ies corresponding to short subchains. These entries are colored gray (see the color scale at the right of Fig. 1) indicating that Vans Boots On Feet the dominant knot type is the unknot, 01, for the closures of these short subchains. As one moves away from the center and closer to the edge of the disk matrix, the individual cells represent subchains that have sufficient length to form trefoil knots as the dominant knot type upon closure. These cells are colored red to indicate the trefoil knot. Notice that cells close to Vans Gilbert Crockett Pro Red
Since the knot configuration, a KnotPlot trefoil, is spread out it takes quite a bit of length to realize the global knot type. the coloring starts much closer to the center of the disk matrices) and where there is a more diverse spectrum of subknots. Note that we only see unknot and trefoil subchains Vans Gray Gum Sole
For the explanation see the main text. The underlying brick wall pattern of the matrix is a consequence of the fact that the longitudinal position of the cell indicates the position of the center vertex of the represented chains. For subchains with even numbers of segments, the centers of these subchains fall at a vertex. For subchains with odd numbers of segments, the centers lie at the middle point of a segment. For each knotted configuration, there is a shortest length at which the global knot is realized. The minimal length subchain or subchains realizing the host knot is ca.
the border between the zones of the 31 knot and the unknot have colors of decreased intensity (red and gray, respectively). This border effect indicates that the corresponding subchains show a decreasing preference to form the indicated knot types as the closures also create increasing numbers of other knot types, for example those knot types that dominate the other side of the apparent border.
in this highly regular trefoil knot due to its relatively simple spatial structure. Similar matrices for other knots are presented in Figs. 2 6. The right panel and the Vans Gum Sole
drawing between the two panels are intended to explain the principle of the matrix.
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