(1) The Current Technical Status and Problems at Home and Abroad.
The invention belongs to the field of arts and crafts. The breakthrough of basic theory of four directions continuation means the new method of successively and repeat design in four directions, new pattern design method and pattern constitution, which is the new breakthrough of design and production technologies. It is applied to academic education of basic theory of four directions continuation, pattern design, architectural ornament and decoration design ,in the field of arts and crafts. It can obviously improve the design level, reduce the cost and raise economic benefits especially in the design and production of fabric printing industry, silk industry and product duplication industry.
At present, the theory teaching, pattern design and production at home and abroad all adopt two methods, one of which is butt method. When pattern repeats, the up and down sides of the unit butt, the unit point directly repeats in the vertical direction; so does the right and left sides; butt the unit point directly repeats in the horizontal direction; cycling effect and rhythm is monotonous and the sense of rhythm is not strong. The other method is jump connection method. The unit point directly repeats in the vertical direction is the same as that of butt method; the right and left two sides in the horizontal direction to each other in the up and down opposite direction on regular basis moves to the certain length and then connects, thus the horizontal direction change of jump connection method is different from that of the butt method. The point in horizontal direction doesn’t directly repeat while the cycling effect is more flexible than that of butt method. However, the point in the vertical direction hasn’t separated from the butt method. It isn’t perfect both in theory and in practice. As is shown in Fig.35, one half, two thirds, three fourths and three fifths belong to jump connection method, and the left top corner in the figure belongs to butt method. 

(2) Main Technical Measures applied to the Invention and Achievement Received
The invention is aimed at the existing problems of the original two cycling methods; the vertical and horizontal directions of butt method (Fig 37)the vertical direction is butt method of jump connection method(Fig38)after cycling, the unit point rank directly reappear, and the cycling effect is rigid. According to the research results, it adopts spiral moving method on five same pattern squares: the squares move along the four sides of the unit, that is the four direction of up, down, right and left in the clockwise or anticlockwise direction with the moving same side distance, which forms the shape of windmill; the continuous cycling is carried out according to this shape, which makes the cycling method of this invention appear, namely technique of successively and spirally repeat design in four directions (Fig.36), as well as form a series of formations; the unit constitution ;the calculating formula determined by the unit of spirally repeat pattern; drawing and cutting skill of spirally repeat pattern; and production crafts etc making;. Compared with butt method and jump connection method, four directions change after cycling, which meet after cycling that the points in the vertical and horizontal directions can’t directly repeat and completely separate from the types of butt method and jump connection method ( Fig.39). The effects of products is more flexible than those of butt method (Fig.37) and jump connection method (Fig.38) so heightens of rhythm; the art effects of pattern unit is enlarged from the aspect of vision; The small unit pattern is so designed rise great unit effects ,it heightens beauty of products, will bring a significant social benefits ..

Introduction to Four directions Continuous Cycling Method
Four directions continuation is technique of that each unit constantly and repeat design in four directions. Each kind cycling method has respective cycling regularity. with its respective regularity, various features of cycling is shown, which results in different effects and imagination.
Ⅰ. Butting Cycling Method Fig.1

Butting cycling method means that two opposite sides of the pattern unit are connected to each other; from the aspect of each point in the unit, it is after cycle equidistant (the length and width of the unit); the points repeatedly appear in the vertical and horizontal lines. For the point itself, formations a pattern unit square is formed, which seems serious, smooth, simple and generous. The production technology is relatively simple, which is mainly applied to production.
Ⅱ. Jump Connection Cycling Method
There are various kinds of jump connection cycling methods. It is sequenced as per the fraction, such as one half, one thirds, two thirds, one fourths , two fourths etc. in the design of fabric printing products, due to the limitation of production and arts effects is close to that of butt method, one-half jump connection and one-thirds jump connection. Thus, after two thirds jump connection isn’t adopted .
1. One-half Jump Connection Cycling Method Fig.2

Its vertical repeated points are the same as those of butt method, but there are three unit distance in the horizontal repeated points. There is one repeated point 1 in the one third position of vertical line of one unit distance; there is one repeated point 2 in the two thirds position of vertical line of two unit distance; the two repeated points are the characteristic of one-thirds jump connection method and equal to three times of butt method.
3. Two-thirds Jump Connection Cycling Method Fig.4

In the vertical direction are butt method; the repeated points are one unit distance, the repeated points in the horizontal direction are two unit distance. but, there is a repeated point in the middle of vertical line of one unit distance which is the characteristic of one-half jump connection cycling method and equal to twice of butt method.
2. One-thirds Jump Connection Cycling Method Fig.3

Its vertical repeated points are the same as those of butt method, but there are three unit distance in the horizontal repeated points. There is one repeated point 1 in the one third position of vertical line of one unit distance; there is one repeated point 2 in the two thirds position of vertical line of two unit distance; the two repeated points are the characteristic of one-thirds jump connection method and equal to three times of butt method.

