Carpet plot¶

A two-dimensional plot using intersecting curvilinear coordinate families to show interactions among several independent and dependent variables for visual interpolation.

Version: v1 · 2026-09-28 · History
Domain-specific #: 8348
Domain group: Applied Sciences & Engineering
Origin domain: Engineering & Design (beyond software)
Subdomains: Engineering Graphics, Design Space Visualization → Engineering & Design (beyond software)

Core Idea¶

A carpet plot maps interacting design variables into a two-dimensional curvilinear grid and overlays one or more responses for interpolation.

Its coordinate families carry information that would otherwise require extra axes or a 3D surface; cheater axes can add another independent variable.

Because the term also names temporal raster displays, the plotting convention must be stated before interpretation.

How would you explain it like I'm…

The Bendy Grid Chart

When a design depends on two choices at once, engineers can draw a special chart that looks like a stretched, slanted net, a bit like a carpet. One set of lines is for the first choice and the other set is for the second. You find where your two choices cross on the net and read off the answer.

The Slanted-Grid Design Chart

Engineers often need to see how two or more design choices, working together, change a result like weight or cost. A carpet plot draws this on a flat page using a slanted, bent grid: one family of lines for each choice. You find where the line for your first choice crosses the line for your second choice, and read the result there, guessing between lines when needed. This saves you from making a 3D picture. Watch out, though: people also use 'carpet plot' for a totally different chart that shows data over time as colored stripes, so you need to know which one you are looking at.

Curvilinear Design-Variable Grid

A carpet plot is an engineering chart that shows how a response depends on several interacting design variables using a two-dimensional curvilinear grid. Each design variable gets its own family of grid lines, and the response is read where the lines intersect, with interpolation between them. Because the grid itself carries information, it can replace extra axes or a 3D surface plot. A trick called a cheater axis shifts the grid sideways so that one more independent variable can be shown without overlapping. The same name is also used for a very different display, a raster plot of data over time, so the plotting convention must be stated before anyone reads values off it.

A carpet plot represents a response that depends on interacting design variables by mapping those variables onto a two-dimensional curvilinear grid, with each variable forming a family of coordinate curves, and overlaying one or more response values for interpolation. Because the coordinate families encode information directly, the plot conveys dependencies that would otherwise need additional axes or a three-dimensional surface. A cheater axis, which offsets the grid along the horizontal direction, allows an additional independent variable to be displayed. Readers interpolate within the curvilinear cells to estimate responses at intermediate variable values. The term is ambiguous: it also names temporal raster displays, so the convention in use must be declared before interpretation.

Structural Signature¶

Sig role-phrases:

independent variables. Define design coordinates. Constitutive inputs. If altered: Unlabeled curves cannot be interpreted.
curvilinear coordinate families. Map variable values into the plane. Constitutive structure. If altered: Ordinary Cartesian axes alone give another plot.
dependent response. Provides values or overlays to read. Constitutive output. If altered: A bare warped grid is not an analytical carpet plot.
interpolation geometry. Supports reading combinations between sampled curves. Diagnostic function. If altered: Folded/crowded grids can undermine it.
labels/legend. Resolve variables, units, and curves. Interpretation rule. If altered: Visual resemblance without mapping is insufficient.
plot convention. Distinguishes engineering carpet from temporal raster usage. Boundary frame. If altered: Shared term does not merge signatures.

What It Is Not¶

Not any warped grid. Variables and mappings must be explicit.
Not a contour plot synonym. Coordinates carry additional design relations.
Not necessarily temporal. Raster usage is another convention.
Not automatically clearer. Crowding and folds can defeat interpolation.

Scope of Application¶

The concept applies in engineering design and related inquiry when its defining roles and evidential frame are explicit.

Engineering design. Explores trade spaces.
Materials science. Relates laminate variables to properties.
Aeronautics. Displays multivariable performance.
Optimization. Reads feasible combinations.
Data visualization. Compares alternate conventions.

Clarity¶

Label every coordinate family, response, unit, interpolation direction, and plot convention. State whether the term means engineering carpet or temporal raster.

Manages Complexity¶

The plot flattens a higher-dimensional relation without discarding all coordinate structure, trading compactness for a learned curvilinear reading procedure. The name is ambiguous across plotting traditions, so a valid use must name the construction. In the engineering carpet plot, two curved coordinate families map independent-variable values into a two-dimensional field; contours or overlays then display one or more dependent variables, enabling interpolation among design combinations. A cheater axis can encode a third independent variable without making the picture an ordinary Cartesian grid. The legibility advantage depends on monotone, nonfolding local geometry and labeled axes; crowded or self-crossing carpets can make interpolation worse. Temporal raster plots are also sometimes called carpet plots, but they encode time-indexed observations as rows or pixels rather than curvilinear design coordinates. Shared name does not make their structural signatures identical.

