A Ternary plot or Ternary Graph is a specialization of a Barycentric plot for three variables. It graphically depicts the ratios of three proportions. It is often used in petrology, mineralogy, and other physical sciences to show the relative compositions of soils and rocks, but it can be more generally applied to any system of three proportions. Petrology is a field of geology which focuses on the study of rocks and the conditions by which they form. ... Mineralogy is an earth science that involves the chemistry, crystal structure, and physical (including optical) properties of minerals. ...
In a ternary plot, the proportions of the three variables a, b, and c must sum to some constant, K. Usually, this constant is represented as 1.0 or 100%. Because a + b + c = K for all substances being graphed, any one variable is not independent of the others, so only two variables must be known to find a sample's point on the graph: for instance, c must be equal to K - a - b. Because the three proportions cannot vary independently, it is possible to graph the intersection of all three variables in only two dimensions.
An example shows how this works for a hypothetical set of three soil samples:
Sample #
Organic matter
Clay
Sand
Notes
Sample 1
80%
10%
10%
Because organic matter and clay make up 90% of this sample, the proportion of sand must be 10%
Sample 2
50%
40%
10%
The proportion of sand is 10% in this sample too, but the proportions of organic matter and clay are different
Sample 3
10%
40%
50%
This sample has the same proportion of clay as in Sample 2 does, but because it has a smaller proportion of organic matter, the proportion of sand must be larger, because all samples' proportions must sum to 100%
A ternary plot is drawn as triangle. Each base, or side, of the triangle represents 0% of a proportion, with the point of the triangle opposite that base representing 100% of that proportion. As a proportions increases in any one sample, the point representing that sample moves from the base to the opposite point of the triangle.
The density plot assigns a grid to the scatterplot and counts the number of points in each cell of that grid, then displays them three-dimensionally with the count as the third dimension.
Experiment with this plot in which the y and x are the residuals and the predicted values from a regression or linear model.
Ternaryplots are a way of displaying the distribution of a three-component mixture.
In Box Plots (the term first used by Tukey, 1970), ranges of values of a selected variable (or variables) are plotted separately for groups of cases defined by values of up to three categorical (grouping) variables, or as defined by Multiple Subsets categories.
In ternaryplots, the triangular coordinate systems are used to plot four (or more) variables (the components X, Y, and Z, and the responses V1, V2, etc.) in two dimensions (ternary scatterplots or contours) or three dimensions (ternary surface plots).
In a categorized ternaryplot, one component graph is produced for each level of the grouping variable (or user-defined subset of data) and all the component graphs are arranged in one display to allow for comparisons between the subsets of data (categories).
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