Provided by: libmath-planepath-perl_113-1_all 
NAME
Math::PlanePath::DekkingCurve -- 5x5 self-similar edge curve
SYNOPSIS
use Math::PlanePath::DekkingCurve;
my $path = Math::PlanePath::DekkingCurve->new;
my ($x, $y) = $path->n_to_xy (123);
DESCRIPTION
This is an integer version of a 5x5 self-similar curve by Dekking,
10 | 123-124-125-... 86--85
| | | |
9 | 115-116-117 122-121 90--89--88--87 84
| | | | | |
8 | 114-113 118-119-120 91--92--93 82--83
| | | |
7 | 112 107-106 103-102 95--94 81 78--77
| | | | | | | | | |
6 | 111 108 105-104 101 96--97 80--79 76
| | | | | |
5 | 110-109 14--15 100--99--98 39--40 75 66--65
| | | | | | | |
4 | 10--11--12--13 16 35--36--37--38 41 74 71--70 67 64
| | | | | | | | | |
3 | 9---8---7 18--17 34--33--32 43--42 73--72 69--68 63
| | | | | |
2 | 5---6 19 22--23 30--31 44 47--48 55--56--57 62--61
| | | | | | | | | | | |
1 | 4---3 20--21 24 29--28 45--46 49 54--53 58--59--60
| | | | | |
Y=0 | 0---1---2 25--26--27 50--51--52
+----------------------------------------------------------------
X=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
The base pattern is the N=0 to N=25 section. It then repeats with rotations or reversals which make the
ends join. For example N=75 to N=100 is the base pattern in reverse, ie. from N=25 down to N=0. Or N=50
to N=75 is reverse and also rotate by -90.
The curve segments are edges of squares in a 5x5 arrangement.
+- - -+- - -+- - 14----15 ---+
| | | | v |> |
^ ^ <| |
10----11----12----13- - 16 --+
| v |> |
|> ^ ^ |
9-----8-----7 -- 18----17 --+
v | | |> |
| ^ |> | ^
+- - 5-----6 - 19 22----23
| <| | <|
| <| ^ | <| |
+- - 4-----3 20----21 -- 24
| v <|
^ ^ |> | | |
0-----1-----2 -- + -- -+- 25
The little notch marks show which square each edge represents. This is the side the curve expands into
at the next level. For example N=1 to N=2 has its notch on the left so the next level N=25 to N=50
expands on the left.
An expansion on the left is a repeat of the base shape, possibly rotated 90, 180 or 270 degrees. An
expansion on the right is the base shape in reverse, as for example N=2 to N=3 on the right becomes N=50
to N=75 traversing to the right at the next level.
FUNCTIONS
See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.
"$path = Math::PlanePath::DekkingCurve->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.
SEE ALSO
Math::PlanePath, Math::PlanePath::DekkingCentres, Math::PlanePath::CincoCurve,
Math::PlanePath::PeanoCurve
HOME PAGE
<http://user42.tuxfamily.org/math-planepath/index.html>
LICENSE
Copyright 2011, 2012, 2013 Kevin Ryde
This file is part of Math-PlanePath.
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/>.