Part of a whole

Quaternary / tetrahedral composition plot

Positions observations by four component proportions using a three-dimensional tetrahedral coordinate system.

Plot
Composition
Multivariate comparison

What it answers

How do four-part compositions differ?

Shape: Points inside a tetrahedron
What it shows: Four-way composition clusters and trade-offs.

Example

The question

How is each blend made up from four ingredients?

Four-part blend recipes inside a tetrahedron (quaternary plot)

A tetrahedron drawn in 3D: each blend sits closer to the ingredients it holds most. B1: oats 40%, nuts 20%, seeds 20%, fruit 20%; B2: oats 10%, nuts 50%, seeds 20%, fruit 20%; B3: oats 20%, nuts 10%, seeds 10%, fruit 60%; B4: oats 25%, nuts 25%, seeds 25%, fruit 25%; B5: oats 50%, nuts 10%, seeds 30%, fruit 10%.

Illustrative data. It belongs to no company.

When to use it

Use it when

Specialised four-component composition analysis.

Avoid it when

General audiences, heavy occlusion or exact lookup needs.

How to read it

Read tetrahedral coordinates with a clear legend or projected companion views.

Note

Specialised 3D composition plot.

The data you need

Layout: Wide composition table
Fields: ID: text; A,B,C,D: nonnegative numbers
One row is: One composition with four components. What is the grain?
Rules: Four components must sum to a common positive total or be normalised. Convert to tetrahedral coordinates for rendering.
Optional: Optional group, colour or size.
Preparation: Check nonnegative components, reconcile the represented whole and aggregate duplicate categories. Define whether records are counts or already normalised shares.
Units: Four component shares sum to 1 or 100%; the common denominator is their total.

A wide table: one row per item, with a separate column for each measure or period.

Worked example

A=(10,20,30,40), B=(25,25,25,25). A is biased toward component D; B lies at the tetrahedron centre.

ID	A	B	C	D
One	10	20	30	40
Two	25	25	25	25

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