Science has gained power by denying or excluding the nature of anything which cannot be formally described in scientific terms. True to form, this is not an outright denial or suppression of evidence. Science is after all bound by its own principles to accept and adapt to that which is incontrovertible or at least verifiable. Complex systems often suggest inconsistencies which cannot be resolved and subsequently they must be reduced to something less than they are. Visualization works out of the grey area of human perception and cognition.
Visualization is part of a process of discovery.
It appears to aid the intuition in identifying relationships, some of which can be later described by formal analysis. In cases where there is no such analysis, the results of visualization cannot be properly integrated back into the scientific domain. Images like those of the Mandelbrot set are uniquely compelling, far beyond the trivial analytic evaluations of it which have been produced to date. Consequently the process of visualizing has been limited by the requirements of the science which seeks to exploit it. And at the same time, it offers inconsistencies that create problems for the scientist.