Comments: 12 pages, 3 figures; minor changes to match version published in JHEP
We consider the butterfly equation on a vector space of a complex scalar field. We show that, in the broadest possible dimensions, the butterfly equation is a simple butterfly equation with no sign of the angle between the vectors. We investigate the butterfly equation in an infinite-dimensional $2$-dimensional vector space and find that it correctly reproduces the Butterfly equation for any cosmological metric.