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#!/usr/bin/perl -w
# Copyright 2011, 2012, 2016 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 5.006;
use strict;
use warnings;
use Math::BaseCnv 'cnv';
use Math::Libm 'M_PI', 'hypot';
use Math::PlanePath::QuintetReplicate;
$|=1;
{
# X+Y maximum NE in level
# k=0 0 0 0 0
# k=1 1,2 1,2 1 1
# k=2 6,7 11,12 4 4
# k=3 31,32 111,112 11 21
# k=4 156,157 1111,1112 24 44
# k=5 2656,2657 41111,41112 55 210
# k=6 15156,15157 441111,441112 134 1014
# k=7 77656,77657 4441111,4441112 295 2140
# k=8 312031,312032 34441111,34441112 602 4402
# k=9 1483906,1483907 334441111,334441112 1465 21330
# k=10 7343281,7343282 3334441111,3334441112 3382 102012
my $path = Math::PlanePath::QuintetReplicate->new;
foreach my $k (0 .. 10) {
my ($n_lo,$n_hi) = $path->level_to_n_range($k);
my $sum_max = 0;
my @n_max;
foreach my $n ($n_lo .. $n_hi) {
my ($x,$y) = $path->n_to_xy($n);
my $sum = $x+$y;
if ($sum == $sum_max) {
push @n_max, $n;
} elsif ($sum > $sum_max) {
$sum_max = $sum;
@n_max = ($n);
}
}
my @n5 = map {cnv($_,10,5)} @n_max;
my $sum5 = cnv($sum_max,10,5);
print "k=$k ",join(',',@n_max)," ",join(',',@n5)," $sum_max $sum5\n";
}
exit 0;
}
{
require Math::BigInt; Math::BigInt->import(try => 'GMP');
my $path = Math::PlanePath::QuintetReplicate->new;
my $n_max = Math::BigInt->new(0);
my $pow = Math::BigInt->new(1);
foreach my $k (0 .. 50) {
my $x_max = 0;
my $new_n_max = 0;
foreach my $d (1 .. 4) {
my $try_n = $n_max + $pow*$d;
my ($x,$y) = $path->n_to_xy($try_n);
if ($x > $x_max) {
$x_max = $x;
$new_n_max = $try_n;
}
}
$n_max = $new_n_max;
my $n5 = cnv($n_max,10,5);
my $x5 = cnv($x_max,10,5);
print "k=$k $n_max\n $n5\n X=$x_max $x5\n";
$pow *= 5;
}
exit 0;
}
{
# X maximum in level
# k=0 0 0 0 0
# k=1 1 1 1 1
# k=2 6 11 3 3
# k=3 106 411 7 12
# k=4 606 4411 18 33
# k=5 3106 44411 42 132
# k=6 15606 444411 83 313
# k=7 62481 3444411 200 1300
# k=8 296856 33444411 478 3403
# k=9 1468731 333444411 1005 13010
# k=10 5374981 2333444411 2204 32304
# high digit 1 at b^k, so I^(d-1)*b^k
# when angle atan(1/2) steps past 90 deg
# atan(1/2)*180/Pi \\ 26.565 deg
# frac(x) = x-floor(x);
# a=(Pi/2)/atan(1/2)
# a=atan(1/2)/(Pi/2)
# a=2*atan(1/2)/Pi
# 1/h+1/a
# h = Pi/(2*atan(2))
# vector(20,n,n--; (floor((a+0)*n+1/2)))
# vector(20,n,n--; frac(n/a))
# vector(20,n, (-sum(n=0,n-1,frac((n+1+1/2)/a)<frac((n+1/2)/a)))%4+1)
# vector(20,n,n--; (-floor(a*n+1/2))%4+1)
# vector(20,n,n--; (ceil(-a*n-1/2))%4+1)
my $path = Math::PlanePath::QuintetReplicate->new;
foreach my $k (0 .. 10) {
my ($n_lo,$n_hi) = $path->level_to_n_range($k);
my $x_max = 0;
my $n_max = 0;
foreach my $n ($n_lo .. $n_hi) {
my ($x,$y) = $path->n_to_xy($n);
if ($x > $x_max) {
$x_max = $x;
$n_max = $n;
}
}
my $n5 = cnv($n_max,10,5);
my $x5 = cnv($x_max,10,5);
print "k=$k $n_max $n5 $x_max $x5\n";
}
exit 0;
}
{
my $level = 6;
my $path = Math::PlanePath::QuintetReplicate->new;
my ($n_lo, $n_hi) = $path->level_to_n_range($level);
print "\\fill foreach \\p in {";
foreach my $n ($n_lo .. $n_hi) {
my ($x,$y) = $path->n_to_xy($n);
print "($x,$y),";
}
print "} ";
print "{ \\p rectangle +(1,1) };\n";
exit 0;
}
{
# min/max for level
require Math::BaseCnv;
require Math::PlanePath::QuintetReplicate;
my $path = Math::PlanePath::QuintetReplicate->new;
my $prev_min = 1;
my $prev_max = 1;
my @mins;
for (my $level = 0; $level < 20; $level++) {
my $n_start = 5**$level;
my $n_end = 5**($level+1) - 1;
my $min_hypot = 128*$n_end*$n_end;
my $min_x = 0;
my $min_y = 0;
my $min_pos = '';
my $max_hypot = 0;
my $max_x = 0;
my $max_y = 0;
my $max_pos = '';
print "level $level n=$n_start .. $n_end\n";
foreach my $n ($n_start .. $n_end) {
my ($x,$y) = $path->n_to_xy($n);
my $h = $x*$x + $y*$y;
# my $h = abs($x) + abs($y);
if ($h < $min_hypot) {
my $n5 = Math::BaseCnv::cnv($n,10,5) . '[5]';
$min_hypot = $h;
$min_pos = "$x,$y $n $n5";
}
if ($h > $max_hypot) {
my $n5 = Math::BaseCnv::cnv($n,10,5) . '[5]';
$max_hypot = $h;
$max_pos = "$x,$y $n $n5";
}
}
# print " min $min_hypot at $min_x,$min_y\n";
# print " max $max_hypot at $max_x,$max_y\n";
# {
# my $factor = $min_hypot / $prev_min;
# my $base5 = Math::BaseCnv::cnv($min_hypot,10,5) . '[5]';
# print " min $min_hypot $base5 at $min_pos factor $factor\n";
# }
{
my $factor = $max_hypot / $prev_max;
my $base5 = Math::BaseCnv::cnv($max_hypot,10,5) . '[5]';
print " max $max_hypot $base5 at $max_pos factor $factor\n";
}
$prev_min = $min_hypot;
$prev_max = $max_hypot;
push @mins, $min_hypot;
}
print join(',',@mins),"\n";
exit 0;
}
{
# Dir4 maximum
require Math::PlanePath::QuintetReplicate;
require Math::NumSeq::PlanePathDelta;
require Math::BigInt;
require Math::BaseCnv;
my $path = Math::PlanePath::QuintetReplicate->new;
my $seq = Math::NumSeq::PlanePathDelta->new (planepath_object => $path,
delta_type => 'Dir4');
my $dir4_max = 0;
foreach my $n (0 .. 600000) {
# my $n = Math::BigInt->new(2)**$level - 1;
my $dir4 = $seq->ith($n);
if ($dir4 > $dir4_max) {
$dir4_max = $dir4;
my ($dx,$dy) = $path->n_to_dxdy($n);
my $n5 = Math::BaseCnv::cnv($n,10,5);
printf "%7s %2b,\n %2b %8.6f\n", $n5, abs($dx),abs($dy), $dir4;
}
}
exit 0;
}
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