vector field
Arrows everywhere, mathematically
A vector field assigns a vector—a quantity with both magnitude and direction—to every point in a region of space.
In physics, vector fields describe phenomena like gravitational pull, magnetic force, or fluid flow, where the strength and direction vary from place to place.
Mathematicians visualize them as arrows of varying lengths pointing in different directions across a plane or through three-dimensional space.
The wind map shows a vector field of air currents across the country.
Continuous change or flow
- divergenceSeparation from common origin
- curlSpiral or loop form
- gradientRate of change across space
- magneticAttracting iron or attention
electric · electromagnetic · Faraday · Maxwell · Gauss · Lorentz · potential · streamlines
Many and various
- differentialRelative difference between things
- tensorMultilinear algebraic object
- tangentLine touching curve once
- HelmholtzThermodynamics and perception
coordinate system · transformation · span · parametric · continuous · smooth · differentiable · boundary conditions
Directed rate of motion
- accelerationRate velocity changes
- momentumProduct of mass, velocity
- trajectoryPath of moving object
- streamlinesMakes more efficient
turbulence · laminar · advection · convection · fluid flow · steady state · perturbation · equilibrium
flux
Continuous change or flow
- divergenceSeparation from common origin
- curlSpiral or loop form
- gradientRate of change across space
magnetic · electric · electromagnetic · Faraday · Maxwell · Gauss · Lorentz · potential · streamlines · source
manifold
Many and various
- differentialRelative difference between things
- tensorMultilinear algebraic object
- tangentLine touching curve once
Helmholtz · coordinate system · transformation · span · parametric · continuous · smooth · differentiable · boundary conditions · domain
velocity
Directed rate of motion
- accelerationRate velocity changes
- momentumProduct of mass, velocity
- trajectoryPath of moving object
streamlines · turbulence · laminar · advection · convection · fluid flow · steady state · perturbation · equilibrium · stability
arrows
Shafted projectiles for bows
sampling · interpolation · contour · isoline · glyph · texture · hedgehog · streamline · grid · resolution