This sort of set off my OCD. Paraview does in fact support octrees; it is just missing proper (any) documentation. Enclosed is a minimum working example.
To make it work, you must enable the HyperOctree Reader, which is part of VTK, but not part of the default Paraview readers.
To enable it, choose Tools -> Manage Plugins -> Load New and Select the enclosed file XMLHyperOctreeReader.xml.
Now, the octree.vto file can be opened.
To do anything useful with the data, you must enable the vtkHyperOctreeXXX classes as custom filters as described (poorly) here:
I am not sure how to do that. There is a vtkHyperOctreeContourFilter filter that returns a vtkUnstructured, class, so using this filer on the HyperOctree grid
would convert it to vtkUnstructured, if the clipping is set such that nothing is clipped. This will in turn enable more or less all of Paraview's functionality.
The grid structure is given such that for each parent node (denoted by zero), the grid must be traversed down to the leaf level (denoted by one) before the parent node numbering can continue. I think.
BR, Arne