# Math-PlanePath Gallery

See also examples/numbers.pl in the Math-PlanePath sources for a sample program printing text numbers. Module links are to the online man pages, and see the full list of online man pages.

### TriangleSpiralSkewed

In the default skew="left", and also "right", "up" and "down. See Math::PlanePath::TriangleSpiralSkewed.

### GreekKeySpiral

turns=2 (the default)

turns=5

turns=1

See Math::PlanePath::GreekKeySpiral. Have a look also at Jo Edkins Greek Key pages.

### Corner

The second image is with wider=4. See Math::PlanePath::Corner.

### CornerAlternating

The second image is with wider=4. See Math::PlanePath::CornerAlternating.

### StaircaseAlternating

The first image lines don't show direction, so it looks the same as the plain Staircase but is going alternately up and back. The second image is with the end_type="square" option. See Math::PlanePath::StaircaseAlternating.

### MPeaks

(See Math::PlanePath::MPeaks.)

### PyramidRows

(See PyramidRows.)

### CellularRule

Samples of rule=30 and rule=73. See Math::PlanePath::CellularRule.

### CellularRule57

See Math::PlanePath::CellularRule57. The second image is rule 57 mirrored, which is rule 99.

### CellularRule190

See Math::PlanePath::CellularRule190. The second image is rule 190 mirrored, which is rule 246.

### VogelFloret

Default phi, and other rotations sqrt 2 and sqrt 5. See Math::PlanePath::VogelFloret.

### PeanoCurve

In the usual base 3 ternary, and higher radix=7.
See Math::PlanePath::PeanoCurve, and Peano's 1890 paper.

### PeanoDiagonals

Second image has corners rounded to show the pattern.
See Math::PlanePath::PeanoDiagonals, and E.H. Moore's 1900 paper figure 3 for this sort of drawing (here is transpose).

### HilbertCurve and HilbertSpiral

If you ever wanted a jumper which is everywhere continuous but nowhere differentiable, try woolly thoughts.

### ZOrderCurve

Here's a cute image of the fibbinary numbers plotted on ZOrderCurve radix 2,

### GrayCode

In the default binary, and higher radix=4. See Math::PlanePath::GrayCode.

### WunderlichSerpentine

The default "alternating", and also "coil" order and radix=7 "alternating". See Math::PlanePath::WunderlichSerpentine, and Wunderlich's 1972 paper from this page in German, scanned pdf.

### WunderlichMeander

See Math::PlanePath::WunderlichMeander, and Wunderlich's 1972 paper from this page in German scanned pdf.

### BetaOmega

See Math::PlanePath::BetaOmega, and papers by Jens-Michael Wierum: definition cached at citeseer, and CCCG paper.

### AR2W2Curve

start_shape=A1 (the default)
start_shape=D2
start_shape=B2
start_shape=B1rev
start_shape=D1rev
start_shape=A2rev
See Math::PlanePath::AR2W2Curve, and the paper by Asano, Ranjan, Roos, Welzl and Widmayer.

### KochelCurve

See Math::PlanePath::KochelCurve, and the paper by Herman Haverkort.

### DekkingCurve and DekkingCentres

See Math::PlanePath::DekkingCurve and Math::PlanePath::DekkingCentres.

### ImaginaryHalf

In the default radix=2, and higher radix=5. Second row is the digit order variations XXY, YXX, XnYX, XnXY, YXnX.

### LTiling

(See Math::PlanePath::LTiling.)

### DigitGroups

In the default radix=2, and higher radix=5. These samples are drawn to just 0 to 2047 and 0 to 15624 respectively to show some of the shape, since continuing on they fill the entire plane. (See Math::PlanePath::DigitGroups.)

### GosperReplicate

Drawn just N=0 to N=2400 (=7^4-1) to show the shape, since continuing on fills the entire plane. See Math::PlanePath::GosperReplicate.

### QuintetReplicate

Drawn just 0 to 3124 (5^5-1) to show the shape, since continuing on fills the entire plane. See Math::PlanePath::QuintetReplicate.

### KochCurve, KochPeaks and KochSnowflakes

See Math::PlanePath::KochCurve, Math::PlanePath::KochPeaks and Math::PlanePath::KochSnowflakes, and Koch's 1904 paper at archive.org (pages 145-174)

### KochSquareflakes

Second image is with the "inward" option. See Math::PlanePath::KochSquareflakes.

### SierpinskiTriangle

align=triangular (the default)
align=right
align=left, showing X<0
align=diagonal
See Math::PlanePath::SierpinskiTriangle.

align=triangular (the default)
align=right
align=left, showing X<0
align=diagonal

Alignments "triangular", "right" "left", "diagonal". See Math::PlanePath::SierpinskiArrowheadCentres.

### SierpinskiCurve

Default arms=1 and a full arms=8. See Math::PlanePath::SierpinskiCurve.

### SierpinskiCurveStair

Default arms=1 and a full arms=8. See Math::PlanePath::SierpinskiCurveStair.

