To what extent do different markets reflect each other? While the Forex market and the stock market are very different, it can be seen that sometimes events in the stock market can see 'equivalent' events in the Forex market. However, this can indeed be a kind of reflection if it is that changes in liquidity and the way asset classes are valued equate to an equivalent kind of event in both markets. 'Risk on/Risk off' encapsulates this kind of thinking and has a logical expression in trading patterns and algorithms. This is a way of looking at Forex pairs as a kind of reflection of market events in other markets by virtue of their importance.
The involvement of Forex pairs in flows of money can also point to this kind of reflective behaviour in stock market events. In this case, the Forex pair in its charting pattern is kind of 'through a glass darkly', moving in response to events in the stock market.

However, Forex has complexity; thus, this kind of movement can be seen as an intermix of structure and volatility. That is, the normal kinds of patterns will occur in Forex, but there can be a kind of enhancement to these patterns, for example, a greater tendency to continue a trend (even if very structured), or a particularly sharp push towards the end of a trend.
During the crash of 2008, it could be seen that major Forex pairs showed a directional symmetry with the stock market, with an 'enhanced' volatility in the downward move, making them particularly complex markets, even if apparently simplified by direction. During intensely volatile moves in more recent times, Forex pairs can also be seen making sharp directional moves, which, when this intensity fades, may revert back towards their more common ground and then resume their former direction as the volatility returns.
What this may point to is a different characteristic in different markets, which interact in certain ways, even if only by traders and programs classifying them as similar in some way. However, the underlying nature of these markets remains, and in this sense of similarity, effectively reflects itself as they respond with patterns.

To say that a market reflects itself is to say that events in other markets do not have a causal relationship but rather allow for a sense of similarity to project from one to the other. But that similarity is the trader's or program's sense of what it is a market may do, a generalised set of patterns to watch out for, that is, trading markets in similar ways.
Nonetheless, markets retain their characteristics, for example, a perceived directional bias, a type of volatility, or a tendency to follow the leader. 'Following the leader' can be seen across markets; it is just more diffuse in some than others. A perceived directional basis can also be noted across markets, but this may be for reasons such as the imposition of fundamentals, which might be a factor more hard-wired in some than others. Volatility can also be seen across markets, but some may have a tendency to sharply drop or rise with greater ease than others.
These reflective features can create a sense of similarity through markets; the tendency for different markets to have different characteristics can point towards a kind of reversion back to the idea of self-reflection, creating a complexity in response.