It is possible to generalize the escape time of a set to a continuous value. Briefly this involves taking into account the magnitude of the first point in the trajectory to pass the bailout value. See [vepst97] for a more detailed explanation.

It should be possible given this generalization to produce a level set for any positive real number. The next step is then to interpolate this value across keyframes. Through interpolation of this value it would be possible to in effect shrink-wrap the surface of the fractal to any desired level of detail.

This could be useful when animating a zoom into the set, keeping the approximate detail per frame constant over the zoom by pushing the escape time limit higher as the camera approaches the set.