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(1) Cobweb Posets


Note. Cobweb is an infinite graded poset designated by natural numbers' valued sequence F = {nF}n≥0.

Cobweb Poset designated by F-Fibonacci numbers
Fig.1 Cobweb Poset designated by F-Fibonacci numbers
Cobweb Poset designated by F-Gaussian integers
Fig.2 Cobweb Poset designated by F-Gaussian integers

(2) Other relevant Cobweb Posets structures


Note. There are two main finite cobweb structures - blocks Pm and layers <Φk → Φn>.


Cobweb blocks designated by F-Gaussian integers
Fig.3 Cobweb blocks designated by F-Gaussian integers
Cobweb blocks designated by F-Natural numbers
Fig.4 Cobweb blocks designated by F-Natural numbers

Note. Cobweb block σPm is obtained from Pm up to permutation σ of its levels Φ.


Example of Cobweb blocks σP3
Fig.5 Example of Cobweb blocks σP3
Example of Cobweb Layer
Fig.6 Example of Cobweb Layer <Φ2 → Φ4>
Example of Cobweb Multi Block
Fig.7 Example of Cobweb Multi Block

(3) Cobweb Tiling and Multi Tiling


Example of Cobweb Tiling
Fig.8 Example of Cobweb Tiling

Note. Cobweb Tiling is a Cobweb partition of certain layer into specific blocks σP.


Example of Cobweb Multi Tiling
Fig.9 Example of Cobweb Multi Tiling

(4) Geometric interpretation of Cobweb Tiling phenomenon


Note. In Geometric interpretation the Cobweb posets are special hiper boxes that size of sizes is designated by sequence F.

Tiles of F-Natural numbers' Cobweb poset
Fig.10 Tiles of F-Natural numbers' Cobweb poset
Tiles of F-Fibonacci numbers' Cobweb poset
Fig.11 Tiles of F-Fibonacci numbers' Cobweb poset
2D Tiling of Natural numbers' Cobweb Poset
Fig.12 2D Tiling of Natural numbers' Cobweb Poset
3D Tiling of Natural numbers' Cobweb Poset
Fig.13 3D Tiling of Natural numbers' Cobweb Poset
Other Cobweb poset tiling
Fig.14 Other Cobweb poset tiling

(5) Other

Zeta matrixes of Cobweb posets
Fig.15 Zeta matrixes of Cobweb posets
Families of Cobweb sequences
Fig.16 Families of Cobweb sequences

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