The general effect of quantitative analysis of the markets is to enforce randomness.
Suppose a strategic quant finds a predictable pattern where a stock always rises on Tuesdays. His institution will commence buying the stock every Monday, and selling on Tuesday. The trading itself pushes the stock price up on Monday and down on Tuesday (in general), so if enough volume is traded the pattern will disappear.
The occasions where this is not true are when there are unavoidable demands due to regulation or when the market is not efficient; at the end of the year there is generally a strong demand for USD to satisfy regulatory or accounting requirements for capital, which push exchange rates and interest rates one way for a short period. It is largely predictable, but only those who are not short of USD can benefit; the pool is too small to correct the imbalance. Similarly, when a whale trades (e.g. the London Whale), the market is not efficient and other factors like liquidity and trade volume come into play.
So the short answer is that any pattern like a resonance pattern should be eliminated in a fast, efficient market, and that there are enormous resources devoted to locating patterns in the numbers in order to exploit and effectively eliminate them. In a physical system, the particles are blind and dumb, and the mechanisms are predictable and consistent. In finance, every participant has complex behaviour, and many of the mechanisms are neither predictable nor consistent, except to consistently act to eliminate predictability.
The history books are full of clever quants who had a sure thing until they didn't. For example, LTCM, the whole MBS setup, etc.
The exception is Goldman.