De Morgan collector and reseacher, Rob Higgins, describs some complex tile patterns.
Just a bit of fun for you here, William De Morgan designed a frieze of birds which even by his standards is complex; you start with the eagle and the other bird looking away from each other and with the background foliage matching up, then go onto a tile of each design in the opposite hand, and mount them upside down, then keep repeating. I can’t imagine it as fun to do the tiling job on this one!
I have three tiles and the image is a composite, it is interesting that the eagle tile had a Fulham mark and the heron-l
ike tiles Chelsea marks, so the design wasn’t just a one-off effort, though I haven’t seen it in situ anywhere. 

Either De Morgan had a brilliant mind that could work in reverse, or he did trial versions on tiles of tracing paper so he could copy them, turn them over to get the inverse image, and unify the background foliage design by drawing across them. Quite amazing either way. 

Huge thanks to Rob for this research. If you are interested in the mathematics behind De Morgan’s complex patterns, then look out for Sublime Symmetry – an exhibition on this theme – which opens on 14th June 2019 at the Russell-Cotes Art Gallery in Bournemouth