A language
you can see.A language you can see.
Color is another explanation. It should help you follow an idea across the page, through an equation, and into a figure.Color is another explanation. It should help you follow an idea across the page, through an equation, and into a figure.
The language of colorOne idea. One visual identity.
The metric turns coordinate steps into physical intervals.
The connection compares directions at neighboring events.
Curvature measures the failure of transport to close.
Stress–energy describes energy, momentum, and pressure.
An observer follows a worldline and carries a clock.
Color follows the object, not its importance. Indices, algebra, constants, and ambiguous symbols stay neutral. A radius called is not automatically curvature. Names, shapes, and equations carry the meaning even without color. Read the design conventions →
Identity before decorationIdentity before decoration
The metric, connection, curvature, stress–energy, and observer each have a persistent identity. We color identified symbols—not whole equations. Operations and indices keep their quiet ink so you can follow what changes and what contracts.The metric, connection, curvature, stress–energy, and observer each have a persistent identity. We color identified symbols—not whole equations. Operations and indices keep their quiet ink so you can follow what changes and what contracts.
Read from left to right: violet curvature, a teal metric, and amber stress–energy. The cosmological constant stays neutral; multiplying a metric does not make it a new kind of metric. The coupling constant is neutral too.Read from left to right: violet curvature, a teal metric, and amber stress–energy. The cosmological constant stays neutral; multiplying a metric does not make it a new kind of metric. The coupling constant is neutral too.
Related objects, distinct shadesRelated objects, distinct shades
Curvature has a violet family, with distinguishable shades for the full Riemann tensor, its Ricci contraction, its scalar trace, and its Weyl part. The volume measure stays close to metric green; the connection stays blue; density and pressure use different warm shades. A four-velocity has the observer’s rose. These refinements follow mathematical roles, so the same letter can remain neutral when its meaning is ambiguous.Curvature has a violet family, with distinguishable shades for the full Riemann tensor, its Ricci contraction, its scalar trace, and its Weyl part. The volume measure stays close to metric green; the connection stays blue; density and pressure use different warm shades. A four-velocity has the observer’s rose. These refinements follow mathematical roles, so the same letter can remain neutral when its meaning is ambiguous.
Context matters more than a letterContext matters more than a letter
The scalar is violet in curvature derivations. Earth’s radius is neutral in the clock experiment. An unindexed might mean a time interval or a trace, so automatic coloring leaves it neutral. The indexed stress–energy tensor is amber. A superscript does not by itself make an object a tensor.
Color cannot do the work aloneColor cannot do the work alone
Each diagram also uses names, arrowheads, distinct positions, solid and dashed paths, and explanatory captions. Equations retain their original notation and accessible MathML. Both reading themes use their own contrast-conscious palette. Mathematical labels in vector figures are generated from explicit LaTeX into scalable glyph paths; labels in 3D scenes use the same KaTeX typography as the book.Each diagram also uses names, arrowheads, distinct positions, solid and dashed paths, and explanatory captions. Equations retain their original notation and accessible MathML. Both reading themes use their own contrast-conscious palette. Mathematical labels in vector figures are generated from explicit LaTeX into scalable glyph paths; labels in 3D scenes use the same KaTeX typography as the book.
Three dimensions need an honest captionThree dimensions need an honest caption
We use depth where it reveals a missing direction: a light cone with two space axes, a sphere’s tangent plane, two independent tidal squeezes, or a family of spatial slices. Every model states what has been suppressed or exaggerated. A black-hole embedding diagram reproduces spatial distances on one slice; its height is neither time nor a gravitational force.We use depth where it reveals a missing direction: a light cone with two space axes, a sphere’s tangent plane, two independent tidal squeezes, or a family of spatial slices. Every model states what has been suppressed or exaggerated. A black-hole embedding diagram reproduces spatial distances on one slice; its height is neither time nor a gravitational force.
Make the experiment yoursMake the experiment yours
Drag to orbit or pinch to zoom. The other labs also provide rotation and reset buttons. Sliders work with the keyboard. The Earth grid moves automatically. Focus the scene and press Space to pause or resume it. It respects reduced-motion preferences and stops rendering when out of view. The already-deformed grid flows continuously, with fresh reference lines arriving from beyond the view. Mercury and the wave have explicit play and pause controls. Their animations stop when out of view; reduced-motion preferences start them paused. If WebGL is unavailable, the corresponding vector figure remains available. Enlarge any vector figure to inspect its labels without shrinking its mathematics.Drag to orbit or pinch to zoom. The other labs also provide rotation and reset buttons. Sliders work with the keyboard. The Earth grid moves automatically. Focus the scene and press Space to pause or resume it. It respects reduced-motion preferences and stops rendering when out of view. The already-deformed grid flows continuously, with fresh reference lines arriving from beyond the view. Mercury and the wave have explicit play and pause controls. Their animations stop when out of view; reduced-motion preferences start them paused. If WebGL is unavailable, the corresponding vector figure remains available. Enlarge any vector figure to inspect its labels without shrinking its mathematics.