ) of the individual printmask 202 ; in the second row 213 , what appears at the left margin of the entire cell 209 is instead the right - hand band of pixels 214 within the printmask 202 . thus in the second row 213 , the left margin 212 ′ of the printmask 202 does not begin until after that right - hand pixel band has been passed . as a result , eight vertical cycles ( fig4 ) of the new dither mask 204 , rather than only two , are needed to catch up with four vertical cycles of the new printmask 202 . the horizontal relations described above are unchanged : in the second through fourth ranks of the diagram , five cycles of the dither mask still match four cycles of the printmask , even though the latter appears offset progressively rightward in those lower ranks . those skilled in this field will understand that an analogous result can be obtained by internal indexing of the printmask 202 vertically , instead of horizontally . furthermore , in principle this same technique can be used in place of the first - introduced actual size mismatch for the horizontal interaction between the two masks . both the size differential 207 and the offset 208 in the accompanying illustration have been chosen to enable a clear showing of the full interaction cell 209 . for this purpose the size differential 207 and offset 208 are each one - quarter of the dither - mask width 203 . choosing such a large fraction , however , actually leads to a rather modest extension of the interaction periodicity — i . e ., only five times the dither - mask width and four times the printmask width . in practice a preferred fraction is one - eighth ( still leading to a binary - sized new mask width , of binary 10001000 ) or even one - sixteenth ( e . g ., printmask width of binary 10000100 ). interaction periodicity in these cases is correspondingly two to four times longer than what is shown ( fig4 ), and the disintegration of patterning effects correspondingly more effective than that illustrated ( fig5 ). when the two mask types are of different sizes , the periodicity of repetition associated with stepping of each mask is correspondingly different . the interaction between the two kinds of masks remains repetitive , but the cycle or periodicity of repetition of the interaction is very long . the basis for this is analogous to the familiar phenomena of beats , in acoustic , optical or electronic oscillations — or again moire patterns in visible effects . it is very well known in all such phenomena that the frequency of the beats is the difference between the frequencies of the individual oscillations . thus in the present case the spatial frequency of the interaction between dither masks and printmasks can be made equal to the difference between the respective spatial frequencies of the two masks . put another way , in wavelength terms the reciprocal of the vertical interaction periodicity is equal to the difference between the reciprocals of the mask lengths ( heights )— 1 interaction   period = 1 dither  -  mask   dimension - 1 printmask   dimension . this difference can be made very large , simply by making the mask lengths very close to each other . it is only required that they not be integral multiples or factors of one another , as they have been almost universally heretofore . like relations hold for the horizontal period and the mask widths . these two relations operate independently , so the repetition can be controlled to different interaction periodicities for length and width , or a common interaction periodicity , as preferred . in mathematical terms , the extended geometry discussed above results from choosing a printmask and dither mask neither of which is an integral multiple of the other . alternatively stated , each mask is neither a factor nor an integral multiple of the other . this causes the nozzles assigned to print each dot of the dither matrix to change each time that matrix is used in printing , until a cycle is completed and the nozzles match the dots again . the length of that cycle is the minimum common multiple of the corresponding dimensions of the two matrices , a condition that can be derived from the mathematical expression presented above : 1 interaction   period = ( printmask   dimension ) - ( dither  -  mask   dimension ) ( printmask   dimension ) · ( dither  -  mask   dimension ) ; so   that -   interaction   period =  ( printmask   dimension ) - ( dither  -  mask   dimension ) ( printmask   dimension ) · ( dither  -  mask   dimension ) =  ( printmask   dimension ) - ( dither  -  mask   dimension ) dimension   differential . and this last expression is the minimum common multiple of the two mask lengths . in the earlier example of a 256 - pixel - square dither matrix , choosing a printmask eight pixels wider , at two hundred sixty - four pixels , leads to a repeating cycle that is 8 , 448 pixel columns wide . this number can be seen as representing the dither - mask width times an extension factor equal to the printmask width expressed in units of the width differential . the extension factor , in other words , is one - eighth of the printmask width , or 264 / 8 = 32 . the 8 , 448 - pixel cycle is thirty - two times as wide as the dither - mask width . with mask widths of five hundred twelve and five hundred twenty pixels respectively , the extension factor is 520 / 8 = 65 , and the overall interaction cell therefore 512 × 65 = 33 , 280 pixels . for a 24 - pixel - per - mm grid , very remarkably this interaction cell is more than 1⅓ m ( 4½ feet ) wide . as noted earlier , printmasks often are accessible for internal modification even in systems whose algorithms are cast in silicon . hence the type of modification described above is amenable to insertion into an already complete printing regimen , particularly with respect to printmask width — that is to say , the horizontal or scan - axis dimension . even in a product development that is not thus constrained the invention may yet be of great value since it minimizes the amount of firmware or hardware ( asic elements ) required to avoid patterning along the scan axis . as to the vertical or printing - medium advance axis , however , actual expansion of the printmask height may implicate changes in printing - medium advance length as well , and this parameter may not be accessible for modification . particularly for such situations the differential technique may be unavailable for the vertical dimension , but the offset strategy can yet serve . as to this methodology let it be supposed again that the printmask swath height , measured in pixels , is two hundred fifty - six — or a multiple of that value . assigning particular nozzle dot - placement errors consistently to the same pixels of the dither matrix , swath after swath , is a potential source of patterning as explained earlier . to avoid that consistent assignment the mask is internally indexed either horizontally ( fig4 ) or vertically ( not shown ), after printing of each swath . the indexing is by an offset distance that is preferably a power of two — once again to maintain the benefits of such values in data - block management . as an example , the offset may be 2 5 = 32 pixel rows , which distance is one - eighth of the dither - matrix height . even for this rather large offset , the cycle repetition period will be 2 , 048 rows or nearly 9 cm ( 3⅓ inches ). calculation of the overall period for this aspect of the invention follows generally the principles outlined above , but with the difference that the printmask height is in effect multiplied by a factor equal to that same height divided by the offset . in other words , the effective height of the printmask is expanded by the factor — printmask   height offset . consequently the effective height of the printmask becomes : effective printmask   height = ( printmask   height ) · printmask   height offset , and the interaction - cell spatial frequency is then found as the minimum common multiple of this value and the dither - mask width . since the effective printmask height given by the above expression is 256 2 / 32 and the dither - mask dimension is 256 pixels , the latter number is a factor of the former and need not be considered in determining the minimum common multiple . thus the answer is 2 , 048 pixels as stated above . considering another example , 512 - pixel - square printmask and dither mask with an eight - pixel offset , the effective printmask dimension is 512 2 / 8 — which is also the minimum common multiple . the answer here is the same dimension found for the horizontal case considered above , namely more than 1⅓ m ( 4½ feet ). this is larger than the entire printout for all but poster - size and larger images . when the interaction period is modest , even as extended , this invention may be said to build upon the discoveries by garcia relating to spatial - frequency sensitivity of the eye . as pointed out above , however , the periodicity extension achievable with the present invention can be made extremely long — so long in fact as to cover substantially an entire image , at least for relatively large masks and relatively modest image sizes . in that case there is physically no repetition , and the invention need not invoke the garcia spatial - frequency principle . the preferred printer / plotter includes a main case 1 ( fig6 ) with a window 2 , and a left - hand pod 3 that encloses one end of the chassis . within that pod are carriage - support and - drive mechanics and one end of the printing - medium advance mechanism , as well as a pen - refill station containing supplemental ink cartridges . the printer / plotter also includes a printing - medium roll cover 4 , and a receiving bin 5 for lengths or sheets of printing medium on which images have been formed , and which have been ejected from the machine . a bottom brace and storage shelf 6 spans the legs which support the two ends of the case 1 . just above the print - medium cover 4 is an entry slot 7 for receipt of continuous lengths of printing medium 4 . also included are a lever 8 for control of the gripping of the print medium by the machine . a front - panel display 11 and controls 12 are mounted in the skin of the right - hand pod 13 . that pod encloses the right end of the carriage mechanics and of the medium advance mechanism , and also a printhead cleaning station . near the bottom of the right - hand pod for readiest access is a standby switch 14 . within the case 1 and pods 3 , 13 the carriage assembly 20 ( fig7 ) is driven in reciprocation by a motor 31 — along dual support and guide rails 32 , 34 — through the intermediary of a