3. Two-thirds Jump Connection Cycling Method Fig.4

It and one-thirds jump connection , characteristic of this method is basically close; the repeated distance same as of the points in the vertical and horizontal ,there is one repeated point 1 in the two-thirds position of the vertical line of one unit distance of the horizontal repeated point; there is one repeated point 2 in the one-thirds position of vertical line of two unit distance ;It is the reverse form of one-third method, as well as the characteristic of two-thirds jump connection method.
4. Rhombus Cycling Method Fig.5


The cycling method of rhombus unit is the variant of butt method. The parallel opposite sides are connected to each other; the vertical and horizontal repeated points are one unit distance. The characteristic of rhombus is that four sides are of the same length; thus, its repeated points are on the central lines of the two sides opposite sides, as well as on two diagonals which are vertical to each other. It is halve rhombus and having the characteristic of one-half jump connection method. It since butt connection method one-half jump connection method ,it is rarely applied to the production.
Based on the analysis of the several jump connection methods, it is found that its rhythm be in advance of butt method. The repeated points are up and down to increase the sense of rhythm. The changes are subtle, contain and lively so it is mainly used in the production.
The four directions continuous cycle method that is applied to the current theory and practice in the world belongs to the above two methods.
Technique of successively and spirally repeat design in four directions.
ⅠGeneration of Spiral Cycling
Based on the analysis and research on the two methods, it is concluded that the jump connection method evolves from butt method; its vertical direction not have separate from butt method. Does it completely separate from butt method?
1. Joint Adopting Double Jump Fig.6

The cycling method of rhombus unit is the variant of butt method. The parallel opposite sides are connected to each other; the vertical and horizontal repeated points are one unit distance. The characteristic of rhombus is that four sides are of the same length; thus, its repeated points are on the central lines of the two sides opposite sides, as well as on two diagonals which are vertical to each other. It is halve rhombus and having the characteristic of one-half jump connection method. It since butt connection method one-half jump connection method ,it is rarely applied to the production.
Based on the analysis of the several jump connection methods, it is found that its rhythm be in advance of butt method. The repeated points are up and down to increase the sense of rhythm. The changes are subtle, contain and lively so it is mainly used in the production.
The four directions continuous cycle method that is applied to the current theory and practice in the world belongs to the above two methods.
Technique of successively and spirally repeat design in four directions.
ⅠGeneration of Spiral Cycling
Based on the analysis and research on the two methods, it is concluded that the jump connection method evolves from butt method; its vertical direction not have separate from butt method. Does it completely separate from butt method?
1. Joint Adopting Double Jump Fig.6


By analysis the jump form, it is concluded that the jump form is used in the horizontal direction while the butt method is adopted in the vertical direction. Thus, it belongs to single jump form. What about using double jump? As is shown in Fig.6, there is a parallelogram called ABCD, it four sides’ midpoints are respectively that: E is the midpoint of side AB; F is the midpoint of side BC; G is the midpoint of side CD; H is the midpoint of DA. Thus, the down one half of the left side EB and the up one half of the right side DG are formed; the up one half of the left side AE and the down one half of the right side GC are formed; the left one half of the up side AH and the right one half of the down side FC are formed; the right one half of the up side HD and the left one half of the down side BF are formed; these sides are connected to each other and eight parallelograms are formed; constitution a new parallelogram called A’B’C’D’ which belongs to butt method unit. in unit There are ten parallelograms called ABCD, but four parallelograms CBAD, ADCB, CBAD, ADCB result from partial overlap of eight parallelograms. it is only used in weave design, but in dye textile the arts design of not . solve the overlap phenomenon of hinge question..
2. Emerge of Spiral Cycle Method Figure 7

