What can surfaces provide us? Surfaces provide an easier way to interpret data, especially big data. Surfaces can be used in conjunction with 2D visualizations for additional confirmation. For example, surfaces of the market can be used with normal 2D price curves to get a better understanding of the market’s dynamics. Therefore surfaces can fill in gaps of understanding that lower dimensions do not seem to reveal.
As for the theoretical framework, chaos theory is used because of the emerging properties that the market seems to exhibit. Complexity science—which is a branch from chaos theory—highly suggests emergent behavior of nonlinear systems, such as the financial markets. We can envision three different state–spaces composing of buyers and sellers. In first state–space the population is heterogeneous but equally distributed, whereby influence by neighboring traders are considered minimum. In second state–space the populations of buyers and sellers are still equal, but the traders of similar types are coalescing into segregated masses. Within this second state–space you can see that a phase transition is about to take place but it is not clear if buyers or the sellers will triumph. In technical trading this can be seen clearly in a Bollinger band pinch, whereby a big move either up or down can result. Lastly, in the third state–space we see that a certain population type has overcome the other population and exhibits a severe herd effect. It is important to mention that this herd effect is also present in second state–space example but only local to its community.