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#!/usr/bin/perl -w
# Copyright 2011, 2012, 2013, 2015, 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/>.
use 5.004;
use strict;
# uncomment this to run the ### lines
# use Smart::Comments;
{
# A023531 L-system
my %to;
%to = (S => 'STF+', # TF second form "TriangleSpiral2" in a023531.l
T => 'TF',
F => 'F',
'+' => '+');
%to = (S => 'SFT+', # FT first form "TriangleSpiral" in a023531.l
T => 'FT',
F => 'F',
'+' => '+');
my $str = 'S';
foreach (1 .. 7) {
my $padded = $str;
$padded =~ s/./$& /g; # spaces between symbols
print "$padded\n";
$str =~ s{.}{$to{$&} // die}ge;
}
$str =~ s/F(?=[^+]*F)/F0/g;
$str =~ s/F//g;
$str =~ s/\+/1/g;
$str =~ s/S|T//g;
print $str,"\n";
require Math::NumSeq::OEIS;
my $seq = Math::NumSeq::OEIS->new (anum => 'A023531');
my $want = '';
while (length($want) < length($str)) {
my ($i,$value) = $seq->next;
$want .= $value;
}
$str eq $want or die "oops";
print "end\n";
exit 0;
}
{
# A010054 L-system
my %to = (S => 'S+TF',
T => 'TF',
F => 'F', '+' => '+');
my $str = 'S+TF';
$str = 'S';
foreach (1 .. 7) {
my $pad = $str;
$pad =~ s/./$& /g;
print "$pad\n";
$str =~ s{.}{$to{$&} // die}ge;
}
exit 0;
}
{
# A010054 characteristic of triangular numbers
# turn seq with Language::Logo
require Math::NumSeq::OEIS;
my $seq = Math::NumSeq::OEIS->new(anum=>'A010054');
# $seq->next;
require Language::Logo;
my $lo = Logo->new(update => 20, port=>8222);
$lo->command("seth 0; forward 50; pendown; forward 200; backward 200; penup; backward 50; pendown");
for (;;) {
logo_blob(5);
my ($i,$value) = $seq->next;
$lo->command("left ".($value*120));
if ($i > 0) {
}
$lo->command("forward 30");
}
$lo->disconnect("Finished...");
exit 0;
sub logo_blob {
my ($size) = @_;
my $half = $size/2;
$lo->command("
penup; forward $half; pendown;
left 90; forward $half;
left 90; forward $size;
left 90; forward $size;
left 90; forward $size;
left 90; forward $half;
right 90;
penup; backward $half; pendown
");
}
}
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