Comments by "" (@jmitterii2) on "Golden Ratio and Fibonacci Numbers (extra bit)" video.

Any series where you sum the prior sequence is by asserted definition going to build from it because the prior will both be summed, then repeated, that's what the function does by definition. What's nice about the sequence is that any time you do this summing for sequences you get the golden ratio rather it approaches it for that summing the prior function repeating. Symmetry breaking where the function stops doing the same thing over and over is more interesting as it becomes more complexity is increased. Random number generators etc. use infinite series, but if you get start to change the functions in the series you no longer get a golden ratio, you get an asymmetric arbitrage or essentially a nonsensical imbalance, useful in testing if a particular function itself is changing over time in a particular data series where you had too few significant figures that couldn't provide you the data outright.
1