Using PHP how do I use recursive programming and mkdir() to create this hierarchy?

Recursion isn't really needed and just makes things more confusing. This solution uses a queue directly to be more straightforward.

So, assuming you have a pattern like '#/#', you push that into a queue. Then you take it off, and replace the first '#' in it with one of your characters. This effectively multiplies the number of items in the queue by 16. You repeat this process, taking an item off, doing the replacement, and putting them back in, until you have replaced every '#' in every item in the queue.

Then you can just create the directories as usual.

$partitionMap = '#/##';

makeFolders('./myfolder', $partitionMap);

function makeFolders($path, $pmap) {

  // Use number of characters and number of '#' to compute total combinations
  $characters = array(
    '0', '1', '2', '3', '4', '5', '6', '7',
    '8', '9', 'a', 'b', 'c', 'd', 'e', 'f'
  );
  $count = substr_count($pmap, '#');
  $num_results = pow(count($characters), $count);

  // Start array with path and pmap
  $combos = array( $path . '/' . $pmap );

  // Go through array, replacing each '#' with one of the characters.
  while (count($combos) < $num_results) {
    $str = array_shift($combos);

    foreach ($characters as $c) {
      array_push($combos, preg_replace('/#/', $c, $str, 1));
    }
  }

  // Create the directories, using third 'TRUE' parameter
  // to avoid creating parents manually
  foreach ($combos as $dir) {
    mkdir($dir, 0755, TRUE);
  }
}

I found this on the internet somewhere. seems to work if you're not using relative path. i.e. "../basepath/newpath1/newpath2". Still trying to figure it out.

/**
 * recursively create a long directory path
 */
function createPath($path, $rwd=0777) {
    if (is_dir($path)) return true;
    rev_path = substr($path, 0, strrpos($path, '/', -2) + 1 );
$return = createPath($prev_path);
    return ($return && is_writable($prev_path)) ? mkdir($path, $rwd, true) : false;
}

Hope it helps somebody. I think its fairly elegant. Just a comment, recursion is a very common practice in all programming languages and has it's places. Try to understand it, don't denigrate it just because you refuse to learn how to code it. As an example, try to get a file list without recursion or functions and you'll lose yourself very quickly.

As long as you do not need long directory names (up to 8 hex digits on 32 bit systems), you can use this (all three versions have constant memory complexity):

// Example for "#/##"
for ($i = 0; $i <= 0x0FFF; $i++) {
    $d = sprintf("%01x/%02x", $i & 0x00F, ($i & 0xFF0) >> 4);
    echo $d, "\n";
    mkdir($d, 0777, true);
}

And with use of your format strings:

function mkhexdir($format) {
    // Parse format string
    $fmt_N = array_map('strlen', explode('/', $format));
    $bit_count = array_sum($fmt_N) * 4;
    $max = 1 << $bit_count;

    // Prepare format string for sprintf
    $fmt_printf = join('/', array_map(function($n) { return '%0'.$n.'x';}, $fmt_N));

    // Generate all dirs
    for ($i = 0; $i < $max; $i++) {
        $args = array();
        $offset = $bit_count;
        foreach ($fmt_N as $len) {
            $offset -= $len * 4;
            $b = (1 << ($len * 4)) - 1;
            $args[] = ($i >> $offset) & $b;
        }
        $d = vsprintf($fmt_printf, $args);
        echo $d, "\n";
        mkdir($d, 0777, true);
    }
}

mkhexdir('#/##/##');

Or another version that uses regular expression:

function mkhexdir($format) {
    // Parse format string
    $fmt_N = array_map('strlen', explode('/', $format));
    $digits = array_sum($fmt_N);
    $max = 1 << ($digits * 4);

    // Prepare format string for sprintf
    $fmt_printf = '%0'.$digits.'x';

    // Prepare regular expression to format path
    $src = '/^('.join(')(',
            array_map(function($n){ return str_repeat('.', $n);}, $fmt_N))
            .')$/';
    $dst = '\\'.join('/\\',
            array_map(function($n){ return $n + 1;}, array_keys($fmt_N)));

    // Generate all dirs
    for ($i = 0; $i < $max; $i++) {
        $d = preg_replace($src, $dst, sprintf($fmt_printf, $i));
        echo $d, "\n";
    }
}

mkhexdir('#/##/##');