Creating a multilevel array using parentIds in PHP

Question

I'm trying to setup a list that can have multiple levels, using parentId to define its parent. The first item's parentId is NULL. Example of some entries:

id parentId name
1    NULL     item1
2    NULL     item2
3    1        item3
4    2        item4
5    3        item5
6    3        item6

So, 1 and 2 are main items; 3 is a child of 1; 4 is a child of 2; 5 is a child of 3 (which is a child of 1 itself); 6 is also a child of 3 (which is a child of 1 itself); etc.

I'm stuck creating an array that correctly adds these items to the right levels. It should look like this:

Array
(
    [1] => Array
        (
            [name] => item1
            [parentId] => 
            [children] => Array
                (
                    [3] => Array
                        (
                            [name] => item3
                            [parentId] => 1
                            [children] => Array
                                (
                                    [5] => Array
                                        (
                                            [name] => item5
                                            [parentId] => 3
                                        )

                                    [6] => Array
                                        (
                                            [name] => item6
                                            [parentId] => 3
                                        )

                                )

                        )

                )

        )

    [2] => Array
        (
            [name] => item2
            [parentId] => 
            [children] => Array
                (
                    [4] => Array
                        (
                            [name] => item4
                            [parentId] => 2
                        )

                )

        )

)

But say I go through all the items using foreach(), and I get to item 5. Its parentId is 3, but at that point, I have no idea where this parent 3 is located in the array, and how to add children to that parent.

Is there a trick to loop through these items, and put them all in place the right way?