NAME
Math::PlanePath::DekkingCentres  5x5 selfsimilar
SYNOPSIS
use Math::PlanePath::DekkingCentres;
my $path = Math::PlanePath::DekkingCentres>new;
my ($x, $y) = $path>n_to_xy (123);
DESCRIPTION
This is a variation on a 5x5 selfsimilar curve from
F. M. Dekking, "Recurrent Sets", Advances in Mathematics, volume 44, 1982, pages 79104, section 4.9 "GosperType Curves"
and which is a horizontal mirror image of the Ecurve of McKenna 1978.
The form visits the "centres" of the 5x5 selfsimilar unit squares of the pattern. The result is some diagonal steps, but replications wholly within 5x5 areas.
...
 /
9  115116 122123124 8988 868584
   \  \  
8  114 117118 121120 90 92 87 8283
  \ / / \ 
7  113112 106 119 102 91 9493 81 77
 / /  /  / / / 
6  111 107 105 103 101 9596 80 78 76
  \ \   \ \  
5  110109108 104 100999897 79 75
 \
4  1011 131415 3536 383940 74 70 666564
  \    \    \ \ 
3  9 7 12 1716 34 32 37 4241 73 71 69 67 63
 / \  / \  / / /
2  8 5 6 18 22 33 3031 43 47 72 55 68 6261
 / / /  / / /  / \ 
1  4 3 19 21 23 2928 44 46 48 5453 5657 60
 \ \   \ \   \  
Y=0  0 1 2 20 24252627 45 49505152 5859
+
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
SEE ALSO
Math::PlanePath, Math::PlanePath::DekkingCurve, Math::PlanePath::CincoCurve, Math::PlanePath::PeanoCurve
HOME PAGE
http://user42.tuxfamily.org/mathplanepath/index.html
LICENSE
Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 Kevin Ryde
This file is part of MathPlanePath.
MathPlanePath 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.
MathPlanePath 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 MathPlanePath. If not, see <http://www.gnu.org/licenses/>.