photo 2) piece ~40cm

Ladderweed (Cystophora scalaris)
3) midrib is a series of cups alternately rotated 180 degrees. (Bryozoa on centre)
4) blades arise at the deep end of each cup
5) sperical bladders, thin blades

drawing http://collections.tepapa.govt.nz/objectdetails.aspx?irn=832255&term=Nancy+Adams+Seaweed

photo page 28 shows C. scalaris and C. torulosa side by side http://ir.canterbury.ac.nz/bitstream/10092/1364/1/thesis_fulltext.pdf