NAME¶
Math::PlanePath::DekkingCentres -- 5x5 self-similar
SYNOPSIS¶
use Math::PlanePath::DekkingCentres;
my $path = Math::PlanePath::DekkingCentres->new;
my ($x, $y) = $path->n_to_xy (123);
DESCRIPTION¶
This is a variation of a 5x5 self-similar curve by F. M. Dekking. This form
visits the "centres" of the 5x5 self-similar blocks. The result is
diagonal steps, but replications wholly within 5x5 areas.
...
| /
9 | 115-116 122-123-124 89--88 86--85--84
| | | \ | \ | |
8 | 114 117-118 121-120 90 92 87 82--83
| | \ / |/ \ |
7 | 113-112 106 119 102 91 94--93 81 77
| / / | / | / / / |
6 | 111 107 105 103 101 95--96 80 78 76
| | \ \ | | \ \ | |
5 | 110-109-108 104 100--99--98--97 79 75
| \
4 | 10--11 13--14--15 35--36 38--39--40 74 70 66--65--64
| | \ | | | \ | | | |\ \ |
3 | 9 7 12 17--16 34 32 37 42--41 73 71 69 67 63
| |/ \ | |/ \ | |/ |/ /
2 | 8 5-- 6 18 22 33 30--31 43 47 72 55 68 62--61
| / / / | / / / | / \ |
1 | 4-- 3 19 21 23 29--28 44 46 48 54--53 56--57 60
| \ \ | | \ \ | | \ | |
Y=0 | 0-- 1-- 2 20 24--25--26--27 45 49--50--51--52 58--59
+---------------------------------------------------------------
X=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
The base pattern is the N=0 to N=24 section. It repeats with rotations or
reversals which make the ends join. For example N=75 to N=99 is the base
pattern in reverse. Or N=50 to N=74 is reverse and also rotate by -90.
FUNCTIONS¶
See "FUNCTIONS" in Math::PlanePath the behaviour common to all path
classes.
- "$path = Math::PlanePath::DekkingCentres->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.
Level Methods¶
- "($n_lo, $n_hi) = $path->level_to_n_range($level)"
- Return "(0, 25**$level - 1)".
SEE ALSO¶
Math::PlanePath, Math::PlanePath::DekkingCurve, Math::PlanePath::CincoCurve,
Math::PlanePath::PeanoCurve
HOME PAGE¶
<
http://user42.tuxfamily.org/math-planepath/index.html>
LICENSE¶
Copyright 2011, 2012, 2013, 2014 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/>.