Provided by: libmath-planepath-perl_125-1_all bug

NAME

       Math::PlanePath::CellularRule57 -- cellular automaton 57 and 99 points

SYNOPSIS

        use Math::PlanePath::CellularRule57;
        my $path = Math::PlanePath::CellularRule57->new;
        my ($x, $y) = $path->n_to_xy (123);

DESCRIPTION

       This is the pattern of Stephen Wolfram's "rule 57" cellular automaton

           <http://mathworld.wolfram.com/ElementaryCellularAutomaton.html>

       arranged as rows

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

           -9 -8 -7 -6 -5 -4 -3 -2 -1 X=0 1  2  3  4  5  6  7  8  9

       The triangular numbers N=10,15,21,28,etc, k*(k+1)/2, make a 1/2 sloping diagonal upwards.

       On rows with odd Y there's a solid block at either end then 1 of 3 cells to the left and 2
       of 3 to the right of the centre.  On even Y rows there's similar 1 of 3 and 2 of 3 middle
       parts, but without the solid ends.  Those 1 of 3 and 2 of 3 are successively offset so as
       to make lines going up towards the centre as can be seen in the following plot.

           ***********  *  *  *  * * ** ** ** ************
                       *  *  *  *  ** ** ** **
             **********  *  *  *  * ** ** ** ***********
                        *  *  *  * * ** ** **
               *********  *  *  *  ** ** ** **********
                         *  *  *  * ** ** **
                 ********  *  *  * * ** ** *********
                          *  *  *  ** ** **
                   *******  *  *  * ** ** ********
                           *  *  * * ** **
                     ******  *  *  ** ** *******
                            *  *  * ** **
                       *****  *  * * ** ******
                             *  *  ** **
                         ****  *  * ** *****
                              *  * * **
                           ***  *  ** ****
                               *  * **
                             **  * * ***
                                *  **
                               *  * **
                                 * *
                                   *
                                  *

   Mirror
       The "mirror => 1" option gives the mirror image pattern which is "rule 99".  The point
       numbering shifts but the total points on each row is the same.

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

           -9 -8 -7 -6 -5 -4 -3 -2 -1 X=0 1  2  3  4  5  6  7  8  9

   N Start
       The default is to number points starting N=1 as shown above.  An optional "n_start" can
       give a different start, in the same pattern.  For example to start at 0,

           n_start => 0

           22 23 24       25       26 27    28 29 30 31
                       18       19    20 21
                 11 12       13    14    15 16 17
                           8        9 10
                        4        5     6  7
                              2     3
                                    1
                                 0

FUNCTIONS

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

       "$path = Math::PlanePath::CellularRule57->new ()"
       "$path = Math::PlanePath::CellularRule57->new (mirror => $bool, n_start => $n)"
           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.

       "$n = $path->xy_to_n ($x,$y)"
           Return the point number for coordinates "$x,$y".  $x and $y are each rounded to the
           nearest integer, which has the effect of treating each cell as a square of side 1.  If
           "$x,$y" is outside the pyramid or on a skipped cell the return is "undef".

SEE ALSO

       Math::PlanePath, Math::PlanePath::CellularRule, Math::PlanePath::CellularRule54,
       Math::PlanePath::CellularRule190, Math::PlanePath::PyramidRows

       <http://mathworld.wolfram.com/ElementaryCellularAutomaton.html>

HOME PAGE

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

LICENSE

       Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017 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/>.