NAME

Math::PlanePath::GosperSide -- one side of the Gosper island

SYNOPSIS

use Math::PlanePath::GosperSide;
my $path = Math::PlanePath::GosperSide->new;
my ($x, $y) = $path->n_to_xy (123);

DESCRIPTION

This path is a single side of the Gosper island, in integers ("Triangular Lattice" in Math::PlanePath).

                                    20-...        14
                                   /
                           18----19               13
                          /
                        17                        12
                          \
                           16                     11
                          /
                        15                        10
                          \
                           14----13                9
                                   \
                                    12             8
                                   /
                                 11                7
                                   \
                                    10             6
                                   /
                            8---- 9                5
                          /
                   6---- 7                         4
                 /
                5                                  3
                 \
                   4                               2
                 /
          2---- 3                                  1
        /
 0---- 1                                       <- Y=0

 ^
X=0 1  2  3  4  5  6  7  8  9 10 11 12 13 ...

The path slowly spirals around counter clockwise, with a lot of wiggling in between. The N=3^level point is at

N = 3^level
angle = level * atan(sqrt(3)/5)
      = level * 19.106 degrees
radius = sqrt(7) ^ level

A full revolution for example takes roughly level=19 which is about N=1,162,000,000.

Both ends of such levels are in fact sub-spirals, like an "S" shape.

The path is both the sides and the radial spokes of the GosperIsland path, as described in "Side and Radial Lines" in Math::PlanePath::GosperIslands. Each N=3^level point is the start of a GosperIslands ring.

FUNCTIONS

$path = Math::PlanePath::GosperSide->new ()

Create and return a new path object.

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

Return the X,Y coordinates of point number $n on the path. Points begin at 0 and if $n < 0 then the return is an empty list.

Fractional $n gives a point on the straight line between integer N.

SEE ALSO

Math::PlanePath, Math::PlanePath::GosperIslands, Math::PlanePath::KochCurve

Math::Fractal::Curve

HOME PAGE

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

LICENSE

Copyright 2011 Kevin Ryde

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/>.