Think remove quadrilaterals of overlap.
Must cut off one of the two quadrilaterals forming this overlapping .Number the eight quadrilaterals from one to eight in clockwise direction, then cut off four of cut off one quadrilateral every other, therefore, it forms ㈠ ㈢ ㈤ ㈦ spirally in clockwise direction, shown in full line, and ㈡ ㈣ ㈥ ㈧ spirally in anticlockwise direction, shown in hidden line. Two new units of A’BAD and CBC’D in abutting joint are shown with boundary line. Consequently, ㈠ ㈢ ㈤ ㈦ full line clockwise spiral cycle method and ㈡ ㈣ ㈥ ㈧ hidden line anticlockwise spiral cycle method are established, thus the spiral cycle method is produced and emerges. Five quadrilaterals are in clockwise type, such as DACG (Ⅰ), DBFC(Ⅱ), AEBC(Ⅲ), HABD (Ⅳ) and A’ACA(Ⅴ); five quadrilaterals are in anticlockwise type, such as EBDA(1), ACDH(2), BCGD(3), BFCA(4) and ACC’C(5), and each has a space for five quadrilaterals, which has its own special effect and space effect on production.
Generally speaking, each side of its unit forms cycle method through moving 1/2 side length by spiral method and connects in four directions, so it is called four directions continuous spiral method, which is shown in 1/2×1/2.
3. Spiral Cycle Connection Rule Figure 8

A. Clockwise Spiral Cycle Method
Full line segment HD and BF, GC and AE are in connection. Hidden line segment AH, FC, DG and EB place of not connection, so they shall not be limited by unit boundary and leave appropriate space.
B. Anticlockwise Spiral Cycle Method
It is the converse type of clockwise spiral cycle against A. Hidden line segment AH and FC, DG and EB are in connection. Full line segment HD, BF, GC and AE of not connection and not limited by unit boundary.
ⅡFormation of Ladder Unit
The butt unit formed by two spiral cycle in Figure 7 has five spaces of each, which shall be applied in design and used for adjust the space size as you like. It is also the feature of spiral cycle type. not use this space this cycle type shall also be established through full place pattern. Please see figure 7 again for the features of in the two new butt unit A’BAD and CBC’D: there are several unit exactly have several space, thus a ladder shape shall be constructed through combine one of the upper one space and lower one unit together. Then with ladder shape do unit in design full place pattern. Finally the ladder unit emerges for utilizing in production.
Ⅲ Connection method and cut draw method for Ladder Unit
1. Connection method Figure 9

Connect AG and DC, AF and HC, GB and FE, BH and ED.
2. Cut and Design draw method.
A: Figure 10: clip △GBH in figure 9, attach it in the vacancy of △FED in figure 10, and connect GB and FE, BH and ED design draw Therefore, the parallelepiped AGHCDF is shaped.


B: Figure 11: clip at the position from G to D in figure 10 and move quadrilateral AGDF, so as to connect AG and DC design draw.

C: Figure 12: move quadrilateral GHCD in figure 11 after B item, so as to connect AF and HC design draw. So all joint points of ladder unit have been drawn, namely the design of such pattern unit has been done.


ⅣComposition of Ladder Unit
Figure a is composition shaped of utilizing space figure b is composition shaped of not utilizing space full place pattern.
1. One point, figure 13
2. Two points, figure 14
3. Three points, figure 15
4. Tour points, figure 16
5. Five points, figure 17
6. Six points, figure 18
7. Seven points, figure 19
8. Eight points, figure20 





The first needle is flat stitch; the second needle is stitch of needle; the third needle is the adding stitch between the second and first, in a straight line with the two stitches; the fourth needle move one needle distance for matching with top right corner stitch of zincograph unit, the fifth needle is adding stitch between the fourth and second needle, in a straight line with the four stitches; the sixth needle move half needle distance as one stitch; the seventh needle is as two stitches; the eighth needle is as three stitches; the ninth needle is as four stitches; the tenth needle is as five stitches; the eleventh needle is as six stitches, after the stitch collocation shall be circulated in following procedures until the width required for production is achieved.
Reduce machine carving process: raise all adding needles for first order of reducing carving, and then raise all needles after checking and supplementary carving for missing flower form. Move the refuting grid to second order, and then put down all adding needles for second reducing carving. Take down the cylinder from machine after checking half order is vacancy, afterwards, fit the second cylinder until the complete set of cylinder whole finished.
For the half-order reducing carving, select the gear of five order mumber and move grid to the second order, without any change in other operation.
Ⅵ Type and Feature of Spiral Cycle
1. Square form: while the unit direction all around cycle, the fraction ratio for movement of joint point of its horizontal side and vertical side is equal.
(1) × spiral form Figure 21