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#!/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;
# uncomment this to run the ### lines
#use Smart::Comments;
{
# dx,dy on even radix
require Math::PlanePath::PeanoCurve;
require Math::BigInt;
require Math::BaseCnv;
foreach my $radix (4, 2, 6, 8) {
print "radix=$radix\n";
my $path = Math::PlanePath::PeanoCurve->new (radix => $radix);
my $limit = 4000000000;
{
my %seen_dx;
for my $len (0 .. 8) {
for my $high (1 .. $radix-1) {
my $n = Math::BigInt->new($high);
foreach (1 .. $len) { $n *= $radix; $n += $radix-1; }
my ($dx,$dy) = $path->n_to_dxdy($n);
$dx = abs($dx);
my ($x,$y) = $path->n_to_xy($n);
my $xr = Math::BaseCnv::cnv($x,10,$radix);
my $dr = Math::BaseCnv::cnv($dx,10,$radix);
my $nr = Math::BaseCnv::cnv($n,10,$radix);
print "N=$n [$nr] dx=$dx [$dr] x=[$xr]\n";
unless ($seen_dx{$dx}++) {
}
}
}
}
{
my %seen_dy;
for my $len (0 .. 8) {
for my $high (1 .. $radix-1) {
my $n = Math::BigInt->new($high);
foreach (1 .. $len) { $n *= $radix; $n += $radix-1; }
my ($dx,$dy) = $path->n_to_dxdy($n);
$dy = abs($dy);
unless ($seen_dy{$dy}++) {
my $dr = Math::BaseCnv::cnv($dy,10,$radix);
my $nr = Math::BaseCnv::cnv($n,10,$radix);
print "N=$n [$nr] dy=$dy [$dr]\n";
}
}
}
}
print "\n";
}
exit 0;
}
{
# abs(dY) = count low 2-digits, mod 2
# abs(dX) = opposite, 1-abs(dY)
# x x
# vertical when odd number of low 2s ..0222
# N+1 carry propagates to change ..1000
# y y
# high y+1 complements x from 0->2 so X unchanged
# Y becomes Y+1 02 -> 10, or if complement then Y-1 20 -> 12
#
my $radix = 3;
require Math::PlanePath::PeanoCurve;
require Math::NumSeq::PlanePathDelta;
require Math::NumSeq::DigitCountLow;
require Math::BigInt;
require Math::BaseCnv;
my $path = Math::PlanePath::PeanoCurve->new (radix => $radix);
my $seq = Math::NumSeq::PlanePathDelta->new (planepath_object => $path,
delta_type => 'AbsdX');
my $cnt = Math::NumSeq::DigitCountLow->new (radix => 3, digit => 2);
foreach my $n (0 .. 40) {
my ($dx,$dy) = $path->n_to_dxdy($n);
my $absdx = abs($dx);
my $absdy = abs($dy);
my $c = $cnt->ith($n);
my $by_c = $c & 1;
my $diff = $absdy == $by_c ? '' : ' ***';
# my $n = $n+1;
my $nr = Math::BaseCnv::cnv($n,10,$radix);
printf "%3d %7s %2d,%2d low=%d%s\n",
$n, $nr, abs($dx),abs($dy), $c, $diff;
# print "$n,";
if ($absdx != 0) {
}
}
exit 0;
}
{
# Dir4 maximum
my $radix = 6;
require Math::PlanePath::PeanoCurve;
require Math::NumSeq::PlanePathDelta;
require Math::BigInt;
require Math::BaseCnv;
my $path = Math::PlanePath::PeanoCurve->new (radix => $radix);
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 $nr = Math::BaseCnv::cnv($n,10,$radix);
printf "%7s %2b,\n %2b %8.6f\n", $nr, abs($dx),abs($dy), $dir4;
}
}
exit 0;
}
{
# axis increasing
my $radix = 4;
my $rsquared = $radix * $radix;
my $re = '.' x $radix;
require Math::NumSeq::PlanePathN;
foreach my $line_type ('Y_axis', 'X_axis', 'Diagonal') {
OUTER: foreach my $serpentine_num (0 .. 2**$rsquared-1) {
my $serpentine_type = sprintf "%0*b", $rsquared, $serpentine_num;
# $serpentine_type = reverse $serpentine_type;
$serpentine_type =~ s/($re)/$1_/go;
### $serpentine_type
my $seq = Math::NumSeq::PlanePathN->new
(
planepath => "WunderlichSerpentine,radix=$radix,serpentine_type=$serpentine_type",
line_type => $line_type,
);
### $seq
# my $path = Math::NumSeq::PlanePathN->new
# (
# e,radix=$radix,serpentine_type=$serpentine_type",
# line_type => $line_type,
# );
my $prev = -1;
for (1 .. 1000) {
my ($i, $value) = $seq->next;
if ($value <= $prev) {
# print "$line_type $serpentine_type decrease at i=$i value=$value cf prev=$prev\n";
# my $path = $seq->{'planepath_object'};
# my ($prev_x,$prev_y) = $path->n_to_xy($prev);
# my ($x,$y) = $path->n_to_xy($value);
# # print " N=$prev $prev_x,$prev_y N=$value $x,$y\n";
next OUTER;
}
$prev = $value;
}
print "$line_type $serpentine_type all increasing\n";
}
}
exit 0;
}
{
# max Dir4
my $radix = 4;
require Math::BaseCnv;
print 4-atan2(2,1)/atan2(1,1)/2,"\n";
require Math::NumSeq::PlanePathDelta;
my $seq = Math::NumSeq::PlanePathDelta->new (planepath => "PeanoCurve,radix=$radix",
delta_type => 'Dir4');
my $dx_seq = Math::NumSeq::PlanePathDelta->new (planepath => "PeanoCurve,radix=$radix",
delta_type => 'dX');
my $dy_seq = Math::NumSeq::PlanePathDelta->new (planepath => "PeanoCurve,radix=$radix",
delta_type => 'dY');
my $max = 0;
for (1 .. 10000000) {
my ($i, $value) = $seq->next;
# foreach my $k (1 .. 1000000) {
# my $i = $radix ** (4*$k+3) - 1;
# my $value = $seq->ith($i);
if ($value > $max
# || $i == 0b100011111
) {
my $dx = $dx_seq->ith($i);
my $dy = $dy_seq->ith($i);
my $ri = Math::BaseCnv::cnv($i,10,$radix);
my $rdx = Math::BaseCnv::cnv($dx,10,$radix);
my $rdy = Math::BaseCnv::cnv($dy,10,$radix);
my $f = $dy ? $dx/$dy : -1;
printf "%d %s %.5f %s %s %.3f\n", $i, $ri, $value, $rdx,$rdy, $f;
$max = $value;
}
}
exit 0;
}
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