NAME

Math::PlanePath -- points on a path through the 2-D plane

SYNOPSIS

use Math::PlanePath;
# only a base class, see the subclasses for actual operation

DESCRIPTION

This is the 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         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      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 lattice distance
PythagoreanTree        primitive triples by tree

PeanoCurve             3x3 self-similar quadrant traversal
WunderlichSerpentine   transpose parts of PeanoCurve
HilbertCurve           2x2 self-similar quadrant traversal
HilbertSpiral          2x2 self-similar whole-plane traversal
ZOrderCurve            replicating Z shapes
GrayCode               Gray code splits
WunderlichMeander      3x3 "R" pattern quadrant traversal
BetaOmega              2x2 self-similar half-plane traversal
AR2W2Curve             2x2 self-similar of four shapes
KochelCurve            3x3 self-similar two shapes
CincoCurve             5x5 self-similar

ImaginaryBase          replicating in four directions
ImaginaryHalf          half-plane replicate three directions
CubicBase              replicating in three directions
SquareReplicate        3x3 replicating squares
CornerReplicate        2x2 replicating squares
LTiling                self-simlar L shapes
DigitGroups            digit groups of high zero
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 "+" shape
QuintetCentres           likewise, but centres of squares
QuintetReplicate       self-similar "+" tiling

DragonCurve            paper folding
DragonRounded            same but rounding-off vertices
DragonMidpoint         paper folding midpoints
AlternatePaper         paper folding in alternating directions
TerdragonCurve         ternary dragon
TerdragonRounded       ternary dragon, rounded corners
TerdragonMidpoint      ternary dragon midpoints
R5DragonCurve          radix-5 dragon curve
R5DragonMidpoint       radix-5 dragon curve midpoints
CCurve                 "C" curve
ComplexPlus            base i+r
ComplexMinus           base i-r, 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 down from the Y to X axes
DiagonalsAlternating   diagonals Y to X and back again
DiagonalsOctant        diagonals from Y axis to 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
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
CoprimeColumns         coprime X,Y
DivisibleColumns       X divisible by Y
WythoffArray           Fibonacci recurrences
PowerArray             powers in rows
File                   points from a disk file

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

Number Types

The $n and $x,$y parameters can be either integers or floating point. The paths are meant to do something sensible with fractions. But expect rounding-off for big floating point exponents.

Floating point infinities (when available) give nan or infinite returns of some kind (some unspecified kind as yet). n_to_xy() on negative infinity is an empty return, the same as other negative $n. Calculations which break an input into digits of some base shouldn't loop infinitely on infinities.

Floating point nans (when available) give nan, infinite, or empty/undef returns, but again of some unspecified kind as yet, though in any case not going into infinite loops.

Many of the classes can operate on overloaded number types as inputs and give corresponding outputs.

Math::BigInt        maybe perl 5.8 up, for ** operator
Math::BigRat
Math::BigFloat
Number::Fraction    1.14 or higher (for abs())

This is slightly experimental and some classes might truncate a bignum or a fraction to a float as yet. In general the intention is to make the code generic enough that it can act on sensible number types. Recent versions of the bignum modules might be required, perhaps Perl 5.8 or higher for the ** exponentiation operator in particular.

For reference, an undef input to $n, $x,$y, etc, is meant to provoke an uninitialized value warnings (when warnings are enabled), but currently doesn't croak etc. Perhaps that will change, but the warning at least prevents bad inputs going unnoticed.

FUNCTIONS

In the following Foo is one of the various subclasses, see the list above and under "SEE ALSO".

$path = Math::PlanePath::Foo->new (key=>value, ...)

Create and return a new path object. Optional key/value parameters may control aspects of the object.

($x,$y) = $path->n_to_xy ($n)

Return X,Y coordinates of point $n on the path. If there's no point $n then the return is an empty list, so for example

my ($x,$y) = $path->n_to_xy (-123)
  or next;   # no negatives in $path

Paths start from $path->n_start below, though some will give a position for N=0 or N=-0.5 too.

$rsquared = $path->n_to_rsquared ($n)

Return the radial distance R^2 of point $n, or undef if there's no point $n. This is simply $x**2+$y**2 but for a few paths this can be calculated with less work than $x,$y.

$n = $path->xy_to_n ($x,$y)

Return the N point number at coordinates $x,$y. If there's nothing at $x,$y then return undef.

my $n = $path->xy_to_n(20,20);
if (! defined $n) {
  next;   # nothing at this X,Y
}

$x and $y can be fractional and the path classes will give an integer $n which contains $x,$y within a unit square, circle, or intended figure centred on the integer $n.