### DragonRounded

1 arm and 3 arms. See Math::PlanePath::DragonRounded.

### DragonMidpoint

1 arm and 4 arms. See Math::PlanePath::DragonMidpoint.

### AlternatePaper

The second image has the vertices rounded off to show the pattern. See Math::PlanePath::AlternatePaper.

### AlternatePaperMidpoint

1 arm and 8 arms. See Math::PlanePath::AlternatePaperMidpoint.

### TerdragonRounded

1 arm and 6 arms. See Math::PlanePath::TerdragonRounded.

### TerdragonMidpoint

1 arm and 6 arms. See Math::PlanePath::TerdragonMidpoint.

### TerdragonRounded

1 arm and 6 arms. See Math::PlanePath::TerdragonRounded.

### R5DragonCurve

1 arm and 4 arms. The second and third images have the vertices rounded off to show the pattern. See Math::PlanePath::R5DragonCurve.

### R5DragonMidpoint

1 arm and 4 arms. See Math::PlanePath::R5DragonMidpoint.

### CCurve

(See Math::PlanePath::CCurve.)

### ComplexPlus

Default i+1, and with realpart=2 for i+2 . See Math::PlanePath::ComplexPlus.

### ComplexMinus

Default i-1, and with realpart=2 for i-2. These samples are points 0 to 1023 and 0 to 3124 respectively to show the shape, since continuing on they fill the entire plane.
(See Math::PlanePath::ComplexMinus.)

### ComplexRevolving

This sample is points 0 to 1023 to show the shape, since continuing on it fills the entire plane. (See Math::PlanePath::ComplexRevolving.)

### Hypot and HypotOctant

(See Hypot and Math::PlanePath::HypotOctant.)

### TriangularHypot

In the default "even" points, and "odd", "all", "hex", "hex_rotated" and "hex_centred". See Math::PlanePath::TriangularHypot.)

### PythagoreanTree

UAD tree lines, high to low and low to high
FB and UMT tree lines.
UArD tree rows in AB and PQ
AB points.
AC points.
BC points (see the POD on why it's straight lines).
SM points, short and medium legs.
SC points, short leg and hypotenuse, 0 < X < sqrt(1/2)*Y.
MC points, medium leg and hypotenuse, wedge sqrt(1/2)*Y < X < Y.

See Math::PlanePath::PythagoreanTree. Also see H. Lee Price's paper at arxiv.org on FB, and my mathematical write-up on UMT.

### CfracDigits

radix=2 first few points showing growth pattern

### GcdRationals

pairs_order="rows" (the default)
pairs_order="rows_reverse"
pairs_order="rows" to N=68*67/2 showing growth pattern.
pairs_order=diagonals_down to N=47^2 showing growth pattern.

Notice in the last two images how growth rows and diagonals are sheared down to wedges of successive integer part int(X/Y). The wedges are slope X=2*Y, X=3*Y, etc. The diagonals case nicely covers the quadrilateral X≤d, X+Y≤2*d.

See Math::PlanePath::GcdRationals and Lance Fortnow's blog entry.

### RationalsTree

Points visited
SB as tree and by rows
CW as tree.
HCS, AYT as trees.
Bird, Drib as trees.
L as tree.
See Math::PlanePath::RationalsTree.

### ChanTree

k=3 as points and tree lines
k=4 and k=5 as points
See Math::PlanePath::ChanTree and paper by "Analogs of the Stern Sequence", Integers 2011, .

### DivisibleColumns

With divisor_type="all" and "proper". See Math::PlanePath::DivisibleColumns.

### UlamWarburton

First few points to show the shape.
Tree structure.
parts=2 line segments.
parts=1 tree structure.
See Math::PlanePath::UlamWarburton.

### UlamWarburtonQuarter

parts=1 points.
parts=octant points.
parts=octant_up lines.
This is the first few points to show the shape. Continuing on fills 6/16 of the plane. See Math::PlanePath::UlamWarburtonQuarter.

The following in the separate Math-PlanePath-Toothpick distribution.

### LCornerTree

parts=4 and parts=1
parts=octant and parts=octant+1
parts=octant_up and parts=octant_up+1
parts=wedge and parts=wedge+1
parts=diagonal
parts=diagonal-1
See Math::PlanePath::LCornerTree.

### OneOfEight

parts=4
parts=1
parts=octant
parts=wedge
parts=3mid
parts=3side
parts=1 non-leaf nodes.
The non-leaf image highlights the branching from the diagonals. Notice that on each branch the sub-branches on the "near" side of the branch are 1 position earlier than on the "far" side. See Math::PlanePath::OneOfEight.

### HTree

(See Math::PlanePath::HTree.)

### ToothpickTree and ToothpickReplicate

parts=3 as tree.
parts=octant as tree.
parts=wedge as toothpicks.
See Math::PlanePath::ToothpickTree and Math::PlanePath::ToothpickReplicate.