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We use the octahedron recurrence to give a simplified statement and proof ofa formula for iterated birational rowmotion on a product of two chains, firstdescribed by Musiker and Roby. Using this, we show that weights of certainchains in rectangles shift in a predictable way under the action of rowmotion.We then define generalized Stanley-Thomas words whose cyclic rotation uniquelydetermines birational rowmotion on the product of two chains. We also discussthe relationship between rowmotion and birational RSK and give a birationalanalogue of Greene's theorem in this setting.

Birational Rowmotion and the Octahedron Recurrence