an embodiment of the invention will be described below in detail with reference to the drawings . a semiconductor device manufacturing method according to this embodiment will be described with reference to fig1 a and 1b and fig2 a to 2f . forming of gate patterns of a nand flash memory by the semiconductor device manufacturing method will be described here . fig1 a and 1b illustrate gate patterns of an nand flash memory . fig1 a shows a plan view of the gate patterns . fig1 b shows a sectional view of the gate patterns taken along the broken line a - a ′ in fig1 a . as shown in fig1 a , the gate patterns 1 include : line - and - space - shaped patterns 2 ( line - and - space patterns 2 ) having a number x of parallel line patterns ( l 1 to lx ) arranged periodically with given spaces ; and aperiodic patterns 3 disposed aperiodically adjacent to opposite end portions of the line - and - space patterns 2 . the line - and - space patterns 2 are functioning as word lines , and the periodic patterns 3 are functioning as select gate patterns sg 1 and sg 2 . the fact that “ the select gate patterns are aperiodic ” means that the select gate patterns are aperiodic relative to the line - and - space patterns 2 . accordingly , the select gate patterns may be periodic to each other or may be periodic relative to other patterns ( except dummy patterns which will be described later ) than the line - and - space patterns 2 . in this embodiment , in the line - and - space patterns 2 , the line sizes ( w 1 to wx ) and the space sizes ( s 1 to sx ) are equal to one another . the line size , the space size and the number of lines can be set respectively arbitrarily . for example , the line size and the space size can be set to be in a range of from about 30 nm to about 60 nm and the number of lines can be set to be 16 , 32 , 64 or 128 . though not shown , extracted patterns on which contacts with upper layer wiring are to be disposed are connected to the line patterns of the line - and - space patterns 2 respectively . the distance between each select gate pattern sg 1 or sg 2 and the line - and - space patterns 2 is larger than the line size and space size of the line - and - space patterns 2 . for example , the distance between each select gate pattern sg 1 or sg 2 and the line - and - space patterns 2 can be set to be about three times as much as the line size and space size . in this embodiment , a dummy pattern 4 is provided between the line - and - space periodic patterns 2 and each aperiodic pattern 3 . the dummy patterns 4 are formed so as to be electrically independent of the periodic patterns 2 and the aperiodic patterns 3 . the dummy patterns 4 are line - shaped patterns parallel with the respective line patterns of the line - and - space patterns 2 . the dummy patterns 4 are formed adjacent to the line - and - space patterns 2 . each dummy pattern 4 is formed distant from a corresponding end line pattern ( l 1 , lx ) of the line - and - space patterns 2 by the same size ( so , sx + 1 ) as the space size ( s 1 to sx ) of the line - and - space patterns 2 . accordingly , the distance between each end line pattern ( l 1 , lx ) of the line - and - space patterns 2 and a pattern adjacent to the end line pattern ( l 1 , lx ) is equalized to the distance between the central line pattern ( lx / 2 ) of the line - and - space patterns 2 and a pattern adjacent to the central line pattern ( lx / 2 ), so that the same peripheral environment is provided in each line pattern . the size of each dummy pattern 4 is equal to the size of each line pattern ( l 1 to lx ) of the line - and - space patterns 2 . accordingly , the size of each end line pattern ( l 1 , lx ) of the line - and - space patterns 2 and the size of the central line pattern ( lx / 2 ) of the line - and - space patterns 2 are equalized to the size of a pattern adjacent to the end line pattern ( l 1 , lx ) and the size of a pattern adjacent to the central line pattern ( lx / 2 ), so that the same peripheral environment is provided in each line pattern . as shown in fig1 b , the line - and - space patterns 2 , the select gate patterns ( aperiodic patterns 3 ) and the dummy patterns 4 are formed on a semiconductor substrate 5 through a gate insulating film ( not shown ) and made of polysilicon materials respectively . a method of forming the gate patterns 1 of the semiconductor device shown in fig1 a and 1b will be described below with reference to fig2 a to 2f . fig2 a to 2f are sectional views illustrating the method of forming the gate patterns 1 of the semiconductor device shown in fig1 b . first , as shown in fig2 a , a target film 6 of a gate pattern material such as a polysilicon film is formed on a semiconductor substrate 5 through a gate insulating film ( not shown ). then , a first film 7 of a laminated structure having a silicon oxide film 7 a and an amorphous silicon film 7 b is formed on the target film 6 . a resist film is formed on the first film 7 through an antireflection film ( not shown ) in a coating manner . then , after a photo mask is disposed in an exposure device , a mask pattern image is formed in the resist film by the exposure device . the resist film is developed to form resist patterns 8 . the resist patterns 8 include : line - and - space patterns 9 having a number ( 1 + x / 2 ) of parallel line patterns arranged periodically with given spaces ; and aperiodic patterns 10 disposed adjacent to the line - and - space patterns . then , as shown in fig2 b , the amorphous silicon film 7 b masked with the resist patterns 8 is processed . then , the resist patterns 8 are removed , and the amorphous silicon film 7 b is subjected to slimming in an etching manner . then , the silicon oxide film 7 a masked with the slimmed amorphous silicon film 