Computational Pathways in FTSPs - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)+--- Thread: Computational Pathways in FTSPs ( /showthread.php?tid=892) |

Computational Pathways in FTSPs - MikeSmith - 06/23/2014
the PDF shows computational pathways in Functional Type Shifting Patterns 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. 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. [attachment=1072] RE: Computational Pathways in FTSPs - MikeSmith - 06/25/2014
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 [attachment=1074] |