@ninjacolin *I don’t understand this set of sentences. Could you rephrase?*

I’ll try—I have a background in physics but this stuff wasn’t even known by the time I said goodbye to physics & moved on to other fields…

Once we had Newton’s laws of motion and a full analytical approach to describing physical systems—i.e., by the close of the 19th Century—there was great confidence among physicists in the “clockwork universe”—if you know the position and momentum of every particle, then (in principle) you could work out how the future will unfold. This is the epitome of determinism.

Sure, you can’t predict (let’s say) how billiard balls will fly apart on the break shot, but that’s just because details are lacking. If you could somehow measure everything with great precision then you could predict every ball’s trajectory. Small deviations from initial conditions give rise only to small deviations from future behavior, so approximate knowledge of a system’s present state is sufficient at estimating future states.

Eventually, however, it became obvious that non-linear dynamics—the rules that govern the behavior of most real-world physical systems—often give rise to chaotic behavior, characterized by (as described above) sensitive dependence on initial conditions. This changes the entire view. Now you have to know exactly—*with infinite precision*—what the initial state is before you can predict future behavior. Otherwise the system is inherently unpredictable, even though it still qualifies as deterministic.

Physicists speak of “phase space” as a multi-dimensional description of a many-body system. In this mathematical view, as a system evolves it traces a path through phase space. In the old view this path was simple and smooth. With chaos theory, however, this path is itself a fractal that defies detailed description. This is the connection between fractals and chaos.

I defer to others to explain it more clearly. If I knew more I could probably do better!