For paths which completely tile the plane there's always an $n to return, but for the spread-out paths an $x,$y position may fall in between (no $n close enough).

@n_list = $path->xy_to_n_list ($x,$y)

Return a list of N point numbers at coordinates $x,$y. If there's nothing at $x,$y then return a empty list.

my @n_list = $path->xy_to_n(20,20);

Most paths have just a single N for a given X,Y, but for those like DragonCurve and TerdragonCurve where multiple N's give the same X,Y this method returns the list of those N values.

($n_lo, $n_hi) = $path->rect_to_n_range ($x1,$y1, $x2,$y2)

Return a range of N values covering or exceeding a rectangle with corners at $x1,$y1 and $x2,$y2. The range is inclusive. For example,

my ($n_lo, $n_hi) = $path->rect_to_n_range (-5,-5, 5,5);
foreach my $n ($n_lo .. $n_hi) {
  my ($x, $y) = $path->n_to_xy($n) or next;
  print "$n  $x,$y";
}

The return may be an over-estimate of the range, and many of the points between $n_lo and $n_hi might be outside the rectangle. But the range at least bounds the N values which occur in the rectangle. Classes which can guarantee an exact lo/hi range say so in their docs.

$n_hi is usually no more than an extra partial row, revolution, or self-similar level. $n_lo is often merely the starting $path->n_start(), which is fine if the origin is in the desired rectangle but something away from the origin might actually start higher.

$x1,$y1 and $x2,$y2 can be fractional and if they partly overlap some N figures then those N's are included in the return.

If there's no points in the rectangle then the return can be a "crossed" range like $n_lo=1, $n_hi=0 (which makes a foreach do no loops). But rect_to_n_range() might not notice there's no points in the rectangle and instead over-estimate the range.

$n = $path->n_start()

Return the first N in the path. In the current classes this is either 0 or 1.

Some classes have secret dubious undocumented support for N values below this (zero or negative), but n_start() is the intended starting point.

$f = $path->n_frac_discontinuity()

Return the fraction of N at which there's discontinuities in the path. For example if there's a jump in the coordinates between N=7.4999 and N=7.5 then the returned $f is 0.5. Or $f is 0 if there's a discontinuity between 6.999 and 7.0.

If there's no discontinuities in the path, so that for example fractions between N=7 to N=8 give smooth X,Y values (of some kind) then the return is undef.

This is mainly of interest for drawing line segments between successive N points. If there's discontinuities then the idea is to draw from say N=7.0 to N=7.499 and then another line from N=7.5 to N=8. The returned $f is whether there's discontinuities anywhere in $path.

$bool = $path->x_negative()

$bool = $path->y_negative()

Return true if the path extends into negative X coordinates and/or negative Y coordinates respectively.

$bool = Math::PlanePath::Foo->class_x_negative()

$bool = Math::PlanePath::Foo->class_y_negative()

$bool = $path->class_x_negative()

$bool = $path->class_y_negative()

Return true if any paths made by this class extend into negative X coordinates and/or negative Y coordinates, respectively.

For some classes the X or Y extent may depend on parameter values.

$arms = $path->arms_count()

Return the number of arms in a "multi-arm" path.

For example in SquareArms this is 4 and each arm increments in turn, so the first arm is N=1,5,9,13, etc, starting from $path->n_start() and incrementing by 4 each time.

$str = $path->figure()

Return a string name of the figure (shape) intended to be drawn at each $n position. This is currently either

"square"     side 1 centred on $x,$y
"circle"     diameter 1 centred on $x,$y

Of course this is only a suggestion since PlanePath doesn't draw anything itself. A figure like a diamond for instance can look good too.

$aref = Math::PlanePath::Foo->parameter_info_array()

@list = Math::PlanePath::Foo->parameter_info_list()

Return an arrayref of list describing the parameters taken by a given class. This meant to help making widgets etc for user interaction in a GUI. Each element is a hashref

{
  name        =>    parameter key arg for new()
  share_key   =>    string, or undef
  description =>    human readable string
  type        =>    string "integer","boolean","enum" etc
  default     =>    value
  minimum     =>    number, or undef
  maximum     =>    number, or undef
  width       =>    integer, suggested display size
  choices     =>    for enum, an arrayref
}

type is a string, one of

"integer"
"enum"
"boolean"
"string"
"filename"

"filename" is separate from "string" since it might require subtly different handling to reach Perl as a byte string, whereas a "string" type might in principle take Perl wide chars.