drive belt 35 . the motor 31 is under the control of signals 57 from a digital electronic microprocessor ( essentially all of fig1 except the print engine 50 ). in a block diagrammatic showing , the carriage assembly 20 travels to the right 55 and left ( not shown ) while discharging ink 54 . a very finely graduated encoder strip 33 is extended taut along the scanning path of the carriage assembly 20 , and read by an automatic optoelectronic sensor 133 , 233 to provide position and speed information 52 for the microprocessor . ( in fig1 , signals in the print engine are flowing from left to right except the information 52 fed back from the encoder sensor 233 — as indicated by the associated leftward arrow .) the codestrip 33 thus enables formation of color inkdrops at ultrahigh resolution ( typically 24 pixels / mm ) and precision , during scanning of the carriage assembly 20 in each direction . a currently preferred location for the encoder strip 33 is near the rear of the carriage tray ( remote from the space into which a user &# 39 ; s hands are inserted for servicing of the pen refill cartridges ). immediately behind the pens is another advantageous position for the strip 36 ( fig3 ). the encoder sensor 133 ( for use with the encoder strip in its forward position 33 ) or 233 ( for rearward position 36 ) is disposed with its optical beam passing through orifices or transparent portions of a scale formed in the strip . a cylindrical platen 41 ( fig8 )— driven by a motor 42 , worm 43 and worm gear 44 under control of signals 46 from the processor 15 — rotates under the carriage - assembly 20 scan track to drive sheets or lengths of printing medium 4 a in a medium - advance direction perpendicular to the scanning . print medium 4 a is thereby drawn out of the print - medium roll cover 4 , passed under the pens on the carriage 20 to receive inkdrops 54 for formation of a desired image , and ejected into the print - medium bin 5 . the carriage assembly 20 includes a previously mentioned rear tray 21 ( fig9 ) carrying various electronics . it also includes bays 22 for preferably four pens 23 - 26 holding ink of four different colors respectively — preferably cyan in the leftmost pen 23 , then magenta 24 , yellow 25 and black 26 . each of these pens , particularly in a large - format printer / plotter as shown , preferably includes a respective ink - refill valve 27 . the pens , unlike those in earlier mixed - resolution printer systems , all are relatively long and all have nozzle spacing 29 ( fig1 ) equal to one - twelfth millimeter — along each of two parallel columns of nozzles . these two columns contain respectively the odd - numbered nozzles 1 to 299 , and even - numbered nozzles 2 to 300 . the two columns , thus having a total of one hundred fifty nozzles each , are offset vertically by half the nozzle spacing , so that the effective pitch of each two - column nozzle array is approximately one - twenty - fourth millimeter . the natural resolution of the nozzle array in each pen is thereby made approximately twenty - four nozzles ( yielding twenty - four pixels ) per millimeter , or 600 per inch . preferably black ( or other monochrome ) and color are treated identically as to speed and most other parameters . in the preferred embodiment the number of printhead nozzles used is always two hundred forty , out of the three hundred nozzles ( fig1 ) in the pens . this arrangement allows for software / firmware adjustment of the effective firing height of the pen over a range of ± 30 nozzles , at approximately 24 nozzles / mm , or ± 30 / 24 =± 1¼ mm . this adjustment is achieved without any mechanical motion of the pen along the print - medium advance direction . alignment of the pens can be automatically checked and corrected through use of the extra nozzles . as will be understood , the invention is amenable to use with a very great variety in the number of nozzles actually operated . a . basic processing options — data - processing arrangements for the present invention can take any of a great variety of forms . to begin with , image - processing and printing - control tasks 332 , 40 can be shared ( fig1 ) among one or more processors in each of the printer 320 and an associated computer and / or raster image processor 30 . a raster image processor (“ rip ”) is nowadays often used to supplement or supplant the role of a computer or printer — or both — in the specialized and extremely processing - intensive work of preparing image data files for use , thereby releasing the printer and computer for other duties . processors in a computer or rip typically operate a program known as a “ printer driver ”. these several processors may or may not include general - purpose multitasking digital electronic microprocessors ( usually found in the computer 30 ) which run software , or general - purpose dedicated processors ( usually found in the printer 320 ) which run firmware , or application - specific integrated circuits ( asics , also usually in the printer ). as is well - understood nowadays , the specific distribution of the tasks of the present invention among all such devices , and still others not mentioned and perhaps not yet known , is primarily a matter of convenience and economics . on the other hand , sharing is not required . if preferred the