By A G Schaake; J C Turner; D A Sedgwick
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Extra resources for Braiding : new and automatic methods for constructing knots and braids
R-L Fig. 40 - The resulting Algorithm-tables. 1 : - 0 8'-4: P-11: x-10 Foundaclon T u r k ' s heod 5p/4b Fig. 41 - The half-cycles in the braiding of the foundation Turk's Head Knot. A-2: A-0: 0 ' - 4 : P-12: X-10 Interwoven T u r k ' s head 7pI4b 2 ... n .... Half -oyole 2 Fig. 42 - The half-cycles in the braiding of the interwoven Turk's Head Knot. After substitution of A = 2 , L = 1, R = 1in the Algorithm-table for B* = 4 , s = 7 we obtain L - 1 = 0 , R - 1 = 0 , A - 1 = 1 and hence the lower table of Fig.
This table supplies us with the following braiding algorithm associated with 3 t e p 1': 1. L-R : free run. 2. R+L: 0. 0. 3. L+R: 11-0. 4. R-L: 5. L+R : 21-0. 0-21-0. 6. R + L : 7. L ---+ R : 0 - U - 0 . 8. R-+L : U-0-U-0. The respective grid-diagrams associated with the above half-cycles are given in Fig. 41. After completion of 'Step 1'' we are ready to start with 'Step 2'' which is the interbraidig of the Turk's Head Knot with s = 7 parts. When this interbraiding is completed, we have two left bight-boundaries and two right bight-boundaries; hence A = 2 In the grid-diagram belonging to the Standard Herringbone Pineapple Knot which is obtained after the completion of the Steps 1 and 2, a lower-left to upper-right half-cycle of the 'Step 1' Turk's Head Knot runs from the left bight-boundary 2 to the right bight-boundary 2, and a lower-left to upper-right half-cycle of the 'Step 2' Turk's Head Knot runs from the left bight-boundary 1 to the right bight-boundary 1.
Fig. 43 - The positioning of the interbraided Turk's Head Knots. Since A = 5 we can braid this Standard Herringbone Pineapple Knot in 5! = 120 different wavs. We shall discuss in detail two out of these 120 different wavs. This should provide the reader with a thorough grounding in these new methods, so that he will be able to braid any Standard Herringbone Pineapple Knot with ease. 44. As mentioned before, it is essential that, for a good understanding, the reader draws up some grid-diagrams of different Standard Herringbone Pineapple Knots on Isometric graph paper (see Ref.