NAME

Math::PlanePath::QuadricIslands -- quadric curve rings

SYNOPSIS

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

DESCRIPTION

This is concentric islands made from four sides of the QuadricCurve,

        27--26                     3
         |   |
    29--28  25  22--21             2
     |       |   |   |
    30--31  24--23  20--19         1
         | 4--3          |
34--33--32    | 16--17--18     <- Y=0
 |         1--2  |
35--36   7---8  15--14            -1
         |   |       |
     5---6   9  12--13            -2
             |   |
            10--11                -3

             ^
-3  -2  -1  X=0  1   2   3   4

The initial figure is the square N=1,2,3,4 then for the next level each straight side expands to 4x longer and a zigzag like N=5 through N=13 and the further sides to N=36.

                          *---*
                          |   |
*---*     becomes     *---*   *   *---*
                              |   |
                              *---*
   * <------ *
   |         ^
   |         |
   |         |
   v         |
   * ------> *

Level Ranges

Counting the innermost square as level 0, each ring is

length = 4 * 8^level     many points
Nlevel = 1 + length[0] + ... + length[level-1]
       = (4*8^level + 3)/7
Xstart = - 4^level / 2
Ystart = - 4^level / 2

For example the lower partial ring shown above is level 2 starting N=(4*8^2+3)/7=37 at X=-(4^2)/2=-8,Y=-8.

The innermost square N=1,2,3,4 is on 0.5 coordinates, for example N=1 at X=-0.5,Y=-0.5. This is centred on the origin and consistent with the (4^level)/2. Points from N=5 onwards are integer X,Y.

   4-------3    Y=+1/2
   |       |
   |   o   |
           |
   1-------2    Y=-1/2

X=-1/2   X=+1/2

FUNCTIONS

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

$path = Math::PlanePath::QuadricIslands->new ()

Create and return a new path object.

Level Methods

($n_lo, $n_hi) = $path->level_to_n_range($level)

Return per "Level Ranges" above,

( ( 4 * 8**$level + 3) / 7,
  (32 * 8**$level - 4) / 7 )

SEE ALSO

Math::PlanePath, Math::PlanePath::QuadricCurve, Math::PlanePath::KochSnowflakes, Math::PlanePath::GosperIslands

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/>.