#!/usr/bin/perl -w
# Copyright 2011, 2012, 2013, 2014 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 => 12;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::TerdragonCurve;
# uncomment this to run the ### lines
# use Smart::Comments '###';
my $path = Math::PlanePath::TerdragonCurve->new;
sub ternary_digit_above_low_zeros {
my ($n) = @_;
if ($n == 0) {
return 0;
}
while (($n % 3) == 0) {
$n = int($n/3);
}
return ($n % 3);
}
#------------------------------------------------------------------------------
# A057682 level X
# A057083 level Y
foreach my $elem (['A057682', 1, 0, 0, [0,1]], # X
['A057083', 1, 1, 1, [] ], # Y
['A057681', 2, 0, 0, [1,1]], # X arms=2
['A103312', 2, 0, 0, [0,1,1]], # X arms=2
['A057682', 2, 1, 0, [0] ], # Y arms=2
['A057681', 3, 1, 0, [1,1]], # Y arms=3
['A103312', 3, 1, 0, [0,1,1]], # Y arms=3
) {
my ($anum, $arms, $coord, $initial_level, $initial_got) = @$elem;
my $path = Math::PlanePath::TerdragonCurve->new (arms => $arms);
MyOEIS::compare_values
(anum => $anum,
func => sub {
my ($count) = @_;
require Math::BigInt;
my @got = @$initial_got;
for (my $k = $initial_level; @got < $count; $k++) {
my ($n_lo,$n_hi) = $path->level_to_n_range(Math::BigInt->new($k));
my @coords = $path->n_to_xy($n_hi);
push @got, $coords[$coord];
}
return \@got;
});
}
#------------------------------------------------------------------------------
# A092236 etc counts of segments in direction
foreach my $elem ([1, 'A057083', [], 1],
[0, 'A092236', [], 0],
[1, 'A135254', [0], 0],
[2, 'A133474', [0], 0]) {
my ($dir, $anum, $initial_got, $offset_3k) = @$elem;
MyOEIS::compare_values
(anum => $anum,
max_value => 9,
func => sub {
my ($count) = @_;
my @got = @$initial_got;
my $n = $path->n_start;
my $total = 0;
my $k = 2*$offset_3k;
while (@got < $count) {
### @got
my $n_end = 3**$k;
for ( ; $n < $n_end; $n++) {
$total += (dxdy_to_dir3($path->n_to_dxdy($n)) == $dir);
}
if ($offset_3k) {
push @got, $total - 3**($k-1);
} else {
push @got, $total;
}
$k++;
}
return \@got;
});
}
sub dxdy_to_dir3 {
my ($dx,$dy) = @_;
if ($dx == 2 && $dy == 0) {
return 0;
}
if ($dx == -1) {
if ($dy == 1) {
return 1;
}
if ($dy == -1) {
return 2;
}
}
return undef;
}
#------------------------------------------------------------------------------
# A111286 boundary length is 2 then 3*2^k for points N <= 3^k
MyOEIS::compare_values
(anum => 'A111286',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got = (1);
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length ($path, 3**$k,
lattice_type => 'triangular');
}
return \@got;
});
# A007283 boundary length is 3*2^k for points N <= 3^k
MyOEIS::compare_values
(anum => 'A007283',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got = (3); # path initial boundary=2 vs bvalues=3
for (my $k = 1; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length ($path, 3**$k,
lattice_type => 'triangular');
}
return \@got;
});
# A164346 boundary even powers, is 3*4^n
# also one side, odd powers
MyOEIS::compare_values
(anum => 'A164346',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got = (3);
for (my $k = 1; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length ($path, 3**(2*$k),
lattice_type => 'triangular');
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A164346',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length ($path, 3**(2*$k+1),
lattice_type => 'triangular',
side => 'left');
}
return \@got;
});
# A002023 boundary odd powers 6*4^n
# also even powers one side
MyOEIS::compare_values
(anum => 'A002023',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length ($path, 3**(2*$k+1),
lattice_type => 'triangular');
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A002023',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 1; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length ($path, 3**(2*$k),
lattice_type => 'triangular',
side => 'right');
}
return \@got;
});
#------------------------------------------------------------------------------
# A003945 R[k] boundary length
MyOEIS::compare_values
(anum => 'A003945',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length ($path, 3**$k,
side => 'right',
lattice_type => 'triangular');
}
return \@got;
});
#------------------------------------------------------------------------------
# A042950 V[k] boundary length
MyOEIS::compare_values
(anum => 'A042950',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length ($path, 2 * 3**$k,
side => 'left',
lattice_type => 'triangular');
}
return \@got;
});
#------------------------------------------------------------------------------
# A118004 1/2 enclosed area odd levels points N <= 3^(2k+1), is 9^k-4^k
# area[k] = 2*(3^(k-1)-2^(k-1))
# area[2k+1]/2 = 2*(3^(2k+1-1)-2^(2k+1-1))/2
# = 9^k - 4^k
MyOEIS::compare_values
(anum => 'A118004',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 0; @got < $count; $k++) {
my $area = MyOEIS::path_enclosed_area ($path, 3**(2*$k+1),
lattice_type => 'triangular');
push @got, $area/2;
}
return \@got;
});
# A056182 enclosed area is 2*(3^(k-1)-2^(k-1)) for points N <= 3^k
MyOEIS::compare_values
(anum => 'A056182',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 1; @got < $count; $k++) {
push @got, MyOEIS::path_enclosed_area ($path, 3**$k,
lattice_type => 'triangular');
}
return \@got;
});
