```
#!/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
# 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/>.
# Usage: perl ulam-spiral-xpm.pl >/tmp/foo.xpm # write image file
# xzgv /tmp/foo.xpm # view file
#
# This is a bit of fun drawing Ulam's spiral of primes in the SquareSpiral
# path. The output is XPM format (which is plain text) and any good image
# viewer program should display it.
#
# Optional args
#
# perl ulam-spiral-xpm.pl SIZE
# or
# perl ulam-spiral-xpm.pl SIZE SCALE
#
# make the image SIZExSIZE pixels, and SCALE to expand each point to a
# SCALExSCALE square instead of a single pixel.
#
use 5.004;
use strict;
use Math::PlanePath::SquareSpiral;
my $size = 200;
my $scale = 1;
if (@ARGV >= 2) {
$scale = $ARGV[1];
}
if (@ARGV >= 1) {
$size = $ARGV[0];
}
my $path = Math::PlanePath::SquareSpiral->new;
my $x_origin = int($size / 2);
my $y_origin = int($size / 2);
my ($n_lo, $n_hi)
= $path->rect_to_n_range (-$x_origin, -$y_origin,
-$x_origin+$size, -$y_origin+$size);
# Find the prime numbers 2 to $n_hi by sieve of Eratosthenes.
# Could also use Math::Prime::TiedArray or Math::Prime::XS.
#
my @primes = (0, # 0
0, # 1
1, # 2 prime
1, # 3 prime
(0,1) x ($n_hi/2)); # rest alternately even/odd
my $i = 3;
foreach my $i (3 .. int(sqrt($n_hi)) + 1) {
next unless $primes[$i];
foreach (my $j = 2*$i; $j <= $n_hi; $j += $i) {
$primes[$j] = 0;
}
}
# Draw the primes into an array of rows strings.
#
my @rows = (' ' x $size) x $size;
foreach my $n ($n_lo .. $n_hi) {
next unless $primes[$n];
my ($x, $y) = $path->n_to_xy ($n);
$x = $x + $x_origin;
$y = $y_origin - $y; # inverted
# $n_hi is an over-estimate in general, check x,y actually in desired size
if ($x >= 0 && $x < $size && $y >= 0 && $y < $size) {
substr ($rows[$y], $x,1) = '*';
}
}
# Expand @rows points by $scale, horizontally and vertically.
#
if ($scale > 1) {
foreach (@rows) {
s{(.)}{$1 x $scale}eg; # expand horizontally
}
@rows = map { ($_) x $scale} @rows; # expand vertically
$size *= $scale;
}
# XPM format is easy to print.
# Output is about 1 byte per pixel.
#
print <<"HERE";
/* XPM */
static char *ulam_spiral_xpm_pl[] = {
"$size $size 2 1",
" c black",
"* c white",
HERE
foreach my $row (@rows) {
print "\"$row\",\n";
}
print "};\n";
exit 0;
```