Given the behavior of leaves in a vacuum it make sense that friction and air resistance determine their natural behavior that we are familiar with. The mathematical functions that determine the path of a falling planar object have been a subject of significant research since the 1800's, when James Clerk Maxwell began studying falling playing cards.

Exact prediction and modelling of all the affecting factors (for instance, what determines whether a planar object tumbles in loops or drifts for side-to-side) still elude description, but in 1994, researchers at the University of Tokyo modeled an interesting aspect of friction acting on a sheet of falling paper.

It appears that as a sheet's coefficient of kinetic friction in a simplified system is incrementally increased, a series of phases in flight patterns occurs:
    Least friction: 1) " Drifts to one side, steadily rotating or flipping over as it falls."
                              2) "Erratic tumbling."
                              3) " Begins to flutter, swaying chaotically from side to side during its downward course."
                              4) "Swaying motion becomes regular."
    Most Friction: 5) "Sideways movements decrease to zero, and it falls straight down." [6]

Until quite recently, researchers believed that falling pieces of paper acted "like an airplane wing," catching an edge on the air, propelling the sheet upwards like a roller coaster. The problem with this model was that the air would require a greater viscosity than is actually present in many instances of this phenomenon.

In 2004, a group from Cornell University discovered through computer modelling of surrounding airflow that sheets get an additional lift proportional to its velocity times the rate of turning. This new effect "overwhelms the airfoil effect even between flips, when the sheet moves through the air quickly but rotates only slowly." [3]