perl-Math-PlanePath

Points on a path through the 2-D plane

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.