Library

checkerplot(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    box = nothing,
    hicontrast = false,
    kwargs...
)

Takes a complex function and produces a checker plot.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

If none of the below options are set, the plot defaults to rect = true.

• real plots black and white stripes orthogonal to the real axis at a rate of one stripe per unit increase. If set to a number this will be used as width instead.

• imag plots black and white stripes orthogonal to the imaginary axis at a rate of one stripe per unit increase. If set to a number this will be used as width instead.

• rect is a shortcut for real = true and imag = true.

• angle plots black and white stripes orthogonal to the phase angle at a rate of eight stripes per full rotation. Can be set to an integer to specify a different rate.

• abs plots black and white stripes at a rate of one stripe per unit increase of the natural logarithm of the magnitude. If set to a number this is used as the base of the logarithm. When set to a function, unit increases of its output are used instead.

• polar is a shortcut for angle = true and abs = true. Can also be set to the basis to use for abs, then a suitable rate for angle will be selected.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

• hicontrast uses black and white instead of the softer defaults.

Remaining keyword arguments are passed to the plotting backend.

checkerplot(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    box = nothing,
    hicontrast = false,
    kwargs...
)

Takes a complex function and produces a checker plot.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

If none of the below options are set, the plot defaults to rect = true.

• real plots black and white stripes orthogonal to the real axis at a rate of one stripe per unit increase. If set to a number this will be used as width instead.

• imag plots black and white stripes orthogonal to the imaginary axis at a rate of one stripe per unit increase. If set to a number this will be used as width instead.

• rect is a shortcut for real = true and imag = true.

• angle plots black and white stripes orthogonal to the phase angle at a rate of eight stripes per full rotation. Can be set to an integer to specify a different rate.

• abs plots black and white stripes at a rate of one stripe per unit increase of the natural logarithm of the magnitude. If set to a number this is used as the base of the logarithm. When set to a function, unit increases of its output are used instead.

• polar is a shortcut for angle = true and abs = true. Can also be set to the basis to use for abs, then a suitable rate for angle will be selected.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

• hicontrast uses black and white instead of the softer defaults.

Remaining keyword arguments are passed to the plotting backend.

domaincolor(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    abs = false,
    grid = false,
    color = true,
    all = false,
    box = nothing,
    kwargs...
)

Takes a complex function and produces its domain coloring plot.

Red corresponds to phase $0$, yellow to $\frac{\pi}{3}$, green to $\frac{2\pi}{3}$, cyan to $\pi$, blue to $\frac{4\pi}{3}$, and magenta to $\frac{5\pi}{3}$.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

• abs toggles the plotting of the natural logarithm of the magnitude as lightness ramps between level curves. If set to a number, this will be used as base of the logarithm instead, if set to Inf, zero magnitude will be colored black and poles white. Further granular control can be achieved by passing a named tuple with any of the parameters base, transform, or alpha. base changes the base of the logarithm, as before. transform is the function applied to the magnitude (m -> log(base, m) by default), and alpha changes the rate at which zeros and poles are colored and implies base = Inf.

• grid plots points with integer real or imaginary part as black dots. More complicated arguments can be passed as a named tuple in a similar fashion to checkerplot.

• color toggles coloring of the phase angle. Can also be set to either the name of, or a ColorScheme, or a function θ -> Color. If set to :print a desaturated version of the default is used.

• all is a shortcut for abs = true, grid = true, and color = true.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

Remaining keyword arguments are passed to the plotting backend.

domaincolor(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    abs = false,
    grid = false,
    color = true,
    all = false,
    box = nothing,
    kwargs...
)

Takes a complex function and produces its domain coloring plot.

Red corresponds to phase $0$, yellow to $\frac{\pi}{3}$, green to $\frac{2\pi}{3}$, cyan to $\pi$, blue to $\frac{4\pi}{3}$, and magenta to $\frac{5\pi}{3}$.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

• abs toggles the plotting of the natural logarithm of the magnitude as lightness ramps between level curves. If set to a number, this will be used as base of the logarithm instead, if set to Inf, zero magnitude will be colored black and poles white. Further granular control can be achieved by passing a named tuple with any of the parameters base, transform, or alpha. base changes the base of the logarithm, as before. transform is the function applied to the magnitude (m -> log(base, m) by default), and alpha changes the rate at which zeros and poles are colored and implies base = Inf.

