NAME

Math::PlanePath::MathImageGosperSide -- one side of the gosper island

SYNOPSIS

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

DESCRIPTION

In progress.

This path is a single side of the GosperIsland, extended out in integers.

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

It 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=116,000,000.

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

FUNCTIONS

$path = Math::PlanePath::MathImageGosperSide->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 surrounding integer N.

SEE ALSO

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

Math::Fractal::Curve

HOME PAGE

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

LICENSE

Copyright 2011 Kevin Ryde

Math-Image 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-Image 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-Image. If not, see <http://www.gnu.org/licenses/>.