 The equation depends on a driving function "ζ"("t") taking values in the boundary of "D".If "D" is the unit disk and the curve "γ" is parameterized by "capacity", then Loewner's equation is

When "D" is the upper half plane the Loewner equation differs from this by changes of variable and is

The driving function "ζ" and the curve "γ" are related by
where "ƒ""t" and "g""t" are extended by continuity.Let "D" be the upper half plane and consider an SLE0, so the driving function "ζ" is a Brownian motion of diffusivity zero.