#!/usr/bin/perl -w
# Copyright 2012, 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 5.004;
use strict;
use Test;
plan tests => 8;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::KochCurve;
# uncomment this to run the ### lines
#use Smart::Comments '###';
#------------------------------------------------------------------------------
# A002450 number of right turns N=1 to N < 4^k
#
# 2
# / \ /
# 0---1 3---4
# A020988 number of left turns N=1 to N < 4^k = (2/3)*(4^n-1).
# duplicate A084180
MyOEIS::compare_values
(anum => 'A020988',
max_value => 100_000,
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Left');
my @got;
my $total = 0;
my $target = 1;
while (@got < $count) {
my ($i,$value) = $seq->next;
if ($i == $target) {
push @got, $total;
$target *= 4;
}
$total += $value;
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A002450',
max_value => 100_000,
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Right');
my @got;
my $total = 0;
my $target = 1;
while (@got < $count) {
my ($i,$value) = $seq->next;
if ($i == $target) {
push @got, $total;
$target *= 4;
}
$total += $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A177702 - abs(dX) from N=1 onwards, repeating 1,1,2
MyOEIS::compare_values
(anum => 'A177702',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathDelta;
my $seq = Math::NumSeq::PlanePathDelta->new (planepath => 'KochCurve',
delta_type => 'AbsdX');
$seq->seek_to_i(1);
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A217586
# Not quite turn sequence ...
# differs 0<->1 at n=2^k
#
# a(1) = 1
# if a(n) = 0 then a(2*n) = 1 and a(2*n+1) = 0 # opposite low bit
# if a(n) = 1 then a(2*n) = 0 and a(2*n+1) = 0 # both 0
#
# a(2n+1)=0 # odd always left
# a(2n) = 1-a(n) # even 0 or 1 as odd or even
# a(4n) = 1-a(2n) = 1-(1-a(n)) = a(n)
# a(4n+2) = 1-a(2n+1) = 1-0 = 1 # 4n+2 always right
# except a(0+2) = 1-a(1) = 1-1 = 0
# A Right N differ
# 1 0 1 *
# 0 1 10 *
# 0 0 11
# 1 0 100 *
# 0 0 101
# 1 1 110
# 0 0 111
# 0 1 1000 *
# 0 0 1001
# 1 1 1010
# 0 0 1011
# 0 0 1100
# 0 0 1101
# 1 1 1110
# 0 0 1111
# 1 0 10000 *
# 0 0
# 1 1
# 0 0
# 0 0
# 0 0
# 1 1
# 0 0
# 1 1
MyOEIS::compare_values
(anum => q{A217586},
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Right');
my @got;
while (@got < $count) {
# $seq->next;
my ($i,$value) = $seq->next;
if (is_pow2($i)) { $value ^= 1; }
push @got, $value;
# push @got, A217586_func($i)
}
return \@got;
});
sub A217586_func {
my ($n) = @_;
if ($n < 1) {
die "A217586_func() must have n>=1";
}
{
while (($n & 3) == 0) {
$n >>= 2;
}
if ($n == 1) {
return 1;
}
if (($n & 3) == 2) {
if ($n == 2) { return 0; }
else { return 1; }
}
if ($n & 1) {
return 0;
}
}
# {
# if ($n == 1) {
# return 1;
# }
# if (A217586_func($n >> 1)) {
# if ($n & 1) {
# return 0;
# } else {
# return 0;
# }
# } else {
# if ($n & 1) {
# return 0;
# } else {
# return 1;
# }
# }
# }
#
# {
# if ($n == 1) {
# return 1;
# }
# my $bit = $n & 1;
# if (A217586_func($n >> 1)) {
# return 0;
# } else {
# return $bit ^ 1;
# }
# }
}
sub is_pow2 {
my ($n) = @_;
while ($n > 1) {
if ($n & 1) {
return 0;
}
$n >>= 1;
}
return ($n == 1);
}
#------------------------------------------------------------------------------
# A035263 is turn left=1,right=0 at OFFSET=1
# morphism 1 -> 10, 0 -> 11
MyOEIS::compare_values
(anum => 'A035263',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Left');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
# also left=0,right=1 at even N
MyOEIS::compare_values
(anum => 'A035263',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Right');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
if (($i & 1) == 0) {
push @got, $value;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A073059 a(4k+3)= 1 ..11 = 1
# a(4k+2) = a(4k+4) = 0 ..00 ..10 = 0
# a(16k+13) = 1 1101
# a(4n+1) = a(n) ..01 = base4 above
# a(n) = 1-A035263(n-1) is Koch 1=left,0=right by morphism OFFSET=1
# so A073059 is next turn 0=left,1=right
# ???
#
# MyOEIS::compare_values
# (anum => q{A073059},
# func => sub {
# my ($count) = @_;
# require Math::NumSeq::PlanePathTurn;
# my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
# turn_type => 'Left');
# my @got = (0);
# while (@got < $count) {
# $seq->next;
# my ($i,$value) = $seq->next;
# push @got, $value;
# }
# return \@got;
# });
#------------------------------------------------------------------------------
# A096268 - morphism turn 1=right,0=left
# but OFFSET=0 is turn at N=1
MyOEIS::compare_values
(anum => 'A096268',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Right');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A029883 - Thue-Morse first diffs
MyOEIS::compare_values
(anum => 'A029883',
fixup => sub {
my ($bvalues) = @_;
@$bvalues = map {abs} @$bvalues;
},
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Left');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A089045 - +/- increment
MyOEIS::compare_values
(anum => 'A089045',
fixup => sub {
my ($bvalues) = @_;
@$bvalues = map {abs} @$bvalues;
},
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Left');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A003159 - N end in even number of 0 bits, is positions of left turn
MyOEIS::compare_values
(anum => 'A003159',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Left');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
if ($value == 1) { # left
push @got, $i;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A036554 - N end in odd number of 0 bits, position of right turns
MyOEIS::compare_values
(anum => 'A036554',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'KochCurve',
turn_type => 'Right');
my @got;
while (@got < $count) {
my ($i,$value) = $seq->next;
if ($value == 1) { # right
push @got, $i;
}
}
return \@got;
});
#------------------------------------------------------------------------------
exit 0;