system may be designed and constructed for performance of all data processing in one or another of the fig1 modules — in particular , for example , the printer 320 . regardless of the distributive specifics , the overall system typically includes a memory 232 m for holding color - corrected image data . these data may be developed in the computer or raster image processor , for example with specific artistic input by an operator , or may be received from an external source . ordinarily the input data proceed from image memory 232 m to an image - processing stage 332 that includes some form of program memory 333 — whether card memory or hard drive and ram , or rom or eprom , or asic structures . the memory 232 m provides instructions 334 , 336 for automatic operation of rendition 335 and printmasking 337 . image data cascades through these latter two stages 335 , 337 in turn , resulting in new data 338 specifying the colorants to be deposited in each pixel , in each pass of the printhead carriage 20 over the printing medium 41 . it remains for these data to be interpreted to form : actual printhead - actuating signals 53 ( for causing precisely timed and precisely energized ink ejection or other colorant deposition 54 ), actual carriage - drive signals 57 ( for operating a carriage - drive motor 35 that produces properly timed motion 55 of the printhead carriage across the printing medium ), and actual print - medium - advance signals 46 ( for energizing a medium - advance motor 42 that similarly produces suitably timed motion of the print - medium platen 43 and thereby the medium 41 ). such interpretation is performed in the printing control module 40 . in addition the printing control module 40 may typically be assigned the tasks of receiving and interpreting the encoder signal 52 fed back from the encoder sensor 233 . the printing - control stage 40 necessarily contains electronics and program instructions for interpreting the colorant - per - pixel - per - pass information 338 . most of this electronics and programming is conventional , and represented in the drawing merely as a block 81 for driving the carriage and pen . that block in fact may be regarded as providing essentially all of the conventional operations of the printing control stage 40 . b . alternative subsystems for reducing repetitive patterning — also appearing in fig1 are certain specific modules and associated data - flow paths 71 - 78 implementing the present invention . it is very important to note that certain of these illustrated specific functions are alternatives , rather than subsystems that would typically coexist within any single printer / computer / rip system . this is mainly a matter of the particular environment in which the invention is to operate . in particular if the program memory 333 for a particular printer has yet to be designed and fabricated — or if it exists already but permits modification of the dither mask or printmask sizes ( particularly widths ), then the preferred mode of practice for at least the scan - axis repetition control takes the form of novel differential - constraint means 71 . the constraint - means block 71 is symbolized as having control paths 72 , 73 to the rendition and printmask stages 336 , 337 respectively . physically , this simply means that the two mask - establishing functions 82 , 83 within those stages 336 , 337 have been coordinated , in the apparatus design . “ mask - establishing functions ” are performed in essence by algorithm and memory circuits that cooperate to set aside data blocks of specific sizes for masks , and also to fill those masks with specified values — and in due course to appropriately retrieve and use those numbers . in the dither - masking stage 82 the values are thresholds , and in the printmasking stage 83 they are typically pass numbers — both as well known in the art . according to the present invention , by virtue of this precoordination symbolized as a constraint - means block 71 , masks in the two stages are sized to satisfy certain constraints . the most important of those constraints is that the dither mask and printmask sizes not be integral factors or multiples of one another . in particular , each mask differs from an integral factor or multiple of the other mask by some differential . a next most - important of the constraints is that this differential , measured in pixels , be a multiple of two — and preferably a multiple of eight . it is secondarily desirable that one of the mask sizes be a multiple of two hundred fifty - six pixels . these secondary constraints or preferences essentially are simply statements of the amenability of the present invention to a substantially conventional programming and operating environment they are “ important ” and “ desirable ” not because the invention fails to operate successfully with a differential of three or seven — or with some odd mask size of forty three , or three hundred seven — but rather because the invention has greatest value under the stated conditions . another preferable condition is that the differential be at least three pixels ; the purpose of this minimum differential is simply that the differential have some actual effect in stepping the boundaries between repeating tiles of the masks far enough to clear very small features