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| In [[mathematics]], a [[complex function]] is a [[Function (mathematics)|function]] with the [[complex number]]s (see the [[imaginary numbers]] and the [[complex plane]]) as both its [[Domain of a function|domain]] and [[codomain]]. The '''complex color wheel method''' assigns a [[color]] to the point of complex plane.
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| ==Methods ==
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| The assignment of color to complex point could be diverse, but usually one of the following two:
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| * the [[Origin (mathematics)|origin]] is white, 1 is red, −1 is [[cyan]], and a point at the infinity is black,
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| or
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| * the origin is black, 1 is red, −1 is cyan, and a point at the infinity is white.
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| [[File:Color map fs.png|thumbnail|thumb|270px|HL plot of z : the origin is black, -1 is red, 1 is cyan, and a point at the infinity is white]]
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| [[Image:Sin1perz.png|thumb|270px|Color wheel graph of complex function <math>\sin(1/z)</math> (according to the first definition). Black parts inside refer to numbers having large absolute values. This function has an essential singularity at <math>z=0</math>.]]
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| More precisely, the argument of the complex number defines the hue value while the modulus defines the light value of the color in the [[HSL and HSV|HLS]] ([[hue]], [[lightness]], [[Colorfulness|saturation]]) color model; for a given (H,L) pair we choose the maximal saturation value. In both assignments, vivid colors of the rainbow are rotating in a continuous way on the complex unit circle, so the 6th [[Root of unity|roots of unity]] (counted from the 0th, the 1) are: red, yellow, green, cyan, blue, and violet. In addition, it is common in the assignments that the gradiations of colors belonging to two complex numbers close to each other are close to each other, and that colors of complex numbers of the same [[Argument (complex analysis)|argument]] are gradiations of the same color – the one which has greater [[absolute value]] is darker (according to the first definition) or lighter (according to the second definition).
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| However, the HSL color space is not perceptually uniform, leading to streaks of perceived brightness at yellow, cyan, and magenta, even though their absolute values are the same as red, green, and blue, and a halo around L=0.5. Use of the [[Lab_color_space|Lch color space]] corrects this, but makes the images more drab.
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| == History ==
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| The color wheel method was probably first used in publication by [[Larry Crone]] in 1987.{{Citation needed|date=March 2011}}
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| == Other references ==
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| * [http://wmi.math.u-szeged.hu/~kovzol/rtzme/doku.php?id=color_wheel_method Color wheel method]
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| * [http://web.archive.org/web/20120511021419/http://w.american.edu/cas/mathstat/lcrone/ComplexPlot.html Color Graphs of Complex Functions]
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| * [http://rtzme.sf.net Real-Time Zooming Math Engine]
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| [[Category:Complex analysis]]
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| [[Category:Color]]
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