Math::PlanePath - points on a path through the 2-D plane River stage one • 4 direct dependents • 5 total dependents

This is a base class for some mathematical paths which map an integer position $n to and from coordinates "$x,$y" in the 2D plane. The current classes include the following. The intention is that any "Math::PlanePath::Something" is a PlanePath, and s...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::File - points from a file River stage one • 4 direct dependents • 5 total dependents

This path reads X,Y points from a file to present in PlanePath style. It's slightly preliminary yet but is handy to get numbers from elsewhere into a PlanePath program. The intention is to be flexible about the file format and to auto-detect as far a...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::Rows - points in fixed-width rows River stage one • 4 direct dependents • 5 total dependents

This path is rows of a given fixed width. For example width=7 is width => 7 3 | 22 23 24 ... 2 | 15 16 17 18 19 20 21 1 | 8 9 10 11 12 13 14 Y=0 | 1 2 3 4 5 6 7 ------------------------------- X=0 1 2 3 4 5 6 N Start The default is to number points s...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::Hypot - points in order of hypotenuse distance River stage one • 4 direct dependents • 5 total dependents

This path visits integer points X,Y in order of their distance from the origin 0,0, or anti-clockwise from the X axis among those of equal distance,...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::Corner - points shaped around in a corner River stage one • 4 direct dependents • 5 total dependents

This path puts points in layers working outwards from the corner of the first quadrant....

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::MPeaks - points in expanding M shape River stage one • 4 direct dependents • 5 total dependents

This path puts points in layers of an "M" shape...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::CCurve - Levy C curve River stage one • 4 direct dependents • 5 total dependents

This is an integer version of the "C" curve by Lévy. "Les Courbes Planes ou Gauches et les Surfaces Composée de Parties Semblables au Tout", Journal de l'École Polytechnique, July 1938 pages 227-247 and October 1938 pages 249-292 <http://gallica.bnf....

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::NumSeq::PlanePathN - sequence of N values from PlanePath module River stage one • 4 direct dependents • 5 total dependents

This module presents N values from a "Math::PlanePath" as a sequence. The default is the X axis, or the "line_type" parameter (a string) can choose among "X_axis" X axis "Y_axis" Y axis "X_neg" X negative axis "Y_neg" Y negative axis "Diagonal" leadi...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::Columns - points in fixed-height columns River stage one • 4 direct dependents • 5 total dependents

This path is columns of a given fixed height. For example height 5 would be | 4 | 5 10 15 20 <--- height==5 3 | 4 9 14 19 2 | 3 8 13 18 1 | 2 7 12 17 ... Y=0 | 1 6 11 16 21 ---------------------- X=0 1 2 3 4 ... N Start The default is to number point...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::LTiling - 2x2 self-similar of four pattern parts River stage one • 4 direct dependents • 5 total dependents

This is a self-similar tiling by "L" shapes. A base "L" is replicated four times with end parts turned +90 and -90 degrees to make a larger L, +-----+-----+ |12 | 15| | +--+--+ | | |14 | | +--+ +--+--+ | | |11 | | +--+ +--+ |13 | | | +-----+ +-----+-...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::HexArms - six spiral arms River stage one • 4 direct dependents • 5 total dependents

This path follows six spiral arms, each advancing successively, ...--66 5 \ 67----61----55----49----43 60 4 / \ \ ... 38----32----26----20 37 54 3 / \ \ \ 44 21----15---- 9 14 31 48 ... 2 / / \ \ \ \ \ 50 27 10---- 4 3 8 25 42 65 1 / / / / / / / 56 3...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::GrayCode - Gray code coordinates River stage one • 4 direct dependents • 5 total dependents

This is a mapping of N to X,Y using Gray codes. 7 | 63-62 57-56 39-38 33-32 | | | | | 6 | 60-61 58-59 36-37 34-35 | 5 | 51-50 53-52 43-42 45-44 | | | | | 4 | 48-49 54-55 40-41 46-47 | 3 | 15-14 9--8 23-22 17-16 | | | | | 2 | 12-13 10-11 20-21 18-19 |...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::ChanTree - tree of rationals River stage one • 4 direct dependents • 5 total dependents

This path enumerates rationals X/Y in a tree as per Song Heng Chan, "Analogs of the Stern Sequence", Integers 2011, <http://www.integers-ejcnt.org/l26/l26.pdf> The default k=3 visits X,Y with one odd, one even, and perhaps a common factor 3^m....

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::KochPeaks - Koch curve peaks River stage one • 4 direct dependents • 5 total dependents

This path traces out concentric peaks made from integer versions of the self-similar "KochCurve" at successively greater replication levels. 29 9 / \ 27----28 30----31 8 \ / 23 26 32 35 7 / \ / \ / \ 21----22 24----25 33----34 36----37 6 \ / 20 38 5 ...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::HexSpiral - integer points around a hexagonal spiral River stage one • 4 direct dependents • 5 total dependents

This path makes a hexagonal spiral, with points spread out horizontally to fit on a square grid. 28 -- 27 -- 26 -- 25 3 / \ 29 13 -- 12 -- 11 24 2 / / \ \ 30 14 4 --- 3 10 23 1 / / / \ \ \ 31 15 5 1 --- 2 9 22 <- Y=0 \ \ \ / / 32 16 6 --- 7 --- 8 21 ...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::KochCurve - horizontal Koch curve River stage one • 4 direct dependents • 5 total dependents

This is an integer version of the self-similar Koch curve, Helge von Koch, "Une Méthode Géométrique Élémentaire pour l'Étude de Certaines Questions de la Théorie des Courbes Planes", Acta Arithmetica, volume 30, 1906, pages 145-174. <http://archive.o...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::BetaOmega - 2x2 half-plane traversal River stage one • 4 direct dependents • 5 total dependents

This is an integer version of the Beta-Omega curve Jens-Michael Wierum, "Definition of a New Circular Space-Filling Curve: Beta-Omega-Indexing", Technical Report TR-001-02, Paderborn Center for Parallel Computing, March 2002. The curve form here make...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::Diagonals - points in diagonal stripes River stage one • 4 direct dependents • 5 total dependents

This path follows successive diagonals going from the Y axis down to the X axis. 6 | 22 5 | 16 23 4 | 11 17 24 3 | 7 12 18 ... 2 | 4 8 13 19 1 | 2 5 9 14 20 Y=0 | 1 3 6 10 15 21 +------------------------- X=0 1 2 3 4 5 N=1,3,6,10,etc on the X axis is...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::Staircase - integer points in stair-step diagonal stripes River stage one • 4 direct dependents • 5 total dependents

This path makes a staircase pattern down from the Y axis to the X,...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

Math::PlanePath::HIndexing - self-similar right-triangle traversal River stage one • 4 direct dependents • 5 total dependents

This is an infinite integer version of H-indexing per Rolf Niedermeier, Klaus Reinhardt and Peter Sanders, "Towards Optimal Locality In Mesh Indexings", Discrete Applied Mathematics, volume 117, March 2002, pages 211-237. <http://theinf1.informatik.u...

KRYDE/Math-PlanePath-127 - 17 Aug 2019 13:14:00 GMT

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