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#!/usr/bin/perl -w
# Copyright 2011, 2013 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 5.010;
use strict;
use warnings;
use List::Util 'sum';
use Math::PlanePath::KochCurve;
{
# A056832 All a(n) = 1 or 2; a(1) = 1; get next 2^k terms by repeating
# first 2^k terms and changing last element so sum of first 2^(k+1) terms
# is odd.
#
# Is lowest non-zero base4 digit(n) 1,3->a(n)=1 2->a(n)=2.
# a(2^k) flips 1<->2 each time for low non-zero flipping 1<->2.
# a(2^k) always flips because odd sum becomes even on duplicating.
#
my @a = (1);
for my $i (1 .. 6) {
push @a, @a;
unless (sum(@a) & 1) {
$a[-1] = 3-$a[-1]; # 2<->1
print "i=$i flip last\n";
}
print @a,"\n";
}
foreach my $i (1 .. 64) {
my $d = base4_lowest_nonzero_digit($i);
if ($d != 2) { $d = 1; }
print $d;
}
print "\n";
exit 0;
}
sub base4_lowest_nonzero_digit {
my ($n) = @_;
while (($n & 3) == 0) {
$n >>= 2;
if ($n == 0) { die "oops, no nonzero digits at all"; }
}
return $n & 3;
}
sub base4_lowest_non3_digit {
my ($n) = @_;
while (($n & 3) == 3) {
$n >>= 2;
}
return $n & 3;
}
{
my $path = Math::PlanePath::KochCurve->new;
foreach my $n (0 .. 16) {
my ($x,$y) = $path->n_to_xy($n);
my $rot = n_to_total_turn($n);
print "$n $x,$y $rot\n";
}
print "\n";
exit 0;
sub n_to_total_turn {
my ($n) = @_;
my $rot = 0;
while ($n) {
if (($n % 4) == 1) {
$rot++;
} elsif (($n % 4) == 2) {
$rot --;
}
$n = int($n/4);
}
return $rot;
}
}
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