#!/usr/bin/perl -w
# Copyright 2011, 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;
use POSIX ();
use Math::Trig 'pi';
use Math::PlanePath::SierpinskiArrowhead;
# uncomment this to run the ### lines
use Smart::Comments;
{
# dSumAbs
require Math::NumSeq::PlanePathDelta;
my $seq = Math::NumSeq::PlanePathDelta->new (planepath => 'SierpinskiCurveStair,arms=6',
delta_type => 'dSumAbs');
for (1 .. 300) {
my ($i,$value) = $seq->next;
print "$value,";
if ($i % 6 == 5) {
print "\n";
}
}
exit 0;
}
{
# A156595 Mephisto Waltz first diffs xor as turns
require Tk;
require Tk::CanvasLogo;
require Math::NumSeq::MephistoWaltz;
my $top = MainWindow->new;
my $width = 1200;
my $height = 800;
my $logo = $top->CanvasLogo(-width => $width, -height => $height)->pack;
my $turtle = $logo->NewTurtle('foo');
$turtle->LOGO_PU();
$turtle->LOGO_FD(- $height/2*.9);
$turtle->LOGO_PD();
my $step = 5;
$turtle->LOGO_FD($step);
my $seq = Math::NumSeq::MephistoWaltz->new;
my ($i,$prev) = $seq->next;
for (;;) {
my ($i,$value) = $seq->next;
my $turn = $value ^ $prev;
$prev = $value;
last if $i > 10000;
if ($turn) {
$turtle->LOGO_FD($step);
if ($i & 1) {
$turtle->LOGO_RT(120);
} else {
$turtle->LOGO_LT(120);
}
} else {
$turtle->LOGO_FD($step);
}
$logo->createArc($turtle->{x}+2, $turtle->{y}+2,
$turtle->{x}-2, $turtle->{y}-2);
}
Tk::MainLoop();
exit;
}
{
# dX,dY
require Math::PlanePath::SierpinskiCurve;
my $path = Math::PlanePath::SierpinskiCurve->new;
foreach my $n (0 .. 32) {
# my $n = $n + 1/256;
my ($x,$y) = $path->n_to_xy($n);
my ($x2,$y2) = $path->n_to_xy($n+1);
my $sx = $x2-$x;
my $sy = $y2-$y;
my $sdir = dxdy_to_dir8($sx,$sy);
my ($dx,$dy) = $path->_WORKING_BUT_HAIRY__n_to_dxdy($n);
my $ddir = dxdy_to_dir8($dx,$dy);
my $diff = ($dx != $sx || $dy != $sy ? ' ***' : '');
print "$n $x,$y $sx,$sy\[$sdir] $dx,$dy\[$ddir]$diff\n";
}
# return 0..7
sub dxdy_to_dir8 {
my ($dx, $dy) = @_;
return atan2($dy,$dx) / atan2(1,1);
if ($dx == 1) {
if ($dy == 1) { return 1; }
if ($dy == 0) { return 0; }
if ($dy == -1) { return 7; }
}
if ($dx == 0) {
if ($dy == 1) { return 2; }
if ($dy == -1) { return 6; }
}
if ($dx == -1) {
if ($dy == 1) { return 3; }
if ($dy == 0) { return 4; }
if ($dy == -1) { return 5; }
}
die 'oops';
}
exit 0;
}
{
# Mephisto Waltz 1/12 slice of plane
require Tk;
require Tk::CanvasLogo;
require Math::NumSeq::MephistoWaltz;
my $top = MainWindow->new;
my $width = 1000;
my $height = 800;
my $logo = $top->CanvasLogo(-width => $width, -height => $height)->pack;
my $turtle = $logo->NewTurtle('foo');
$turtle->LOGO_RT(45);
$turtle->LOGO_PU();
$turtle->LOGO_FD(- $height*sqrt(2)/2*.9);
$turtle->LOGO_PD();
$turtle->LOGO_RT(135);
$turtle->LOGO_LT(30);
my $step = 5;
$turtle->LOGO_FD($step);
my $seq = Math::NumSeq::MephistoWaltz->new;
for (;;) {
my ($i,$value) = $seq->next;
last if $i > 10000;
if ($value) {
$turtle->LOGO_RT(60);
$turtle->LOGO_FD($step);
} else {
$turtle->LOGO_LT(60);
$turtle->LOGO_FD($step);
}
}
Tk::MainLoop();
exit;
}
{
require Tk;
require Tk::CanvasLogo;
require Math::NumSeq::PlanePathTurn;
my $top = MainWindow->new();
my $logo = $top->CanvasLogo->pack;
my $turtle = $logo->NewTurtle('foo');
my $seq = Math::NumSeq::PlanePathTurn->new
(planepath => 'KochCurve',
turn_type => 'Left');
$turtle->LOGO_RT(45);
$turtle->LOGO_FD(10);
for (;;) {
my ($i,$value) = $seq->next;
last if $i > 64;
if ($value) {
$turtle->LOGO_RT(45);
$turtle->LOGO_FD(10);
$turtle->LOGO_RT(45);
$turtle->LOGO_FD(10);
} else {
$turtle->LOGO_LT(90);
$turtle->LOGO_FD(10);
$turtle->LOGO_LT(90);
$turtle->LOGO_FD(10);
}
}
Tk::MainLoop();
exit;
}
{
# filled fraction
require Math::PlanePath::SierpinskiCurve;
require Number::Fraction;
my $path = Math::PlanePath::SierpinskiCurve->new;
foreach my $level (1 .. 20) {
my $Ntop = 4**$level / 2 - 1;
my ($x,$y) = $path->n_to_xy($Ntop);
my $Xtop = 3*2**($level-1) - 1;
$x == $Xtop or die "x=$x Xtop=$Xtop";
my $frac = $Ntop / ($x*($x-1)/2);
print " $level $frac\n";
}
my $nf = Number::Fraction->new(4,9);
my $limit = $nf->to_num;
print " limit $nf = $limit\n";
exit 0;
}
{
# filled fraction
require Math::PlanePath::SierpinskiCurveStair;
require Number::Fraction;
foreach my $L (1 .. 5) {
print "L=$L\n";
my $path = Math::PlanePath::SierpinskiCurveStair->new (diagonal_length=>$L);
foreach my $level (1 .. 10) {
my $Nlevel = ((6*$L+4)*4**$level - 4) / 3;
my ($x,$y) = $path->n_to_xy($Nlevel);
my $Xlevel = ($L+2)*2**$level - 1;
$x == $Xlevel or die "x=$x Xlevel=$Xlevel";
my $frac = $Nlevel / ($x*($x-1)/2);
print " $level $frac\n";
}
my $nf = Number::Fraction->new((12*$L+8),(3*$L**2+12*$L+12));
my $limit = $nf->to_num;
print " limit $nf = $limit\n";
}
exit 0;
}
{
my $path = Math::PlanePath::SierpinskiCurve->new;
my @rows = ((' ' x 79) x 64);
foreach my $n (0 .. 3 * 3**4) {
my ($x, $y) = $path->n_to_xy ($n);
$x += 32;
substr ($rows[$y], $x,1, '*');
}
local $,="\n";
print reverse @rows;
exit 0;
}
{
my @rows = ((' ' x 64) x 32);
foreach my $p (0 .. 31) {
foreach my $q (0 .. 31) {
next if ($p & $q);
my $x = $p-$q;
my $y = $p+$q;
next if ($y >= @rows);
$x += 32;
substr ($rows[$y], $x,1, '*');
}
}
local $,="\n";
print reverse @rows;
exit 0;
}