• grid plots points with integer real or imaginary part as black dots. More complicated arguments can be passed as a named tuple in a similar fashion to checkerplot.

• color toggles coloring of the phase angle. Can also be set to either the name of, or a ColorScheme, or a function θ -> Color. If set to :print a desaturated version of the default is used.

• all is a shortcut for abs = true, grid = true, and color = true.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

Remaining keyword arguments are passed to the plotting backend.

pdphaseplot(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    box = nothing,
    kwargs...
)

Takes a complex valued function and produces a phase plot using ColorCET's CBC1 cyclic color map for protanopic and deuteranopic viewers.

Yellow corresponds to phase $0$, white to $\frac{\pi}{2}$, blue to $\pi$, and black to $\frac{3\pi}{2}$.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

• real plots black to white ramps orthogonal to the real axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• imag plots black to white ramps orthogonal to the imaginary axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• rect is a shortcut for real = true and imag = true.

• angle plots black to white ramps orthogonal to the phase angle at a rate of eight ramps per full rotation. Can be set to an integer to specify a different rate.

• abs plots black to white ramps at a rate of one ramp per unit increase of the natural logarithm of the magnitude. If set to a number this is used as the base of the logarithm. When set to a function, unit increases of its output are used instead.

• polar is a shortcut for angle = true and abs = true. Can also be set to the basis to use for abs, then a suitable rate for angle will be selected.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

Remaining keyword arguments are passed to the plotting backend.

pdphaseplot(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    box = nothing,
    kwargs...
)

Takes a complex valued function and produces a phase plot using ColorCET's CBC1 cyclic color map for protanopic and deuteranopic viewers.

Yellow corresponds to phase $0$, white to $\frac{\pi}{2}$, blue to $\pi$, and black to $\frac{3\pi}{2}$.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

• real plots black to white ramps orthogonal to the real axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• imag plots black to white ramps orthogonal to the imaginary axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• rect is a shortcut for real = true and imag = true.

• angle plots black to white ramps orthogonal to the phase angle at a rate of eight ramps per full rotation. Can be set to an integer to specify a different rate.

• abs plots black to white ramps at a rate of one ramp per unit increase of the natural logarithm of the magnitude. If set to a number this is used as the base of the logarithm. When set to a function, unit increases of its output are used instead.

• polar is a shortcut for angle = true and abs = true. Can also be set to the basis to use for abs, then a suitable rate for angle will be selected.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

Remaining keyword arguments are passed to the plotting backend.

sawplot(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    color = false,
    box = nothing,
    kwargs...
)

Takes a complex function and produces a saw plot.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

If none of the below options are set, the plot defaults to rect = true.

• real plots black to white ramps orthogonal to the real axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• imag plots black to white ramps orthogonal to the imaginary axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• rect is a shortcut for real = true and imag = true.

• angle plots black to white ramps orthogonal to the phase angle at a rate of eight ramps per full rotation. Can be set to an integer to specify a different rate.

• abs plots black to white ramps at a rate of one ramp per unit increase of the natural logarithm of the magnitude. If set to a number this is used as the base of the logarithm. When set to a function, unit increases of its output are used instead.

• polar is a shortcut for angle = true and abs = true. Can also be set to the basis to use for abs, then a suitable rate for angle will be selected.

• color toggles coloring of the phase angle. Can also be set to either the name of, or a ColorScheme, or a function θ -> Color. If set to :print a desaturated version of the default is used.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

Remaining keyword arguments are passed to the plotting backend.

sawplot(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    color = false,
    box = nothing,
    kwargs...
)

Takes a complex function and produces a saw plot.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

If none of the below options are set, the plot defaults to rect = true.

• real plots black to white ramps orthogonal to the real axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• imag plots black to white ramps orthogonal to the imaginary axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• rect is a shortcut for real = true and imag = true.

• angle plots black to white ramps orthogonal to the phase angle at a rate of eight ramps per full rotation. Can be set to an integer to specify a different rate.

