finite field visualization

gistfile1.txt

#!/usr/bin/perl

my %log = ();
my %exp = ();
my $P = 1049;
my $Pm = $P - 1;
my $gen = 1;
my $pi = 3.1415926535;

sub discretelog {
  $m = 1;
  for (my $x = 0; $x < $P; $x++) {
    # print "$m\n";
    $log{$m} = $x;
    $exp{$x} = $m;
    $m = ($m * $gen) % $P;
    if ($m == 1) {
      $x++;
      print STDERR "period: $x\n";
      return $x == $Pm;
    }
  }
}

while (!discretelog() && $gen < $Pm) { $gen++; }

sub point {
  my ($n) = @_;
  my $x = 350 * cos(2 * $pi * $n / $Pm) + 400;
  my $y = 350 * sin(2 * $pi * $n / $Pm) + 400;
  return ($x, $y);
}
print '<svg xmlns="http://www.w3.org/2000/svg" version="1.1">';


for (my $x = 1; $x < $P / 2 - 1; $x++) {
  my $out = $log{$exp{$x} + 1};
  my $out2 = $log{$exp{$P - $x - 1} + 1};
  my $diff = ($out - $out2) % ($P - 1);
  print STDERR "$out $out2 $diff\n";
  my ($x1, $y1) = point($out);
  my ($x2, $y2) = point($out2);
  my $green = int(256 * $x / ($P / 2 - 1));
  print <<EOF
<line x1="$x1" y1="$y1" x2="$x2" y2="$y2"
  style="stroke:rgb($green,$green,128);stroke-width:2"/>
EOF
}

for (my $theta = 0; $theta < $Pm; $theta++) {
  my ($x, $y) = point($theta);
  print <<EOF
 <circle cx="$x" cy="$y" r="2" fill="rgb(40,40,40)"/>
EOF
}

print '</svg>';