Math::PlanePath::MathImageQuintetSide -- one side of the quintet tiling
use Math::PlanePath::MathImageQuintetSide; my $path = Math::PlanePath::MathImageQuintetSide->new; my ($x, $y) = $path->n_to_xy (123);
In progress.
This path is ...
... | 26----27 | 24----25 | 23----22 | 20----21 | 18----19 | 17----16 | 15----14 | 13----12 6 | 11----10 5 | 8---- 9 4 | 6---- 7 3 | 5---- 4 2 | 2---- 3 1 | 0---- 1 <- Y=0 ^ X=0 1 2 3
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(1/2) = level * 26.56 degrees radius = sqrt(5) ^ level
A full revolution for example takes roughly level=14 which is about N=4,780,000.
Both ends of such levels are in fact sub-spirals, like an "S" shape.
See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.
$path = Math::PlanePath::MathImageQuintetSide->new ()
Create and return a new path object.
($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.
$n
$n < 0
Fractional $n gives a point on the straight line between surrounding integer N.
Math::PlanePath, Math::PlanePath::KochCurve
Math::Fractal::Curve
http://user42.tuxfamily.org/math-image/index.html
Copyright 2011, 2012 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/>.
To install App::MathImage::Image::Base::Caca, copy and paste the appropriate command in to your terminal.
cpanm
cpanm App::MathImage::Image::Base::Caca
CPAN shell
perl -MCPAN -e shell install App::MathImage::Image::Base::Caca
For more information on module installation, please visit the detailed CPAN module installation guide.