The snow flake and starling are examples of different orders of complexity.
The snowflake is an example of a second order planar system, that has symmetry of scales, and while beautiful is simple compared to higher orders. It consists of only 2 differential eqs. x and y and the vector field when graphed is swirling, meaning it is stable. Melting vectors go out and growing vector swirl in.
The bird clip is a 2 dimensional planar view of the flight path, that looks very different in 3 dimensions. This system has many differential equations representing the flight paths. This 2 dimensional planar view is called a "Fractal"
and is plotted against time on the x axis, position on the y. Technically its called the "phase plane". Thats, why it changes thru time.
before the advent of increased entropic devices (computers) almost all analysis was done against time. the math was just to complex.
now it is possible to plot each of the differential equations. different phase planes, leaving time out to see what the fractal looks like, or including it in a 3 dimensional "cube". to watch the fractal change. (additional such things as Fourier analysis, Wavelet analysis, Cosine transforms, Laplace transforms can be performed to see what "information" is at each fractal stage. )
Memory systems, (nervous systems) work in much this way and it has been proposed that the fractals they create are metaphorically similar to Jungs Archetypes.