Abstract Reasoning¶

Identify the carpet-plot convention.
Map each coordinate family to a variable.
Check nonfolding and labels.
Locate the response overlay.
Interpolate only within supported regions.

Knowledge Transfer¶

Curvilinear multivariable mapping transfers across engineering domains; the name stops where the graphic is merely a heatmap or unrelated raster convention.

Examples¶

Canonical¶

Two crossing curve families encode mixture proportions and ply angles, while response contours allow elastic-property interpolation inside the sampled design region.

Mapped back: independent variables → proportion and angle; curvilinear coordinate families → two labeled curve sets; dependent response → elastic property contours; interpolation geometry → inside cells; labels/legend → units and values; plot convention → engineering carpet.

Applied / In Practice¶

An aeronautical trade study adds a cheater axis for a third design variable and checks that curves do not fold before reading performance combinations.

Mapped back: independent variables → three design parameters; curvilinear coordinate families → carpet plus cheater axis; dependent response → performance outputs; interpolation geometry → nonfolding local field; labels/legend → annotated scales; plot convention → engineering carpet.

Structural Tensions¶

T1: dimensional compression vs. readability. More variables fit, but crowding can obscure paths. Diagnostic: Can a reader recover values unambiguously?

T2: interpolation vs. extrapolation. The geometry invites reading between curves but not beyond support. Diagnostic: Is the point inside a sampled cell?

Structural–Framed Character¶

Carpet plots are structural representations with design conventions. Individuation is by variable-to-curve mapping; author agency selects projection; visual norms govern readability; temporality is absent in the engineering form; robustness fails under folds or unlabeled transformations. Its strict broader skeleton is Representation. Its character: curvilinear compression of multivariable design relations for planar interpolation.

Structural Core vs. Domain Accent¶

Skeletal core. A many-variable relation is mapped into a lower-dimensional readable surrogate.

Domain-bound accent. Coordinate families, cheater axes, response contours, and engineering interpolation specify the common form.

Why not prime. Representation already captures the portable skeleton; carpet plot is one visualization technique.

This entry is a kind of Representation.

Parent candidate — Representation. The plot is a structured surrogate for a multivariable relation.
Related — contour plot. Both show response fields but encode coordinates differently.

Relationships to Other Abstractions¶

Current abstraction Carpet plot Domain-specific

Parents (1) — more general patterns this builds on

Carpet plot is a kind of Representation Prime

Carpet plot is a domain-specific kind of representation under its frozen identity and differentia.

Hierarchy path (1) — routes to 1 parentless root

Carpet plot → Representation → Abstraction

Neighborhood in Abstraction Space¶

Carpet plot sits in a sparse region of the domain-specific corpus (62^nd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Domain-Specific Measurement Parameters (36 abstractions)

Nearest neighbors

Snake Projection — 0.85
ARGUS distribution — 0.85
Skew-T Log-P Diagram — 0.84
I-bundle — 0.84
Simplicial depth — 0.84

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With¶

Contour plot. Tell: Cartesian response levels or carpet coordinate families?
Surface plot. Tell: Planar mapping or 3D geometry?
Temporal raster. Tell: Alternate namesake convention?
Parallel coordinates. Tell: Polyline across axes or curvilinear field?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Carpet_plot (revision 1333862538).
Preserved source candidate: http://math.materials-sciences.com/webMathematica/MSC/JSP/carpet.jsp
Preserved source candidate: https://web.archive.org/web/20081120214946/http://math.materials-sciences.com/webMathematica/MSC/JSP/carpet.jsp
Preserved source candidate: http://www.esdu.com/cgi-bin/ps.pl?sess=unlicensed_1100107121229jld&t=di&p=di_04008
Preserved source candidate: https://books.google.com/books?id=9jBsLgEACAAJ
Preserved source candidate: http://www.dept.aoe.vt.edu/~mason/Mason_f/SD1CarpetsbySAP.pdf
Preserved source candidate: http://www.gasturb.de/Gtb12Tutorials/GasTurb12DesignParametric.ppt
Preserved source candidate: https://web.archive.org/web/20131106032003/http://www.gasturb.de/Gtb12Tutorials/GasTurb12DesignParametric.ppt
Preserved source candidate: http://www.mathworks.com/matlabcentral/fileexchange/40831-carpet-plot-toolkit

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.