of the image . if on the other hand the program memory 333 , in whatever form it may be , sets both the dither masks and printmasks to be integral factors or multiples of one another , irrevocably , then the size - differential module 71 cannot be present in the apparatus and the invention looks to alternative solutions . initially , however , in this context the question arises : what constitutes “ irrevocably ”. an asic can always be discarded and another designed and built to go in its place , and firmware — much more readily — can be redesigned and loaded into a new rom for field replacement . the invention , however , proceeds from the objective of avoiding all such radical cures . if masks are integral factors or multiples of one another and — as a practical and economic matter — cannot be changed , then the alternative cure is to ( 1 ) establish an offset and ( 2 ) index the printmask ( or dither mask if desired ) by that offset between each pair of printhead scans . most commonly it is the printmask that is more straightforwardly shifted , since printmasks are often or customarily made relatively accessible even in a completed product . suitable offset - establishing means 74 may be conceptualized as directing an offset control signal 75 to the printmasking function 337 . here the symbolism is perhaps more physically apt than in the differential - dimension method discussed above , because in the present case there physically exists either : ( 1 ) an actual algorithmic shifting of a mask pattern , by an actual offset distance , or ( 2 ) an algorithmically selected succession of previously stored printmasks — that were initially generated through shifting a common pattern by such an actual offset . in either event , the apparatus and method must provide not only the offset distance , as from the offset - establishing means 74 and its control path 75 , but also the indexing or shifting action itself . as a practical matter , however , if selection from a sequence is the strategy chosen , the shifting operation may do double duty — because in some printmasking operations the system shuffles masks between scans anyway . the shifting action may be conceptualized as performed by an indexing - means module 76 triggered by a signal 77 from a portion of the carriage and pen drive 81 which interleaves the indexing function between successive scans of the printhead . equivalently , the indexing means 76 and carriage / pen drive 81 may both be synchronized from some common clock ( not shown ). however triggered , the indexing means 76 respond by feeding a signal 78 back to the printmasking stage 337 , to announce that it is time to either ( as described above ) shift the pattern or select the next pattern in sequence . the offset distance by which the mask is shifted , at whichever time that is done , should be smaller than at least one of the masks ( dither mask or printmask ) and preferably satisfy the size conditions discussed earlier . although the dimension - differential and offset forms of the invention have been presented above as alternatives , it is also true that in a system capable of using the dimension - differential strategy the two forms of the invention can be used together . for reasons outlined previously , in many systems it is most natural to use the differential methodology for the scan axis and the offset methodology to extend the period along the printing - medium advance axis . the several forms of the invention may also be seen in terms of method , as distinguished from apparatus . the offset strategy has three main steps , as outlined in the earlier “ summary of the disclosure ”. one of these steps is rendition - stage establishment and operation 401 ( fig1 ). another is printmasking - stage establishment and operation 402 . these steps respectively include using a dither mask and printmask ( for each color ). the printmask is either an integral multiple or integral factor of a dither - mask dimension . this latter condition points up the fact that the dimension - differential method is not being used for the critical dimensions of these masks . the interaction period for these mask - using steps is in the human high - visual - sensitivity range . the third main step is extension 403 of the spatial interaction period to a value well outside that high - sensitivity range . this step has several preferences 404 - 406 that can be conceptualized as nested . the prime substep for performing the period - extension step 403 is causing 404 the spatial period to equal the minimum common multiple ( mcm ) of the one enlarged mask dimension and other ( not enlarged ) mask dimension . this substep 404 in turn is best accomplished by an effective enlargement 405 of one ( or both ) mask dimensions by a factor of eight — or , as noted earlier , at least two . this enlargement is not performed actually , but rather only in effect , and in regard to the interaction . the favored procedure for performing the enlargement 405 is indexing 406 of one of the masks ( usually the printmask ) by an offset that is preferably less than one - eighth of the subject dimension of that mask . the above disclosure is intended as merely exemplary , and not to limit the scope of the invention — which is to be determined by reference to the appended claims .