#!/usr/bin/perl -w
# Copyright 2011 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 .
use 5.006;
use strict;
use warnings;
use Math::Libm 'M_PI', 'hypot';
{
# minimum hypot beyond N=3^level
#
require Math::PlanePath::GosperSide;
require Math::BaseCnv;
my $path = Math::PlanePath::GosperSide->new;
my $prev_min_hypot = 1;
foreach my $level (0 .. 40) {
my $n_level = 3**$level;
my $min_n = $n_level;
my ($x,$y) = $path->n_to_xy($min_n);
my $min_hypot = hypot($x,sqrt(3)*$y);
foreach my $n ($n_level .. 1.0001*$n_level) {
my ($x,$y) = $path->n_to_xy($n);
my $h = hypot($x,sqrt(3)*$y);
if ($h < $min_hypot) {
$min_n = $n;
$min_hypot = $h;
}
}
my $min_n3 = Math::BaseCnv::cnv($min_n, 10, 3);
my $factor = $min_hypot / $prev_min_hypot;
printf "%2d %8d %15s %9.2f %7.4f %7.4g\n",
$level, $min_n, "[$min_n3]", $min_hypot, $factor, $factor-sqrt(7);
$prev_min_hypot = $min_hypot;
}
exit 0;
}
{
# growth of 3^level hypot
#
require Math::PlanePath::GosperSide;
my $path = Math::PlanePath::GosperSide->new;
my $prev_angle = 0;
my $prev_dist = 0;
foreach my $level (0 .. 20) {
my ($x,$y) = $path->n_to_xy(3**$level);
$y *= sqrt(3);
my $angle = atan2($y,$x);
$angle *= 180/M_PI();
if ($angle < 0) { $angle += 360; }
my $delta_angle = $angle - $prev_angle;
my $dist = log(hypot($x,$y));
my $delta_dist = $dist - $prev_dist;
printf "%d %d,%d %.1f %+.3f %.3f %+.5f\n",
$level, $x, $y, $angle, $delta_angle,
$dist, $delta_dist;
$prev_angle = $angle;
$prev_dist = $dist;
}
exit 0;
}