Thanks you for the responses. I have looked at the SPS particle system and indeed it is exactly what I need.
On my modest hardware here at home, I have already gotten very credible results with this suggestion. We're in the same performance envelope as the three.js sample I cited so I am very happy. As jerome said I will not need to view 100x100x100 simultaneously, but it was just for a sense of the scale of the webgl and Babylon.js technology at the moment. I think I will be viewing far fewer than 100k at the moment, let alone 1 million, though I am keen to be able to see a lot because our brains are quite good at discerning patterns even if there are very many thing we are looking at at the same time. Think about grains of sand on a beach or grass: we are able to find even subtle patterns in these (if they exist), even though we may be looking at a million of them or more.
Indeed, JohnK, tensors are highly unintuitive because we can no longer rely on our physical-world intuitions, which are designed for 3d and maybe 4d if you consider time. However they are mathematically enormously useful as we may use projections to "slice" our data into views which can be extremely interesting, and there are major algorithmic benefits if we can keep all the factors affecting our problem in a single memory structure, as the (potentially nonlinear, and potentially very subtle) relationships are more easy to find. Needless to say, however, the memory use is potentially enormous, and of course all the calculation will not be done browser side. Indeed one of the challenges is fast communication between browser and server. It is to manage these data complexities that so many "big data" technologies are now being developed. I'm a bit old fashioned however and am simply adding RAM. 256 Gigabytes RAM in my current compute server machine. Some big companies have petabytes. I personally will not need this (yet). But one area which is massively being left behind, is the visualization side of this scale of data. 3d + animation + interactivity to "slice-on-demand" is going to be mandatory.
I will post as and when I do interesting things will Babylon.js and I thank you for showing me the SPS.
For an example of "projecting" up to 6d onto a 2d screen, have a look at this (fairly old but excellent) video. Note the (exponentially increasing) use of the time dimension to animate in order to see dimensions 4 through 6. Interactivity and slicing would help here too of course.