Math::PlanePath::CellularRule57 -- cellular automaton 57 and 99 points
use Math::PlanePath::CellularRule57; my $path = Math::PlanePath::CellularRule57->new; my ($x, $y) = $path->n_to_xy (123);
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.
*********** * * * * * ** ** ** ************ * * * * ** ** ** ** ********** * * * * ** ** ** *********** * * * * * ** ** ** ********* * * * ** ** ** ********** * * * * ** ** ** ******** * * * * ** ** ********* * * * ** ** ** ******* * * * ** ** ******** * * * * ** ** ****** * * ** ** ******* * * * ** ** ***** * * * ** ****** * * ** ** **** * * ** ***** * * * ** *** * ** **** * * ** ** * * *** * ** * * ** * * * *
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.
mirror => 1
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
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
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
$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.
$x,$y
$x
$y
undef
Math::PlanePath, Math::PlanePath::CellularRule, Math::PlanePath::CellularRule54, Math::PlanePath::CellularRule190, Math::PlanePath::PyramidRows
http://user42.tuxfamily.org/math-planepath/index.html
Copyright 2011, 2012, 2013, 2014, 2015 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.
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To install Math::PlanePath, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Math::PlanePath
CPAN shell
perl -MCPAN -e shell install Math::PlanePath
For more information on module installation, please visit the detailed CPAN module installation guide.