Parallel Coordinates

Twenty-three interactive explorations of Inselberg's geometric framework, from the duality that makes it all work to exceptional root systems and the connections that emerged along the way.

A 5D point can't be pictured directly. Draw five parallel axes and connect the values as a polyline, and the point becomes visible. Correlations appear as crossing patterns; clusters as bundles; hyperplanes as structured signatures.

Alfred Inselberg developed the mathematical foundations over decades. These explorations make the geometry interactive: drag points, brush axes, rotate polytopes.

The vocabulary

Six colors recur across the series, each tied to a geometric role: blue is always a polyline, red is always a convergence or crossing.

polyline
The image of a point, a broken line that zigzags across every axis.
data lines · individual observations · cluster bundles · outlier signatures
point
A Cartesian dot, vertices, reference positions, indexed-point pivots.
polytope vertices · indexed points · group elements in Cayley graphs · lattice sites
crossing
Where polylines intersect, the place correlations and convergences become visible.
dual-image points · convergence patterns · highlighted anomalies · Pareto fronts
brush
The viewer's selection, what gets highlighted when you drag on an axis.
axis brushes · strum brushes · selected subsets · interactive filters
surface
An envelope bounding a family of polylines, hypersurfaces, trade-off curves, workspaces.
tangent envelopes · Pareto fronts · collision envelopes · reachable workspaces · hstar regions
axis
The structural backbone, the parallel rails against which everything else is plotted.
parallel axes · coordinate axes · reordering handles · permutation controls