For "enum" the choices field is the possible values, such as

{ name => "flavour",
  type => "enum",
  choices => ["strawberry","chocolate"],
}

minimum and/or maximum are omitted if there's no hard limit on the parameter.

share_key is designed to indicate when parameters from different NumSeq classes can done by a single control widget in a GUI etc. Normally the name is enough, but when the same name has slightly different meanings in different classes a share_key allows the same meanings to be matched up.

$hashref = Math::PlanePath::Foo->parameter_info_hash()

Return a hashref mapping parameter names $info->{'name'} to their $info records.

{ wider => { name => "wider",
             type => "integer",
             ...
           },
}

GENERAL CHARACTERISTICS

The classes are mostly based on integer $n positions and those designed for a square grid turn an integer $n into integer $x,$y. Usually they give in-between positions for fractional $n too. Classes not on a square grid but instead giving fractional X,Y such as SacksSpiral and VogelFloret are designed for a unit circle at each $n but they too can give in-between positions on request.

All X,Y positions are calculated by separate n_to_xy() calls. To follow a path use successive $n values starting from $path->n_start().

foreach my $n ($path->n_start .. 100) {
  my ($x,$y) = $path->n_to_xy($n);
  print "$n  $x,$y\n";
}

The separate n_to_xy() calls were motivated by plotting just some N points of a path, such as just the primes or the perfect squares. Successive positions in paths might be done in an iterator style more efficiently. The paths with a quadratic "step" are not much worse than a sqrt() to break N into a segment and offset, but the self-similar paths which chop N into digits of some radix might increment instead of recalculate.

A disadvantage of an iterator is that if you're only interested in a particular rectangule or similar region then the iteration may stray outside for a long time, making it much less useful than it seems. For wild paths it can be better to apply xy_to_n() by rows or similar.

Scaling and Orientation

The paths generally make a first move horizontally to the right and/or around from the X axis anti-clockwise, unless there's some more natural orientation. Anti-clockwise is the usual direction for mathematical spirals.

There's no parameters for scaling, offset or reflection as those things are thought better left to a general coordinate transformer, for example to expand or invert for display. But some easy transformations can be had just from the X,Y with

-X,Y        flip horizontally (mirror image)
X,-Y        flip vertically (across the X axis)

-Y,X        rotate +90 degrees  (anti-clockwise)
Y,-X        rotate -90 degrees  (clockwise)
-X,-Y       rotate 180 degrees

Flip vertically makes the spirals go clockwise instead of anti-clockwise, or a flip horizontally the same but starting on the left at the negative X axis. See "Triangular Lattice" below for 60 degree rotations of the triangular grid paths.

The Rows and Columns paths are exceptions to the rule of not having rotated versions of paths. They began as ways to pass in width and height as generic parameters and let the path use the one or the other.

For scaling and shifting see Transform::Canvas, and to rotate as well see Geometry::AffineTransform.

Loop Step

The paths can be characterized by how much longer each loop or repetition is than the preceding one. For example each cycle around the SquareSpiral is 8 more N points than the preceding.

  Step        Path
  ----        ----
    0       Rows, Columns (fixed widths)
   2/2      DiagonalsOctant (2 rows for +2)
    1       Diagonals
    2       SacksSpiral, PyramidSides, Corner, PyramidRows (default)
    4       DiamondSpiral, AztecDiamondRings, Staircase
   4/2      CellularRule54, CellularRule57,
              DiagonalsAlternating (2 rows for +4)
    5       PentSpiral, PentSpiralSkewed
   5.65     PixelRings (average about 4*sqrt(2))
    6       HexSpiral, HexSpiralSkewed, MPeaks,
              MultipleRings (default)
   6/2      CellularRule190 (2 rows for +6)
   6.28     ArchimedeanChords (approaching 2*pi),
              FilledRings (average)
    7       HeptSpiralSkewed
    8       SquareSpiral, PyramidSpiral
  16/2      StaircaseAlternating (up and back for +16)
    9       TriangleSpiral, TriangleSpiralSkewed
   12       AnvilSpiral
   16       OctagramSpiral
  19.74     TheodorusSpiral (approaching 2*pi^2)
  32/4      KnightSpiral (4 loops 2-wide for +32)
   64       DiamondArms (each arm)
   72       GreekKeySpiral
  128       SquareArms (each arm)
 128/4      CretanLabyrinth (4 loops for +128)
  216       HexArms (each arm)

totient     CoprimeColumns, DiagonalRationals
divcount    DivisibleColumns
various     CellularRule

parameter   MultipleRings, PyramidRows

The step determines which quadratic number sequences make straight lines. For example the gap between successive perfect squares increases by 2 each time (4 to 9 is +5, 9 to 16 is +7, 16 to 25 is +9, etc), so the perfect squares make a straight line in the paths of step 2.

