1Math::PlanePath::CellulUasreRrulCeo5n7t(r3i)buted Perl DMoactuhm:e:nPtlaatnieoPnath::CellularRule57(3)
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6 Math::PlanePath::CellularRule57 -- cellular automaton 57 and 99 points
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9 use Math::PlanePath::CellularRule57;
10 my $path = Math::PlanePath::CellularRule57->new;
11 my ($x, $y) = $path->n_to_xy (123);
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14 This is the pattern of Stephen Wolfram's "rule 57" cellular automaton
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16 <http://mathworld.wolfram.com/ElementaryCellularAutomaton.html>
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18 arranged as rows
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20 51 52 53 54 55 56 10
21 38 39 40 41 42 43 44 45 46 47 48 49 50 9
22 33 34 35 36 37 8
23 23 24 25 26 27 28 29 30 31 32 7
24 19 20 21 22 6
25 12 13 14 15 16 17 18 5
26 9 10 11 4
27 5 6 7 8 3
28 3 4 2
29 2 1
30 1 <- Y=0
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32 -9 -8 -7 -6 -5 -4 -3 -2 -1 X=0 1 2 3 4 5 6 7 8 9
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34 The triangular numbers N=10,15,21,28,etc, k*(k+1)/2, make a 1/2 sloping
35 diagonal upwards.
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37 On rows with odd Y there's a solid block at either end then 1 of 3
38 cells to the left and 2 of 3 to the right of the centre. On even Y
39 rows there's similar 1 of 3 and 2 of 3 middle parts, but without the
40 solid ends. Those 1 of 3 and 2 of 3 are successively offset so as to
41 make lines going up towards the centre as can be seen in the following
42 plot.
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44 *********** * * * * * ** ** ** ************
45 * * * * ** ** ** **
46 ********** * * * * ** ** ** ***********
47 * * * * * ** ** **
48 ********* * * * ** ** ** **********
49 * * * * ** ** **
50 ******** * * * * ** ** *********
51 * * * ** ** **
52 ******* * * * ** ** ********
53 * * * * ** **
54 ****** * * ** ** *******
55 * * * ** **
56 ***** * * * ** ******
57 * * ** **
58 **** * * ** *****
59 * * * **
60 *** * ** ****
61 * * **
62 ** * * ***
63 * **
64 * * **
65 * *
66 *
67 *
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69 Mirror
70 The "mirror => 1" option gives the mirror image pattern which is "rule
71 99". The point numbering shifts but the total points on each row is
72 the same.
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74 51 52 53 54 55 56 10
75 38 39 40 41 42 43 44 45 46 47 48 49 50 9
76 33 34 35 36 37 8
77 23 24 25 26 27 28 29 30 31 32 7
78 19 20 21 22 6
79 12 13 14 15 16 17 18 5
80 9 10 11 4
81 5 6 7 8 3
82 3 4 2
83 2 1
84 1 <- Y=0
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86 -9 -8 -7 -6 -5 -4 -3 -2 -1 X=0 1 2 3 4 5 6 7 8 9
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88 N Start
89 The default is to number points starting N=1 as shown above. An
90 optional "n_start" can give a different start, in the same pattern.
91 For example to start at 0,
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93 n_start => 0
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95 22 23 24 25 26 27 28 29 30 31
96 18 19 20 21
97 11 12 13 14 15 16 17
98 8 9 10
99 4 5 6 7
100 2 3
101 1
102 0
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105 See "FUNCTIONS" in Math::PlanePath for behaviour common to all path
106 classes.
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108 "$path = Math::PlanePath::CellularRule57->new ()"
109 "$path = Math::PlanePath::CellularRule57->new (mirror => $bool, n_start
110 => $n)"
111 Create and return a new path object.
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113 "($x,$y) = $path->n_to_xy ($n)"
114 Return the X,Y coordinates of point number $n on the path.
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116 "$n = $path->xy_to_n ($x,$y)"
117 Return the point number for coordinates "$x,$y". $x and $y are
118 each rounded to the nearest integer, which has the effect of
119 treating each cell as a square of side 1. If "$x,$y" is outside
120 the pyramid or on a skipped cell the return is "undef".
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123 Math::PlanePath, Math::PlanePath::CellularRule,
124 Math::PlanePath::CellularRule54, Math::PlanePath::CellularRule190,
125 Math::PlanePath::PyramidRows
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127 <http://mathworld.wolfram.com/ElementaryCellularAutomaton.html>
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130 <http://user42.tuxfamily.org/math-planepath/index.html>
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133 Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020
134 Kevin Ryde
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136 This file is part of Math-PlanePath.
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138 Math-PlanePath is free software; you can redistribute it and/or modify
139 it under the terms of the GNU General Public License as published by
140 the Free Software Foundation; either version 3, or (at your option) any
141 later version.
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143 Math-PlanePath is distributed in the hope that it will be useful, but
144 WITHOUT ANY WARRANTY; without even the implied warranty of
145 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
146 General Public License for more details.
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148 You should have received a copy of the GNU General Public License along
149 with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
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153perl v5.36.0 2022-07-22Math::PlanePath::CellularRule57(3)