Operations

If a periodic (ordered) function operates upon a chaotic (random) function, is the resulting function ordered or chaotic?
If we choose a periodic function such as sin(x), and let x be a random (chaotic) number from -infinity to +infinity. Can a prediction be made about the result? Yes. The result will never exceed 1 in magnitude. But that's it. No other prediction can be made about the resultant numbers.
Now we can try the reverse, and try to choose a random function that takes its seed from a periodic function. Here, we run into a problem. A truly random function that is calculated using arithmetic does not exist. But we can get close to true randomness by proper choice of seeds for the random number generator. In principle, therefore, an operation of randomness on a seed of periodic nature, will produce randomness.
Thus, it appears that the operand loses its qualities to the operator. An ordered function operation produces limits to randomness, and a chaotic operation makes the periodic seed lose its predictability.