In general straight lines on stepped paths are quadratics

N = a*k^2 + b*k + c    where a=step/2

The polygonal numbers are like this, with the (step+2)-gonal numbers making a straight line on a "step" path. For example the 7-gonals (heptagonals) are 5/2*k^2-3/2*k and make a straight line on the step=5 PentSpiral. Or the 8-gonal octagonal numbers 6/2*k^2-4/2*k on the step=6 HexSpiral.

There are various interesting properties of primes in quadratic progressions. Some quadratics seem to have more primes than others. For example see "Lucky Numbers of Euler" in Math::PlanePath::PyramidSides. Many quadratics have no primes at all, or none above a certain point, either trivially if always a multiple of 2 etc, or by a more sophisticated reasoning. See "Step 3 Pentagonals" in Math::PlanePath::PyramidRows for a factorization on the roots making a no-primes gap.

A 4*step path splits a straight line in two, so for example the perfect squares are a straight line on the step=2 "Corner" path, and then on the step=8 SquareSpiral they instead fall on two lines (lower left and upper right). In the bigger step there's one line of the even squares (2k)^2 == 4*k^2 and another of the odd squares (2k+1)^2. The gap between successive even squares increases by 8 each time and likewise between odd squares.

Self-Similar Powers

The self-similar patterns such as PeanoCurve generally have a base pattern which repeats at powers N=base^level. Or some multiple or relationship to such a power for things like KochPeaks and GosperIslands.

Base          Path
----          ----
  2         HilbertCurve, HilbertSpiral, ZOrderCurve (default),
              GrayCode (default), BetaOmega, AR2W2Curve,
              SierpinskiCurve, HIndexing, SierpinskiCurveStair,
              ImaginaryBase (default), ImaginaryHalf (default),
              CubicBase (default) CornerReplicate,
              ComplexMinus (default), ComplexPlus (default),
              ComplexRevolving, DragonCurve, DragonRounded,
              DragonMidpoint, AlternatePaper, CCurve,
              DigitGroups (default), PowerArray (default)
  3         PeanoCurve (default), WunderlichSerpentine (default),
              WunderlichMeander, KochelCurve,
              GosperIslands, GosperSide
              SierpinskiTriangle, SierpinskiArrowhead,
              SierpinskiArrowheadCentres,
              TerdragonCurve, TerdragonRounded, TerdragonMidpoint,
              UlamWarburton, UlamWarburtonQuarter (each level)
  4         KochCurve, KochPeaks, KochSnowflakes, KochSquareflakes,
              LTiling
  5         QuintetCurve, QuintetCentres, QuintetReplicate,
              CincoCurve, R5DragonCurve, R5DragonMidpoint
  7         Flowsnake, FlowsnakeCentres, GosperReplicate
  8         QuadricCurve, QuadricIslands
  9         SquareReplicate
Fibonacci   FibonacciWordFractal, WythoffArray
parameter   PeanoCurve, WunderlichSerpentine, ZOrderCurve, GrayCode,
              ImaginaryBase, ImaginaryHalf, CubicBase, ComplexPlus,
              ComplexMinus, DigitGroups, PowerArray

Many number sequences plotted on these paths tend to be fairly random, or merely show the tiling or path layout rather than much about the number sequence. Sequences related to the base can make holes or patterns picking out parts of the path. For example numbers without a particular digit (or digits) in the relevant base show up as holes. See for example "Power of 2 Values" in Math::PlanePath::ZOrderCurve.

Triangular Lattice

Some paths are on triangular or "A2" lattice points like

  *   *   *   *   *   *
*   *   *   *   *   *
  *   *   *   *   *   *
*   *   *   *   *   *
  *   *   *   *   *   *
*   *   *   *   *   *

These are done in integer X,Y on a square grid by using every second square and offsetting alternate rows. This means X and Y are either both even or both odd, not of opposite parity.

