Consider an unit circle in <math>\mathbf{R}^2</math>, shrinking in on itself at a constant rate, i.e. each point on the boundary of the circle moves along its inwards pointing normal at some fixed speed. The circle will shrink, and eventually collapse down to a point. If an initial distance field is constructed (i.e. a function whose value is the signed euclidean distance to the boundary (positive interior, negative exterior)) on the initial circle, the normalised gradient of this field will be the circle normal.
If the field has a constant value subtracted from it in time, the zero level (which was the initial boundary) of the new fields will also be circular, and will similarly collapse to a point. This is due to this being effectively the temporal integration of the [[Eikonal equation]] with a fixed front velocity.
