138 (Melly: 165, liverpole: 156)

map{$a=1-$_/10;map{$d=$a;$e=$b=$_/20-2;$c=X;map{($d,$e)=(2*$d*$e+$a,$
e**2-$d**2+$b);$c=$"if$d**2+$e**2>4}1..50;print$c}0..59;print$/}0..20
[download]

• 'X' → X
• ' ' → $"
• "\n" → $/
• {...;} → {...}

• $a=1;while($a>=-1){...;$a-=0.1} →
  for(0..20){$a=1-$_/10;...} →
  map{$a=1-$_/10;...}0..20

• $b=-2;while($b<1){...;$b+=0.05} →
  for(1..50){$b=$_/20-2;...} →
  map{$b=$_/20-2;...}1..50

• $g=$d;$d=$d**2-$e**2+$b;$e=2*$g*$e+$a; →
  $d=($g=$d)**2-$e**2+$b;$e=2*$g*$e+$a; →
  ($d,$e)=($d**2-$e**2+$b,2*$d*$e+$a);

Notes:

• My loops counters are even more accurate than yours, since they don't accumulate floating point errors. This causes a slight visual difference which can be eliminated by removing the top and bottom rows (map{$a=.9-$_/10;...}0..18).
• I renamed $e and $d to $d and $e to create a parallel with $a and $b.

Spaced out:

map {
   $a = 1-$_/10;
   map{
      $d = $a;
      $e = $b = $_/20-2;
      $c = X;
      map {
         ($d, $e) = (2*$d*$e+$a, $e**2-$d**2+$b);
         $c = $" if $d**2+$e**2 > 4
      } 1..50;
      print $c
   } 0..59;
   print $/
} 0..20
[download]

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