perl-Math-PlanePath

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 supporting base classes or
related things are further down like 'Math::PlanePath::Base::Xyzzy'.
SquareSpiral           four-sided spiral
PyramidSpiral          square base pyramid
TriangleSpiral         equilateral triangle spiral
TriangleSpiralSkewed   equilateral skewed for compactness
DiamondSpiral          four-sided spiral, looping faster
PentSpiral             five-sided spiral
PentSpiralSkewed       five-sided spiral, compact
HexSpiral              six-sided spiral
HexSpiralSkewed        six-sided spiral skewed for compactness
HeptSpiralSkewed       seven-sided spiral, compact
AnvilSpiral            anvil shape
OctagramSpiral         eight pointed star
KnightSpiral           an infinite knight's tour
CretanLabyrinth        7-circuit extended infinitely

SquareArms             four-arm square spiral
DiamondArms            four-arm diamond spiral
AztecDiamondRings      four-sided rings
HexArms                six-arm hexagonal spiral
GreekKeySpiral         square spiral with Greek key motif
MPeaks                 "M" shape layers

SacksSpiral            quadratic on an Archimedean spiral
VogelFloret            seeds in a sunflower
TheodorusSpiral        unit steps at right angles
ArchimedeanChords      unit chords on an Archimedean spiral
MultipleRings          concentric circles
PixelRings             concentric rings of midpoint pixels
FilledRings            concentric rings of pixels
Hypot                  points by distance
HypotOctant            first octant points by distance
TriangularHypot        points by triangular distance
PythagoreanTree        X^2+Y^2=Z^2 by trees

PeanoCurve             3x3 self-similar quadrant
PeanoDiagonals         across unit squares
WunderlichSerpentine   transpose parts of PeanoCurve
HilbertCurve           2x2 self-similar quadrant
HilbertSides           along sides of unit squares
HilbertSpiral          2x2 self-similar whole-plane
ZOrderCurve            replicating Z shapes
GrayCode               Gray code splits
WunderlichMeander      3x3 "R" pattern quadrant
BetaOmega              2x2 self-similar half-plane
AR2W2Curve             2x2 self-similar of four parts
KochelCurve            3x3 self-similar of two parts
DekkingCurve           5x5 self-similar, edges
DekkingCentres         5x5 self-similar, centres
CincoCurve             5x5 self-similar

ImaginaryBase          replicate in four directions
ImaginaryHalf          half-plane replicate three directions
CubicBase              replicate in three directions
SquareReplicate        3x3 replicating squares
CornerReplicate        2x2 replicating "U"
LTiling                self-similar L shapes
DigitGroups            digits grouped by zeros
FibonacciWordFractal   turns by Fibonacci word bits

Flowsnake              self-similar hexagonal tile traversal
FlowsnakeCentres         likewise but centres of hexagons
GosperReplicate        self-similar hexagonal tiling
GosperIslands          concentric island rings
GosperSide             single side or radial

QuintetCurve           self-similar "+" traversal
QuintetCentres           likewise but centres of squares
QuintetReplicate       self-similar "+" tiling

DragonCurve            paper folding
DragonRounded          paper folding rounded corners
DragonMidpoint         paper folding segment midpoints
AlternatePaper         alternating direction folding
AlternatePaperMidpoint alternating direction folding, midpoints
TerdragonCurve         ternary dragon
TerdragonRounded       ternary dragon rounded corners
TerdragonMidpoint      ternary dragon segment midpoints
AlternateTerdragon     alternate ternary dragon
R5DragonCurve          radix-5 dragon curve
R5DragonMidpoint       radix-5 dragon curve midpoints
CCurve                 "C" curve
ComplexPlus            base i+realpart
ComplexMinus           base i-realpart, including twindragon
ComplexRevolving       revolving base i+1

SierpinskiCurve        self-similar right-triangles
SierpinskiCurveStair   self-similar right-triangles, stair-step
HIndexing              self-similar right-triangles, squared up

KochCurve              replicating triangular notches
KochPeaks              two replicating notches
KochSnowflakes         concentric notched 3-sided rings
KochSquareflakes       concentric notched 4-sided rings
QuadricCurve           eight segment zig-zag
QuadricIslands           rings of those zig-zags
SierpinskiTriangle     self-similar triangle by rows
SierpinskiArrowhead    self-similar triangle connectedly
SierpinskiArrowheadCentres  likewise but centres of triangles

Rows                   fixed-width rows
Columns                fixed-height columns
Diagonals              diagonals between X and Y axes
DiagonalsAlternating   diagonals Y to X and back again
DiagonalsOctant        diagonals between Y axis and X=Y centre
Staircase              stairs down from the Y to X axes
StaircaseAlternating   stairs Y to X and back again
Corner                 expanding stripes around a corner
CornerAlternating      expanding up and down around a corner
PyramidRows            expanding stacked rows pyramid
PyramidSides           along the sides of a 45-degree pyramid
CellularRule           cellular automaton by rule number
CellularRule54         cellular automaton rows pattern
CellularRule57         cellular automaton (rule 99 mirror too)
CellularRule190        cellular automaton (rule 246 mirror too)
UlamWarburton          cellular automaton diamonds
UlamWarburtonQuarter   cellular automaton quarter-plane

DiagonalRationals      rationals X/Y by diagonals
FactorRationals        rationals X/Y by prime factorization
GcdRationals           rationals X/Y by rows with GCD integer
RationalsTree          rationals X/Y by tree
FractionsTree          fractions 0<X/Y<1 by tree
ChanTree               rationals X/Y multi-child tree
CfracDigits            continued fraction 0<X/Y<1 by digits
CoprimeColumns         coprime X,Y
DivisibleColumns       X divisible by Y
WythoffArray           Fibonacci recurrences
WythoffPreliminaryTriangle
PowerArray             powers in rows
File                   points from a disk file


And in the separate Math-PlanePath-Toothpick distribution
ToothpickTree          pattern of toothpicks
ToothpickReplicate     same by replication rather than tree
ToothpickUpist         toothpicks only growing upwards
ToothpickSpiral        toothpicks around the origin

LCornerTree            L-shape corner growth
LCornerReplicate       same by replication rather than tree
OneOfEight
HTree                  H shapes replicated


The paths are object oriented to allow parameters, though many have none.
See 'examples/numbers.pl' in the Math-PlanePath sources for a sample
printout of numbers from selected paths or all paths.

          

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License: GPL-3.0-or-later
URL: https://metacpan.org/release/Math-PlanePath