Ternary diagram

A ternary diagram is the 3-parameter analogue of the 2-parameter spectrum. Though it's two-parameter, like a scatter plot, it has only one degree of freedom, so we can map it onto one dimension: a line.

Degrees of freedom
The three-dimensional equivalent of the spectrum is the ternary diagram: 3-parameter space mapped onto 2D. Not a projection, like a 3D scatter plot, because there are only two degrees of freedom — the parameters of a ternary diagram cannot be independent. This works well for volume fractions, which must sum to one. Hence their popularity for the results of point-count data, like this Folk classification from Hulk & Heubeck (2010).

We can go a step further, natch. You can always go a step further. How about four parameters with three degrees of freedom mapped onto a tetrahedron? Fun to make, not so fun to look at. But not as bad as a pentachoron.

How to make one
The only tools I've used on the battlefield, so to speak are Trinity, for ternary plots, and TetLab, for tetrahedrons (yes, I went there), both Mac OS X only, and both from Peter Appel of Christian-Albrechts-Universität zu Kiel. But there are more...


 * A great many tools are discussed in this StackOverflow thread, mostly using R and Python.
 * Of those tools, ggtern (in R) seems to have a lot of bells and whistles, like contours and density maps.
 * For Python, WxTernary and Veusz look like they may be the best choices.
 * There's a script here too, but it looks a little dated. Ripe for rescuing in a Notebook...
 * If you are stuck in Excel (we can help!), there may be options for you too:
 * W Vaughan
 * Phasediagram.dk
 * Loughborough

Printable template
If you need something to sketch on, here's an editable SVG template (right).