Math::PlanePath::GosperSide -- one side of the Gosper island
use Math::PlanePath::GosperSide; my $path = Math::PlanePath::GosperSide->new; my ($x, $y) = $path->n_to_xy (123);
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 GosperIslands
path, as described in "Side and Radial Lines" in Math::PlanePath::GosperIslands. Each N=3^level point is the start of a GosperIslands
ring.
The path is the same as the TerdragonCurve
except the turns here are by 60 degrees each, whereas TerdragonCurve
is by 120 degrees. See Math::PlanePath::TerdragonCurve for the turn sequence and total direction formulas etc.
See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes.
$path = Math::PlanePath::GosperSide->new ()
Create and return a new path object.
($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.
Math::PlanePath, Math::PlanePath::GosperIslands, Math::PlanePath::TerdragonCurve, Math::PlanePath::KochCurve
http://user42.tuxfamily.org/math-planepath/index.html
Copyright 2011, 2012, 2013, 2014 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/>.