. * . * . * . * . * . *
* . * . * . * . * . * .
. * . * . * . * . * . *
* . * . * . * . * . * .
. * . * . * . * . * . *
* . * . * . * . * . * .

The X axis and diagonals X=Y and X=-Y divide the plane into six equal parts in this grid.

   X=-Y     X=Y
     \     /
      \   /
       \ /
----------------- X=0
       / \
      /   \
     /     \

The diagonal X=3*Y is the middle of the first sixth, representing a twelfth of the plane.

The resulting triangles are flatter than they should be. The triangle base is width=2 and top is height=1, whereas it would be height=sqrt(3) for an equilateral triangle. That sqrt(3) factor can be applied if desired,

X, Y*sqrt(3)          side length 2

X/2, Y*sqrt(3)/2      side length 1

Integer Y values have the advantage of fitting pixels on the usual kind of raster computer screen, and not losing precision in floating point results.

If doing a general-purpose coordinate rotation then be sure to apply the sqrt(3) scale factor first, otherwise any rotation will be wrong. 60 degree rotations can be made within the integer X,Y coordinates directly as follows, all giving integer X,Y results.

(X-3Y)/2, (X+Y)/2       rotate +60   (anti-clockwise)
(X+3Y)/2, (Y-X)/2       rotate -60   (clockwise)
-(X+3Y)/2, (X-Y)/2      rotate +120
(3Y-X)/2, -(X+Y)/2      rotate -120
-X,-Y                   rotate 180

(X+3Y)/2, (X-Y)/2       mirror across the X=3*Y twelfth line

The sqrt(3) factor can be worked into a hypotenuse radial distance calculation as follows if comparing distances from the origin.

hypot = sqrt(X*X + 3*Y*Y)

See for instance TriangularHypot which is triangular points ordered by this radial distance.

FORMULAS

Triangular Calculations

For a triangular lattice the rotation formulas above allow calculations to be done in the rectangular X,Y coordinates which are the inputs and outputs of the PlanePath functions. An alternative is to number vertically on a 60 degree angle with coordinates i,j,

      ...
      *   *   *      2
    *   *   *       1
  *   *   *      j=0
i=0  1   2

Such coordinates are sometimes used for hexagonal grids in board games etc, and using this internally can simplify rotations a little,

-j, i+j         rotate +60   (anti-clockwise)
i+j, -i         rotate -60   (clockwise)
-i-j, i         rotate +120
j, -i-j         rotate -120
-i, -j          rotate 180

Conversions between i,j and the rectangular X,Y are

X = 2*i + j         i = (X-Y)/2
Y = j               j = Y

A third coordinate k at a +120 degrees angle can be used too,

k=0  k=1 k=2
   *   *   *
     *   *   *
       *   *   *
        0   1   2

This is redundant in that it doesn't number anything i,j alone can't already, but it has the advantage of turning rotations into just sign changes and swaps,

-k, i, j        rotate +60
j, k, -i        rotate -60
-j, -k, i       rotate +120
k, -i, -j       rotate -120
-i, -j, -k      rotate 180

The conversions between i,j,k and the rectangular X,Y are like the i,j above but with k worked in too.

X = 2i + j - k        i = (X-Y)/2        i = (X+Y)/2
Y = j + k             j = Y         or   j = 0
                      k = 0              k = Y

HOME PAGE

http://user42.tuxfamily.org/math-planepath/index.html

http://user42.tuxfamily.org/math-planepath/gallery.html

LICENSE

This file is part of Math-PlanePath.

Math-PlanePath is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-PlanePath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.

To install Math::PlanePath, copy and paste the appropriate command in to your terminal.

cpanm

cpanm Math::PlanePath

CPAN shell

perl -MCPAN -e shell
install Math::PlanePath

For more information on module installation, please visit the detailed CPAN module installation guide.

	Global
`s`	Focus search bar
`?`	Bring up this help dialog

	GitHub
`g` `p`	Go to pull requests
`g` `i`	go to github issues (only if github is preferred repository)

	POD
`g` `a`	Go to author
`g` `c`	Go to changes
`g` `i`	Go to issues
`g` `d`	Go to dist
`g` `r`	Go to repository/SCM
`g` `s`	Go to source
`g` `b`	Go to file browse

	Search terms
module: (e.g. module:Plugin)
distribution: (e.g. distribution:Dancer auth)
author: (e.g. author:SONGMU Redis)
version: (e.g. version:1.00)