#------------------------------------------------------------------------------
# A136442 1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,
# OFFSET =0,1,2,3,...
# left 1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0
# N=1,2,3,...
# Not quite
#
# MyOEIS::compare_values
# (anum => 'A136442',
# func => sub {
# my ($count) = @_;
# require Math::NumSeq::PlanePathTurn;
# my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
# turn_type => 'Left');
# my @got = (1);
# while (@got < $count) {
# my ($i, $value) = $seq->next;
# push @got, $value;
# }
# return \@got;
# });
#------------------------------------------------------------------------------
# A060032 - turn 1=left, 2=right as bignums to 3^level
MyOEIS::compare_values
(anum => 'A060032',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'LSR');
my @got;
for (my $level = 0; @got < $count; $level++) {
require Math::BigInt;
my $big = Math::BigInt->new(0);
foreach my $n (1 .. 3**$level) {
my $value = $seq->ith($n);
if ($value == -1) { $value = 2; }
$big = 10*$big + $value;
}
push @got, $big;
}
return \@got;
});
#------------------------------------------------------------------------------
# A189673 - morphism turn 1=left, 0=right, extra initial 0
MyOEIS::compare_values
(anum => 'A189673',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'Left');
my @got = (0);
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A189640 - morphism turn 0=left, 1=right, extra initial 0
MyOEIS::compare_values
(anum => 'A189640',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'Right');
my @got = (0);
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A005823 - N positions with total turn == 0, no ternary 1s
MyOEIS::compare_values
(anum => 'A005823',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'LSR');
my $total_turn = 0;
my @got = (0);
while (@got < $count) {
my ($i, $value) = $seq->next;
$total_turn += $value;
if ($total_turn == 0) {
push @got, $i;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A062756 - ternary count 1s, is cumulative turn
MyOEIS::compare_values
(anum => 'A062756',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'LSR');
my @got;
my $cumulative = 0;
for (;;) {
push @got, $cumulative;
last if @got >= $count;
my ($i, $value) = $seq->next;
$cumulative += $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A080846 - turn 0=left, 1=right
MyOEIS::compare_values
(anum => 'A080846',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'Right');
my @got;
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A038502 - taken mod 3 is 1=left, 2=right
MyOEIS::compare_values
(anum => 'A038502',
fixup => sub {
my ($bvalues) = @_;
@$bvalues = map { $_ % 3 } @$bvalues;
},
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'Right');
my @got;
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value+1;
}
return \@got;
});
#------------------------------------------------------------------------------
# A026225 - N positions of left turns
MyOEIS::compare_values
(anum => 'A026225',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'Left');
my @got;
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($value == 1) {
push @got, $i;
}
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A026225',
func => sub {
my ($count) = @_;
my @got;
for (my $n = 1; @got < $count; $n++) {
if (ternary_digit_above_low_zeros($n) == 1) {
push @got, $n;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A026179 - positions of right turns
MyOEIS::compare_values
(anum => 'A026179',
func => sub {
my ($count) = @_;
my @got = (1); # extra initial 1 ...
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'Right');
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($value == 1) {
push @got, $i;
}
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A026179',
func => sub {
my ($count) = @_;
my @got = (1);
for (my $n = 1; @got < $count; $n++) {
if (ternary_digit_above_low_zeros($n) == 2) {
push @got, $n;
}
}
return \@got;
});
#------------------------------------------------------------------------------
exit 0;