Try these. fc() is just an Inline C version of f().

I'm pretty sure that they are now correct, but you should verify them yourself.

#! perl -slw
use strict;
use Inline C => << '__C__', NAME => "_627288"; # => CLEAN_AFTER_BUILD 
+=> 0;
#include <stdio.h>

int fc( double x, double y, int d ) {
    double bsize = pow( 4, ( d-1 ) );

    if( x == y )
        return d;
    else if( (int)( x / 4 ) == (int)( y / 4 ) )
        return d-1;
    else if( (int)( x / bsize ) == (int)( y / bsize ) )
        return 1 + fc( fmod( x, bsize ), fmod( y, bsize ), d-1 );
    else
        return     fc( fmod( x, bsize ), fmod( y, bsize ), d-1 );
}

__C__

sub f{
    my( $x, $y, $d ) = @_;
    my $bsize = 4**($d-1);

    if( $x == $y ) {
        return $d
    }
    elsif( int( $x / 4 ) == int( $y / 4 ) ) {
        return $d-1;
    }
    elsif( int( $x / $bsize ) == int( $y / $bsize ) ) {
        return 1 + f( $x % $bsize, $y % $bsize, $d-1 );
    }
    else{
        return     f( $x % $bsize, $y % $bsize, $d-1 );
    }
}
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Using this I have produced plots of 1000x1000 chunks upto level 31 successfully. At that point the coordinates get so large that they blow the limits of doubles. I'm also fairly sure that you are loosing precision long before level 31. At level 16 everything appears to check out.

I don't think any single set of 20 lines of code has ever (in the best part of 30 years), given me as much trouble to wrap my brain around as this!