7 b is processed . like the resist patterns 8 , first patterns 11 formed in the first film 7 include : line - and - space patterns 12 having a number ( 1 + x / 2 ) of parallel line patterns arranged periodically ; and aperiodic patterns 13 disposed adjacent to the line - and - space patterns . the line - and - space patterns 12 are formed so that the ratio of the line size to the space size is 1 : 3 . in this embodiment , as the first film 7 formed on the target film 6 , a laminated film having a silicon oxide film 7 a and an amorphous silicon film 7 b is used . however , a laminated film formed of other materials such as a laminated film having a carbon film and an amorphous silicon film , a laminated film having a carbon film and an sog film or a single layer film such as a silicon nitride film may be used as the first film 7 . in this embodiment , the amorphous silicon film 7 b as an upper layer portion of the first film 7 is subjected to slimming . however , the amorphous silicon film 7 b masked with the resist patterns 8 may be processed after the resist patterns 8 are subjected to slimming . in this case , the step of applying slimming to the amorphous silicon film 7 b can be removed . then , as shown in fig2 c , a second film 14 such as an oxide film , a nitride film , etc . is formed on the target film 6 and on the first patterns 11 so that the first patterns 11 are covered with the second film 14 . then , as shown in fig2 d , the second film 14 is etched to form second side wall patterns 15 on side walls of the first patterns 11 . then , as shown in fig2 e , periodically arranged patterns 12 are selectively removed from the first patterns 11 . that is , a resist film is applied on the target film 6 , the first patterns 11 and the second side wall patterns 15 , the resist film is processed to have patterns selectively revealing the periodically arranged patterns 12 of the first patterns 11 and the second side wall patterns 15 formed on side walls thereof , and the revealed periodic patterns 12 are removed with the resist patterns . as a result of selectively removing the first patterns 11 , the second side wall patterns 15 are formed as line - and - space patterns 16 having a number ( x + 2 ) of line patterns parallel with one another and periodically arranged . the line - and - space patterns 16 are formed so that the ratio of the line size to the space size is 1 : 1 . finally , as shown in fig2 f , the target film 6 masked with the first patterns 11 and the second side wall pattern 15 is processed to form gate patterns 1 as shown in fig1 b . in this manner , line - and - space patterns 2 , as word lines , having a number x of line patterns arranged periodically and each separated from the adjacent line patterns , aperiodic select gate patterns 3 arranged adjacent to the line - and - space patterns , and electrically - independent dummy patterns 4 formed between the line - and - space patterns 2 and the select gate patterns 3 are simultaneously formed on the semiconductor substrate 5 as shown in fig1 b . the dummy patterns 4 and the line - and - space patterns 2 formed in the target film 6 are formed simultaneously with the second side wall patterns 15 of periodic line - and - space patterns as a mask . the dummy patterns 4 are provided as two line patterns respectively adjacent to end line patterns of the line - and - space patterns 2 to be periodic with respect to the line - and - space patterns 2 . for this reason , the distance ( space size ) between each end line of the line - and - space patterns 2 and a pattern adjacent to the end line and the distance ( space size ) between the central line of the line - and - space patterns 2 and a pattern adjacent to the central line are equalized . further , the size of a pattern adjacent to the end line of the line - and - space patterns 2 and the size of a pattern adjacent to the central line of the line - and - space patterns 2 are equalized . according to this embodiment , each end line of the periodic line - and - space patterns 2 and the central line of the periodic line - and - space patterns 2 have the same peripheral pattern environment . accordingly , dimensional error caused in an etching process or the like can be suppressed . in this embodiment , the dummy patterns 4 are formed by use of the second side wall patterns 15 that are used to form fine - size target patterns in the target film 6 . as a result , the dummy patterns 4 can be formed while preventing the chip area from being increased . generally , in the semiconductor device , two resist dummy regions are provided between periodic patterns and aperiodic patterns . for example , if two resist patterns are provided correspondingly for the two dummy regions , since two side - wall patterns are formed at both sides of one resist pattern , two dummy patterns are formed in each of the two dummy regions . in this embodiment , only one resist pattern in total is formed to provide the two dummy regions , and the one dummy pattern 4 is respectively assigned between the periodic patterns 2 and each aperiodic pattern 3 . therefore , the area required for providing the dummy regions are reduced as compared with the above comparison example . according to this embodiment , while suppressing dimensional error of patterns , pattern area in the lithography is prevented so that chip area of the semiconductor device is suppressed . in this embodiment , formation of gate patterns of an nand flash memory is described . however , the invention can be applied to formation of other patterns of semiconductor device . for example , when this embodiment is applied to a method of manufacturing a semiconductor device having periodic patterns and aperiodic patterns , dummy patterns can be formed therebetween .