Describe › Standalone plots

Ternary plot

A ternary plot normalises three numeric components to a composition summing to one and places each row inside an equilateral triangle, each vertex meaning 100% of one component.

What is Ternary plot?

A ternary (triangular) diagram displays three-part compositional data — proportions that sum to a constant — in two dimensions, exploiting the fact that a composition on the 2-simplex has only two degrees of freedom. Each row (a, b, c) is closed to (a, b, c)/(a+b+c) and mapped to cartesian coordinates x = b + c/2, y = (√3/2)·c, so vertex A (bottom-left) is 100 % of the first column, vertex B (bottom-right) the second, and vertex C (top) the third; the opposite edge of each vertex is 0 % of that component.

Compositional data is the subject of Aitchison's log-ratio analysis (J. Aitchison, The Statistical Analysis of Compositional Data, 1986): because the parts are constrained to a constant sum, ordinary correlations are misleading and the sample space is the simplex rather than real space. The ternary plot is the classical descriptive view of such data and is standard in geology (soil/rock texture), petrology, and mixture experiments.

When should I use Ternary plot?

  • Any three parts of a whole — soil sand/silt/clay, mixture-experiment blends, cell-type or allele fractions, market-share splits.
  • Spotting clusters or gradients in compositional data before a formal log-ratio analysis.

What data does it need?

Exactly three numeric columns (components A, B, C) plus an optional grouping column for point colour. Rows whose three components are non-finite or sum to a non-positive value are skipped.

What does it report?

A scatter of composition points inside a triangular frame with 20/40/60/80 % gridlines and labelled vertices; the tooltip reports each point's three percentages.

What does it assume?

  • The three components are non-negative parts of a common total (they are re-normalised to sum to one).
  • Only the relative proportions matter — absolute totals are discarded by the closure.

How do I interpret the result?

A point near a vertex is dominated by that component; a point near an edge is depleted in the opposite vertex's component; the centroid is an equal 1/3-1/3-1/3 mix. Because the data lives on the simplex, interpret spread with log-ratio methods rather than Euclidean distance.

See also