``````#!/usr/bin/perl -w

# Copyright 2010, 2011, 2012 Kevin Ryde

# This file is part of Math-PlanePath.
#
# Math-PlanePath is free software; you can redistribute it and/or modify it
# 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/>.

# Usage: perl hilbert-oeis.pl
#
# This spot of code prints sequence A163359 of Sloane's On-Line Encyclopedia
# of Integer Sequences
#
#     http://oeis.org/A163359
#
# which is the Hilbert curve N values which occur on squares numbered
# diagonally in the style of Math::PlanePath::Diagonals,
#
#     0, 3, 1, 4, 2, 14, 5, 7, 13, 15, 58, 6, 8, 12, 16, 59, ...
#
# All points in the first quadrant are reached by both paths, so this is a
# re-ordering or the non-negative integers.
#
# In the code there's a double transpose going on.  A163359 is conceived as
# the Hilbert starting downwards and the diagonals numbered from the X axis,
# but the HilbertCurve code goes to the right first and the Diagonals module
# numbers from the Y axis.  The effect is the same, ie. that the first
# Hilbert step is the opposite axis as the diagonals are numbered from.
#
# Diagonals option direction=>up could be added to transpose \$x,\$y to make
# the first Hilbert step the same axis as the diagonal numbering.  Doing so
# would give sequence A163357.
#

use 5.004;
use strict;
use Math::PlanePath::HilbertCurve;
use Math::PlanePath::Diagonals;

my \$hilbert = Math::PlanePath::HilbertCurve->new;
my \$diagonal  = Math::PlanePath::Diagonals->new;

print "A163359: ";
foreach my \$n (\$diagonal->n_start .. 19) {
my (\$x, \$y) = \$diagonal->n_to_xy (\$n);       # X,Y points by diagonals
my \$hilbert_n = \$hilbert->xy_to_n (\$x, \$y);  # hilbert N at those points
print "\$hilbert_n, ";
}
print "...\n";
exit 0;
``````