Fractal Parallel Coordinates

I've been puzzling over how to represent recursive sets of metagames, which is following the work I'm doing around Nigel Howard's Paradoxes of Rationality. I know that what I am articulating is very fractal-like. What makes it so is not just the recursiveness of the metagame idea, but the fact that the metagame tree has boundaries marked out by the 'blind spots' of individual thinking - where deep recursion breaks down. More importantly, the depth of the recursion of a particular path is the fundamental determiner of an equilibrium point for making a decision. This led me to think that Mandelbrot style visualisations might be useful, since the different colours reflect the different levels of recursion at particular points.

But I'm not interested in this for the pretty pictures! With regard to Metarationality, the distinction between light and dark is a distinction between deep metarationality and shallow metarationality. The dark stuff is an indication of where the equilibrium points are. But can we do better?

Then I started looking for a different kind of coordinate system. Parallel coordinates are very interesting because they highlight visual patterns which are not obvious using Cartesian coordinates. Using parallel coordinates, points become lines. After a presentation by Alfred Inselberg in Vienna (who has pioneered the use of Parallel coordinates), I asked him what fractals look in his parallel system. Not terribly interesting was his reply (I guess a lot of different coloured lines for all the different points). But I'm now thinking about a different approach.

Maybe we should consider 'fractal axes' and then see what parallel coordinates might show. I was looking at this http://azimuth.mathforge.org/discussion/652/useful-fractal-coordinate-system/ from Curtis Faith which presents a fractal-based coordinate system which looks like this..

Now when I'm thinking about metagame trees, and the limits of reasoning, this might have something. Particularly because this kind of fractal geometry provides a way in which a number of metagame trees with different sources (i.e. different people) may be integrated and their dynamics considered.

There's more work to do (as usual). But, as well as being fascinating and potentially useful, it's all very pretty!