NAME¶

Math::PlanePath::CretanLabyrinth -- infinite Cretan labyrinth

SYNOPSIS¶

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

DESCRIPTION¶

This is a Cretan 7-circuit style labyrinth extended out infinitely.

    81--80--79--78--77--76--75--74--73--72--71--70--69         7
     |                                               |
    82 137-138-139-140-141-142-143-144-145-146-147  68         6
     |   |                                       |   |
    83 136 165-164-163-162-161-160-159-158-157 148  67         5
     |   |   |                               |   |   |
    84 135 166  49--50--51--52--53--54--55 156 149  66         4
     |   |   |   |                       |   |   |   |
    85 134 167  48   9-- 8-- 7-- 6-- 5  56 155 150  65         3
     |   |   |   |   |               |   |   |   |   |
    86 133 168  47  10  25--26--27   4  57 154 151  64         2
     |   |   |   |   |   |       |   |   |   |   |   |
    87 132 169  46  11  24  29--28   3  58 153-152  63         1
     |   |   |   |   |   |   |       |   |           |
    88 131 170  45  12  23  30   1-- 2  59--60--61--62    <- Y=0
     |   |   |   |   |   |   |
    89 130 171  44  13  22  31--32--33 186-187-188-189        -1
     |   |   |   |   |   |           |   |           |
    90 129 172  43  14  21--20--19  34 185 112-111 190        -2
     |   |   |   |   |           |   |   |   |   |   |
    91 128 173  42  15--16--17--18  35 184 113 110  ...       -3
     |   |   |   |                   |   |   |   |
    92 127 174  41--40--39--38--37--36 183 114 109            -4
     |   |   |                           |   |   |
    93 126 175-176-177-178-179-180-181-182 115 108            -5
     |   |                                   |   |
    94 125-124-123-122-121-120-119-118-117-116 107            -6
     |                                           |
    95--96--97--98--99-100-101-102-103-104-105-106            -7
                                 ^
    -7  -6  -5  -4  -3  -2  -1  X=0  1   2   3   4

The repeating part is the N=59 to N=189 style groups of 4 circuits going back and forward.

The gaps between the path are the labyrinth walls. Notice at N=2,59,33,186 the "+" joining of those walls which is characteristic of this style labyrinth.

          |   3  |  58  |
          |      |      |
    ------+      |      +-------
                 |
      1       2  |  59      60
                 |
    -------------+--------------       walls
                 |
     32      33  | 186     187
                 |
    ------+      |      +-------
          |      |      |
          |  34  | 185  |

See examples/cretan-walls.pl for a sample program carving out the path from a solid block to leave the walls.

FUNCTIONS¶

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

"$path = Math::PlanePath::CretanLabyrinth->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.

Fractional positions give an X,Y position along a straight line between the integer positions.

"$n = $path->xy_to_n ($x,$y)"

Return the point number for coordinates "$x,$y". If there's nothing at "$x,$y" then return "undef".

"$n = $path->n_start()"

Return 1, the first N in the path.

SEE ALSO¶

Math::PlanePath, Math::PlanePath::SquareSpiral

HOME PAGE¶

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

LICENSE¶

Copyright 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 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/>.