VectorColorFunction
is an option for VectorPlot and related functions that specifies a function to apply to determine colors of field vectors drawn.
Details
- The setting for VectorColorFunction is applied to the coordinates associated with the center of each field vector to determine the color to use to render the field vector.
- With the setting VectorColorFunction->func, the arguments supplied to func are as follows:
-
VectorPlot,ListVectorPlot, StreamPlot,ListStreamPlot, LineIntegralConvolutionPlot, ListLineIntegralConvolutionPlot x, y, vx, vy, Norm[{vx,vy}] VectorDensityPlot, ListVectorDensityPlot,StreamDensityPlot, ListStreamDensityPlot x, y, vx, vy, s VectorPlot3D,ListVectorPlot3D x, y, z, vx, vy, vz, Norm[{vx,vy,vz}] - With the usual default setting VectorColorFunctionScaling->True, the arguments supplied to func are scaled to lie in the range 0 to 1.
- With VectorColorFunctionScaling->False, original unscaled values are used.
- VectorColorFunction->"name" is equivalent to VectorColorFunction->(ColorData["name"][#i]&) where the slot used is as follows: VectorPlot, ListVectorPlot, etc.: #5 (Norm[{vx,vy}]), VectorDensityPlot, ListVectorDensityPlot, etc.: #5 (s), VectorPlot3D and ListVectorPlot3D: #7 (Norm[{vx,vy,vz}]).
- The list of possible color function names is given by ColorData["Gradients"].
- The function specified by VectorColorFunction must return color directives such as RGBColor and Hue or named colors such as Red and Blue.
- It can also return Opacity, as well as Glow and Specularity.
- Combinations of directives can be specified using Directive[g1,g2,…].
Examples
open all close allBasic Examples (1)
Use any color gradient from ColorData:
VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> "Rainbow"]Scope (2)
Vector color functions use the norms of the vectors by default:
{VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> "Rainbow"], VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> (ColorData["Rainbow", #5]&)]}Use the 
or 
position of the vector instead:
{VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> (ColorData["Rainbow", #]&)], VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> (ColorData["Rainbow", #2]&)]}Use the horizontal or vertical component of the vector instead:
{VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> (ColorData["Rainbow", #3]&)], VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> (ColorData["Rainbow", #4]&)]}By default, the vector color function uses values scaled to be between 0 and 1:
VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> (Hue[#5]&)]Use unscaled values with VectorColorFunctionScaling->False:
VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> (Hue[#5]&), VectorColorFunctionScaling -> False]Applications (2)
Use VectorColorFunctionScaling and ColorFunctionScaling with contrasting colors:
VectorDensityPlot[{x + y, -x + y}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> "SolarColors", ColorFunction -> "DeepSeaColors"]Color the vectors according to the logarithm of the vector magnitude:
VectorPlot[{x + y, -x + y}, {x, -10, 10}, {y, -10, 10}, VectorColorFunctionScaling -> False, VectorColorFunction -> (ColorData["Rainbow", Rescale[Log[#5], {-1, Log[10 Sqrt[2]]}, {0, 1}]]&)]Properties & Relations (1)
Use VectorColorFunction to color the vector field in VectorDensityPlot:
VectorDensityPlot[{x + y, -x + y}, {x, -3, 3}, {y, -3, 3}, VectorColorFunction -> "Rainbow"]Use ColorFunction to color the scalar field:
VectorDensityPlot[{x + y, -x + y}, {x, -3, 3}, {y, -3, 3}, ColorFunction -> "Rainbow"]Text
Wolfram Research (2008), VectorColorFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/VectorColorFunction.html.
CMS
Wolfram Language. 2008. "VectorColorFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VectorColorFunction.html.
APA
Wolfram Language. (2008). VectorColorFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VectorColorFunction.html