Patterned framework for a papermaking belt

1. A patterned framework for a papermaking belt having an embryonic-web-contacting surface for carrying an embryonic web of paper fibers and a non-embryonic-web-contacting surface opposite said embryonic-web-contacting surface, said patterned framework comprising:

a continuous network region; and,

a plurality of discrete regions, said discrete regions being isolated from one another by said continuous network region; and,

wherein said continuous network region comprises a pattern formed therein, said pattern comprising a plurality of tessellating unit cells;

wherein each cell of said plurality of unit cells comprises a center and at least two continuous land areas extending in at least two directions from said center, each discrete region being surrounded by a portion of at least one of said continuous land areas;

wherein at least one of said continuous land areas at least bifurcates to form a continuous land area portion having a first width, W 1 , before said bifurcation and at least two continuous land area portions having a second width, W 2 , and a third width, W 3 , respectively, after said bifurcation, each of said at least two continuous land area portions being in continuous communication with said continuous land area portion having said first width; and,

wherein each of said at least two continuous land area portions are disposed at an angle (θ) relative to each other ranging from about 1 degree to about 180 degrees and W 1 ≦W 2 +W 3 .

2. The patterned framework for a papermaking belt of claim 1 wherein said first width is greater than said second width.

3. The patterned framework for a papermaking belt of claim 1 wherein said angle (θ) ranges from about 40 degrees to about 85 degrees.

4. The patterned framework for a papermaking belt of claim 1 wherein said pattern comprises a geometric shape that can be split into parts, each of which is a reduced-size copy of the whole.

5. The patterned framework for a papermaking belt of claim 4 wherein said pattern is selected from the group consisting of fractals, constructals, and combinations thereof.

6. The patterned framework for a papermaking belt of claim 5 wherein said fractal is selected from the group consisting of escape-time fractals, Mandelbrot set fractals, Julia set fractals, Burning Ship fractals, Nova fractals, Lyapunov fractals, an iterated function system, Random fractals, Strange attractors, and combinations thereof.

7. The patterned framework for a papermaking belt of claim 5 wherein said fractal is a Mandelbrot fractal where z 1 =(z 0 ) 2 +z 0 and where z x+1 =((z x ) 2 +z x .

8. A patterned framework for a papermaking belt having an embryonic-web-contacting surface for carrying an embryonic web of paper fibers and a non-embryonic-web-contacting surface opposite said embryonic-web-contacting surface, said patterned framework comprising:

a continuous network region; and,

a plurality of discrete regions, said discrete regions being isolated from one another by said continuous network region;

wherein said continuous network region comprises a pattern formed therein, said pattern comprising plurality of tessellating unit cells;

wherein each cell of said plurality of unit cells comprises a center, at least two continuous land areas extending in at least two directions from said center, each discrete region being surrounded by a portion of at least one of said continuous land areas;

wherein at least one of said continuous land areas at least bifurcates to form a continuous land area portion having a first width, W 1 , before said bifurcation and at least two continuous land area portions, a first of said at least two continuous land area portions having a second width, W 2 , after said bifurcation, a second of said at least two continuous land area portions having a third width, W 3 , after said bifurcation, each of said at least two continuous land area portions being in continuous communication with said continuous land area portion having said first width; and,

wherein each of said at least two continuous land area portions are disposed at an angle (θ) relative to each other ranging from about 1 degree to about 180 degrees and W 1 <W 2 +W 3 .

9. The patterned framework for a papermaking belt of claim 8 wherein said first width is greater than said second width and said third width.

10. The patterned framework for a papermaking belt of claim 9 wherein said second width is greater than said third width.

11. The patterned framework for a papermaking belt of claim 8 wherein said angle (θ) ranges from about 40 degrees to about 85 degrees.

12. The patterned framework for a papermaking belt of claim 11 wherein said second width is equal to said third width.

13. The patterned framework for a papermaking belt of claim 8 wherein said pattern comprises a geometric shape that can be split into parts, each of which is a reduced-size copy of the whole.

14. The patterned framework for a papermaking belt of claim 13 wherein said pattern is selected from the group consisting of fractals, constructals, and combinations thereof.

15. The patterned framework for a papermaking belt of claim 14 wherein said fractal is selected from the group consisting of escape-time fractals, Mandelbrot set fractals, Julia set fractals, Burning Ship fractals, Nova fractals, Lyapunov fractals, an iterated function system, Random fractals, Strange attractors, and combinations thereof.

16. The patterned framework for a papermaking belt of claim 14 wherein said fractal is a Mandelbrot fractal where z 1 =(z 0 ) 2 +z 0 and where z x+1 =((z x ) 2 +z x .

17. A patterned framework for a papermaking belt having an embryonic-web-contacting surface for carrying an embryonic web of paper fibers and a non-embryonic-web-contacting surface opposite said embryonic-web-contacting surface, said patterned framework comprising:

a continuous region; and,

a plurality of discrete regions, said discrete regions being isolated from one another by said continuous region;

wherein said continuous region comprises a pattern formed therein, said pattern comprising a plurality of tessellating unit cells;

wherein each cell of said plurality of tessellating unit cells comprises a center, at least two continuous pillow areas extending in at least two directions from said center, each discrete region being surrounded by a portion of at least one of said continuous region;

wherein at least one of said continuous regions at least bifurcates to form a continuous portion having a first width, W 1 , before said bifurcation and at least two continuous portions having a second width, W 2 , and a third width, W 3 , after said bifurcation respectively, each of said at least two continuous portions having said second and third widths being in continuous communication with said continuous portion having said first width; and,

wherein each of said at least two continuous portions are disposed at an angle (θ) relative to each other ranging from about 1 degree to about 180 degrees and W 1 ≦W 2 +W 3 .

18. The patterned framework for a papermaking belt of claim 17 wherein said pattern is selected from the group consisting of fractals, constructals, and combinations thereof.

19. The patterned framework for a papermaking belt of claim 18 wherein said fractal is a Mandelbrot fractal where z 1 =(z 0 ) 2 +z 0 and where z x+1 =((z x ) 2 +z x .

20. The patterned framework for a papermaking belt of claim 17 wherein said angle (θ) ranges from about 40 degrees to about 85 degrees.