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Imagine a point cloud with multiple dimensions. To plot this and provide an interactive way to "play around", there are the following common ways:

  • parallel axis, star axis
  • 2D scatter plot
  • 3D scatter plot
  • scatter plots + colors + shapes + ...
  • reductions (non-interactive)

So of course you can add even more dimensions by varying different aspects of the plotted points. But it never feels like a real dimensions to the user. Let us call these dimensions secondary while the dimensions that alter the position of a point are primary. The primary dimensions can be scaled, moved and rotated and a user get an intuition how the work together. A rotation between a primary and secondary is mostly forbidden.

Now you can add more primary dimensions by using a good projection to the 2D/3D space (depends if you have a 3D screen). But most projections are very hard to understand. I also feel that the typical 4D hypercube where you get a big and a small cube gives you a very wrong intuition about the dimensions.

So I started an experimental 4D scatter plot. It's a 3D plot where the fourth primary dimension gets mapped to color+transparency. The mapping is with a predefined real value X:

  • -X: blue + full transparent
  • ...: interpolated transparent and light blue
  • 0: white + full visible
  • ...: interpolated transparent and light red
  • +X: red + full transparent

4D scatter plot

The intuition is that you also cannot see objects that are far in the first 3 dimensions. The color is just to differ between the two cases of "far away". Rotation/scaling/moving is possible.

Now my questions are: Does this really help (especially in contrast to a normal color mapping of the 4th dimension)? Is it possible to get a better understanding of 4 dimensions?

Disclaimer: I'm the creator of the mentioned scatter plot. It's open source and non-commercial. I don't collect any user data apart from the standard GitHub data.

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Sadly I find your experimental version more confusing than the standard 4D plots colouring.

Two channel coding

I believe one issue is that for the 4th dimension you use both transparency and colour. In cognitive terms you utilise 2 visual brain processing channels to encode one type of semantic information - this isn't necessary, and the two may actually collide. (To be perfectly precise, to the best of my knowledge we don't really have a dedicated visual channel for transparency; but you can think of it as a cross-channel sub-channel - it still has to make sense.)

Gestalt distracts

Although it may be just the result of arbitrary data in the plots on your site, the fact that it is dots (discrete spaced elements) you show means that when rotating the image all sorts of shapes are formed that set in motion pattern recognition tasks within the brain and distract from what I believe is the actual data you are attempting to show.

No natural depth cues

What else, it appears you do not provide any explicit visual depth cues. In real life further objects will be darker and less focused. This also creates some distorted image that the brain has to compensate for.

4D? We don't get it

Very recent research on the brain demonstrated the possibility that our 3D perception actually translates to 3D-like neural activity paths. Although not confirmed and debated, if such is the case you have further proof to the claim that it is impossible for humans to truly comprehend any data involving more than 3 dimensions, particularly not in its visual form.

Pointers

Perhaps a few pointers:

  • Consider continuous form.
  • I'd go for either transparency OR colour, but not both.
  • Add explicit depth cues.

It has to be said that transparency and depth cues will alter colour, but this is natural and the brain 'expect' that - low-level information will flow through 'correct' paths. But it's a different story when colour is used to encode semantics - that where the brain needs to do some extra work and 'crack' the problem.

Perhaps have a peep at Visual Thinking for Design (Ware, 2008); it may come handy in your case. And if you're not familiar with it already, read about Gestalt principles.

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