/ 
Math-PlanePath-52
River stage one • 3 direct dependents • 4 total dependents
/ Math::PlanePath::CornerReplicate

NAME

Math::PlanePath::CornerReplicate -- replicating squares

SYNOPSIS

use Math::PlanePath::CornerReplicate;
my $path = Math::PlanePath::CornerReplicate->new;
my ($x, $y) = $path->n_to_xy (123);

DESCRIPTION

This path is a self-similar replicating corner fill,

 7  | 63--62  59--58  47--46  43--42  
    |      |       |       |       |  
 6  | 60--61  56--57  44--45  40--41  
    |          |               |      
 5  | 51--50  55--54  35--34  39--38  
    |      |       |       |       |  
 4  | 48--49  52--53  32--33  36--37  
    |                  |              
 3  | 15--14  11--10  31--30  27--26  
    |      |       |       |       |  
 2  | 12--13   8-- 9  28--29  24--25  
    |          |               |      
 1  |  3-- 2   7-- 6  19--18  23--22  
    |      |       |       |       |  
Y=0 |  0-- 1   4-- 5  16--17  20--21  
    +--------------------------------
      X=0  1   2   3   4   5   6   7

The pattern is the initial N=0 to N=3 section,

+-------+-------+
|       |       |
|   3   |   2   |
|       |       |
+-------+-------+
|       |       |
|   0   |   1   |
|       |       |
+-------+-------+

It then repeats as 2x2 blocks arranged in the same pattern, then 4x4 blocks, etc.

Level Ranges

A given replication extends to

Nlevel = 4^level - 1
- (2^level - 1) <= X <= (2^level - 1)
- (2^level - 1) <= Y <= (2^level - 1)

FUNCTIONS

See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.

$path = Math::PlanePath::CornerReplicate->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::ZOrderCurve

HOME PAGE

http://user42.tuxfamily.org/math-planepath/index.html

LICENSE

Copyright 2011 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/>.