Function Repository Resource:

DLMFHue

Source Notebook

Get a color based on the Digital Library of Mathematical Functions (DLMF) color wheel

Contributed by: Jan Mangaldan

ResourceFunction["DLMFHue"][h]

is a color based on the color wheel, as modified by the Digital Library of Mathematical Functions (DLMF).

ResourceFunction["DLMFHue"][h,s,b]

specifies the saturation and brightness.

ResourceFunction["DLMFHue"][h,s,b,a]

specifies opacity a.

Details and Options

The parameters h, s, b, and a must all be between 0 and 1. Values of s, b, and a outside this range are clipped. Values of h outside this range are treated cyclically.

As h varies from 0 to 1, the color corresponding to ResourceFunction["DLMFHue"][h] runs through red, yellow, green, cyan, blue, magenta, and back to red again.

ResourceFunction["DLMFHue"][h] is equivalent to ResourceFunction["DLMFHue"][h,1,1].

The alternative forms ResourceFunction["DLMFHue"][{h,s,b}] and ResourceFunction["DLMFHue"][{h,s,b,a}] can also be used.

ResourceFunction["DLMFHue"][h,s,b,a] is equivalent to Directive[ResourceFunction["DLMFHue"][h,s,b],Opacity[a]].

If no opacity has been specified, ResourceFunction["DLMFHue"][h,s,b] is equivalent to ResourceFunction["DLMFHue"][h,s,b,1].

For more information, see DLMF-About Color Map.

Examples

Basic Examples (2)

Specify the color of a graphic primitive:

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Specify the color with opacity:

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Scope (5)

Visualize the DLMF color wheel:

In[3]:=

$ParametricPlot[{r Cos[\[Theta]], r Sin[\[Theta]]}, {r, 0, 1}, {\[Theta], -\[Pi], \[Pi]}, ColorFunction -> (ResourceFunction["DLMFHue"][#4/(2 \[Pi])] &), ColorFunctionScaling -> False, {Axes -> None, BoundaryStyle -> None, Exclusions -> None, Frame -> None}]$

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DLMFHue[h] is equivalent to DLMFHue[h,1,1]:

In[4]:=

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DLMFHue[{h,s,b}] is equivalent to DLMFHue[h,s,b]:

In[5]:=

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Use Opacity with DLMFHue:

In[6]:=

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Use the opacity argument in DLMFHue directly:

In[7]:=

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Applications (2)

Use with ComplexPlot:

In[8]:=

$ComplexPlot[(-1 + z)/(1 + z + z^2), {z, -2 - 2 I, 2 + 2 I}, ColorFunction -> (ResourceFunction["DLMFHue"][#8/(2 \[Pi])] &), ColorFunctionScaling -> False, Exclusions -> None]$

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Use with ComplexPlot3D:

In[9]:=

$ComplexPlot3D[(-1 + z)/(1 + z + z^2), {z, -2 - 2 I, 2 + 2 I}, ColorFunction -> (ResourceFunction["DLMFHue"][#8/(2 \[Pi])] &), ColorFunctionScaling -> False, Exclusions -> None, PlotRange -> All]$

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Properties and Relations (2)

DLMFHue is a transformed version of Hue:

In[10]:=

$With[{hf = Interpolation[Transpose[{Range[0, 1, 1/4], {0, 1/6, 1/2, 2/3, 1}}], InterpolationOrder -> 1]}, dlmfhue[h_?NumericQ, rest___?NumericQ] := Hue[hf[Mod[h, 1]], rest]]$