Recursive ng-repeat x times

I need to repeat over a deeply nested javascript object in my angular template. The problem is that I have no control over how the data is handed to me, and no way of knowing how deeply nested the data will be.

The data looks like this

{
    category_name: 'cat1'
    children: [
        {
            category_name: 'cat1a',
            children: [...]            
        }
    ]
}

And the template

<div ng-repeat="cat in categories">
    <div ng-repeat="subcat in cat.children">
        {{subcat.name}}
        <!-- 
            would like to programatically place an ng-repeat here too 
            if subcat.children.length > 0 
        -->
    </div>
    {{cat.name}}
</div>

This checks two levels deep, but how can I recursively repeat until there are no children left? I'm thinking I need to create a custom directive that compiles a new ng-repeat as required, I'm just not sure how to go about it.