Visualizing high-dimensional fitness landscapes

I've recently been exploring various ways of improving my intuitive understanding of fitness landscapes. This is a difficult problem, because the parameter spaces I want to be able to think about are often composed of dozens or even hundreds of dimensions. I have found that most authors describing fitness landscapes do so using overly simplified diagrams that somewhat resemble hills or mountain ranges.

In some recent experiments, I've found some nice ways of visualizing the geometry of actual fitness landscapes. I produced the images below by evolving recurrent neural networks to optimize performance on various tasks (e.g. wandering through a virtual maze), and then examining the resulting fitness values of a large number of very nearby points to those evolved solutions. Of course it is impossible to visualize the entire space, because of the high dimensionality; so instead what we are looking at are randomly selected 2D slices through that space. The shading is representative of numeric fitness (dark = low-fitness, light = high-fitness).

Here are a few examples of the results: