Hierarchical 2D Clouds with Wind
This applet shows how a hierarchical 2+1-dimensional function can use a "wind" vector to mimic motion. Such a function can form cloud-like details for a coarse weather model.
Note that this applet is actually performing something closer to a morph than a time-dependent simulation. The first and last frames are the same regardless of the wind direction. Something else I learned here is that rotating clouds do not make a hurricane; it's going to need better drivers for the cloud shapes to get good storms.
2+1 Hierarchical Functions
By "2+1" I mean two space dimensions and one time dimension. There is actually a full three-dimensional hierarchical function underlying this picture, with only one time value visible at a time. It's not necessary to evaluate all the levels of detail of the function at all times to show a specific frame; this applet only evaluates as much as is necessary as each frame is drawn.
See my 1D hierarchical function page for further explanation of hierarchical functions.