The Secret Life Of Chaos.
An award winning BBC4 documentary. Professor Jim Al-Khalili uncovers one of the great mysteries of science – how does a universe that starts off as dust end up with intelligent life?
The latter half of the 20th century exposed the true workings of the natural world to Science. Chaos Theory has destroyed the Newtonian mechanics dream and shown time and time again that nature is not completely deterministic (like an orrery) and that complexity can emerge spontaneously from simple systems without any outside influence whatsoever.
No Ancient Astronauts or Intelligent Designers required.
I haven't had a chance to watch the program you linked to, however, as with so many of these science/math "popularizations", the exceedingly general treatment of the subject matter can sometime leave a general audience with false impressions. Chaos Theory, and it's mathematical expressions, are completely deterministic. It does not involve any intrinsic stochasticity. The apparent
non-deterministic evolution of these non-linear, complex systems is simply a function of;
a) insufficient precision in measurement of initial conditions
b) insufficient computational resources to follow the long-term evolution of the system -- which is a bit of a moot point, as the tiniest error in measurement of initial conditions usually results in a continuous deviation in the physical model from the theoretical calculations.
So, they are completely deterministic, in theory, but non-deterministic in real-life practice...but only due to human limitations, and the error involved in all human designed instruments. I think the confusion may lie in automatically equating non-linear (and unpredictable) with non-deterministic. One does not necessarily follow the other.
A chaotic system is typically highly non-linear, but is fundamentally deterministic.
The simplest example of a highly chaotic system whose behavior quickly becomes intractable over time evolution is the double (compound) pendulum. Compare that with a simple pendulum. Just be adding one additional hinge/pivot and tacking on a second pendulum arm to what was a simple, predictable pendulum, completely changes the dynamics and time evolution of the system...and makes it effectively non-predictable.
Also, the Mandlebrot Set (and fractals, in general) are completely deterministic (after all, they are calculated by iterated mathematical functions)...however, they are used in Chaos Theory as models of systems that feature some of the attributes of Chaos, i.e. great complexity, but are fundamentally predictable, which is why they are such a good model for exploring unpredictable chaotic systems.
All this is not to deny that there appears to be very real, non-deterministic priniciples at work in Nature. Beta Decay (and radioactive decay, in general) is just one example within Quantum Theory.