Provided by: libmath-planepath-perl_113-1_all 
NAME
Math::PlanePath::GosperSide -- one side of the Gosper island
SYNOPSIS
use Math::PlanePath::GosperSide;
my $path = Math::PlanePath::GosperSide->new;
my ($x, $y) = $path->n_to_xy (123);
DESCRIPTION
This path is a single side of the Gosper island, in integers ("Triangular Lattice" in
Math::PlanePath).
20-... 14
/
18----19 13
/
17 12
\
16 11
/
15 10
\
14----13 9
\
12 8
/
11 7
\
10 6
/
8---- 9 5
/
6---- 7 4
/
5 3
\
4 2
/
2---- 3 1
/
0---- 1 <- Y=0
^
X=0 1 2 3 4 5 6 7 8 9 10 11 12 13 ...
The path slowly spirals around counter clockwise, with a lot of wiggling in between. The
N=3^level point is at
N = 3^level
angle = level * atan(sqrt(3)/5)
= level * 19.106 degrees
radius = sqrt(7) ^ level
A full revolution for example takes roughly level=19 which is about N=1,162,000,000.
Both ends of such levels are in fact sub-spirals, like an "S" shape.
The path is both the sides and the radial spokes of the "GosperIslands" path, as described
in "Side and Radial Lines" in Math::PlanePath::GosperIslands. Each N=3^level point is the
start of a "GosperIslands" ring.
The path is the same as the "TerdragonCurve" except the turns here are by 60 degrees each,
whereas "TerdragonCurve" is by 120 degrees. See Math::PlanePath::TerdragonCurve for the
turn sequence and total direction formulas etc.
FUNCTIONS
See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes.
"$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.
SEE ALSO
Math::PlanePath, Math::PlanePath::GosperIslands, Math::PlanePath::TerdragonCurve,
Math::PlanePath::KochCurve
Math::Fractal::Curve
HOME PAGE
<http://user42.tuxfamily.org/math-planepath/index.html>
LICENSE
Copyright 2011, 2012, 2013 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/>.