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Computational Pathways in FTSPs
#1
the PDF shows computational pathways in
Functional Type Shifting Patterns
Smile
the Ordertypes 4, 5, 6, and 7 can be seen clearly in the PDF animation
corresponding to hyper4, 5, 6, and 7
of the form n(^k)n using Knuth up arrow notation
where k = 2, 3, 4, and 5
they are easier to follow and more extensible than the formulae expressions.

Mulanept form for hyper7 or heptation, is a bit more difficult to understand than hyper6 or hexation, with the outer seed value of the hyper7 pure noptile corresponding to the hyperexponent of n(^5)n, the actual combinatorics is always a little fiddly as the outer seed value counts one seedvalue and the hyper6 pure noptiles and are well defined being delineated by the vertical braces (2 are visible the others implied) represented by the vertical blocks of 3 brown squares

The visualisation uses the natural folding pattern, fold left, fold up.
FTSPs is the name for any well defined interpretation, usually corresponding to operations, hence the term " nopt " standing for nested operational power tower.
Sleepy

When looking at the transitions, the squares with borders have a particular and well defined meaning according to the relevant information stages in the computational pathway.


.pdf   copathways.pdf (Size: 347.87 KB / Downloads: 242)



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#2
For pure noptiles there are 8 possible folding patterns:
FLU, FLD, FRU, FRD, FUL, FDL, FUR, FDR
F=Fold L=Left R=Right D=Down U=Up
Example: FLU = Fold Left then Fold Up
FLU is the most natural folding pattern and is used for the other animations
These folding patterns apply to the pure noptiles, the tiling patterns for functional type shifting patterns aka nopt structures
In the PDF " foldnopts " all folding patterns for
ordertypes 4, 5, 6 and 7 are shown
All the details, terminology and examples are in the other papers


.pdf   foldnopts.pdf (Size: 811.58 KB / Downloads: 204)

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