I have a question about chaos, but first a foreword of what I understood.
Noise refers to the random variation of values. Usually unwanted, noise causes a measurement to fluctuate over time.
Chaos happens when starting the system in a slightly different way will lead to drastically different outcomes.
The fundamental difference between noise and chaos is that noise is stochastic whilst chaos is deterministic.
Stochastic means the changes in a system depends on a probability. Suppose you were standing on a line and flipped a coin every second. If it were head you moved right, and if it were tails you moved left. You can’t predict the future because there is only a chance that you go one way or another. This property usually arises from Quantum Mechanics, where things are not for certain, but very likely. Yet most randomness we deal with in most applications is on a level much higher than the Quantum one, e.g., inhomogeneities of nature and materials, air fluctuations (chaotic), particle billiards…
Deterministic means that the system will change the same way from the same starting conditions every time. In this way we could predict the chaotic behaviour if one were to know all the decimal points on a measurement. However, we cannot have perfect information (also restricted by Quantum Mechanics), so the tiny immeasurable differences will be amplified until the system is effectively unpredictable.
Question: can chaos be both stochastic and deterministic? If yes: how/why?