• abs plots black to white ramps at a rate of one ramp per unit increase of the natural logarithm of the magnitude. If set to a number this is used as the base of the logarithm. When set to a function, unit increases of its output are used instead.

• polar is a shortcut for angle = true and abs = true. Can also be set to the basis to use for abs, then a suitable rate for angle will be selected.

• color toggles coloring of the phase angle. Can also be set to either the name of, or a ColorScheme, or a function θ -> Color. If set to :print a desaturated version of the default is used.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

Remaining keyword arguments are passed to the plotting backend.

tphaseplot(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    box = nothing,
    kwargs...
)

Takes a complex valued function and produces a phase plot using ColorCET's CBTC1 cyclic color map for titranopic viewers.

Red corresponds to phase $0$, white to $\frac{\pi}{2}$, cyan to $\pi$, and black to $\frac{3\pi}{2}$.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

• real plots black to white ramps orthogonal to the real axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• imag plots black to white ramps orthogonal to the imaginary axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• rect is a shortcut for real = true and imag = true.

• angle plots black to white ramps orthogonal to the phase angle at a rate of eight ramps per full rotation. Can be set to an integer to specify a different rate.

• abs plots black to white ramps at a rate of one ramp per unit increase of the natural logarithm of the magnitude. If set to a number this is used as the base of the logarithm. When set to a function, unit increases of its output are used instead.

• polar is a shortcut for angle = true and abs = true. Can also be set to the basis to use for abs, then a suitable rate for angle will be selected.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

Remaining keyword arguments are passed to the plotting backend.

tphaseplot(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (720, 720),
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    box = nothing,
    kwargs...
)

Takes a complex valued function and produces a phase plot using ColorCET's CBTC1 cyclic color map for titranopic viewers.

Red corresponds to phase $0$, white to $\frac{\pi}{2}$, cyan to $\pi$, and black to $\frac{3\pi}{2}$.

Arguments

• f is the complex function to plot.

• limits are the limits of the rectangle to plot, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

Keyword Arguments

• pixels is the number of pixels to compute in, respectively, the real and imaginary axis, taking the same for both if only one number is provided.

• real plots black to white ramps orthogonal to the real axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• imag plots black to white ramps orthogonal to the imaginary axis at a rate of one ramp per unit increase. If set to a number this will be used as width instead.

• rect is a shortcut for real = true and imag = true.

• angle plots black to white ramps orthogonal to the phase angle at a rate of eight ramps per full rotation. Can be set to an integer to specify a different rate.

• abs plots black to white ramps at a rate of one ramp per unit increase of the natural logarithm of the magnitude. If set to a number this is used as the base of the logarithm. When set to a function, unit increases of its output are used instead.

• polar is a shortcut for angle = true and abs = true. Can also be set to the basis to use for abs, then a suitable rate for angle will be selected.

• box if set to (a, b, s) shades the area where the output is within the box a and b in the color s when set to (f, s) the colored domain is defined by f(w) == true. Can also be a list of multiple boxes.

Remaining keyword arguments are passed to the plotting backend.

DomainColoring.arenberg(θ; print = false)

Maps a phase angle θ to a color in Oklab space by taking

\[\begin{aligned} L &= .72 - .1 \cos(3\theta), \\ a &= .12 \cos(\theta + .4), \quad\text{and} \\ b &= .12 \sin(\theta + .4) + .02. \end{aligned}\]

If print is set to true, a desaturated version is used which is more easily reproduced on consumer grade printers.

See The Arenberg Phase Wheel for more information.

DomainColoring.arenberg_cielab(θ; print = false)

Superseded by the Oklab version: arenberg.

Maps a phase angle θ to a color in CIE L*a*b* space by taking

\[\begin{aligned} L^* &= 67 - 12 \cos(3\theta), \\ a^* &= 46 \cos(\theta + .4) - 3, \quad\text{and} \\ b^* &= 46 \sin(\theta + .4) - 16. \end{aligned}\]

If print is set to true, a desaturated version is used which is more easily reproduced on consumer grade printers.

DomainColoring.checkerplotshader(
    w :: Complex;
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    box = nothing,
    hicontrast = false,
)

Takes a complex value w and shades it as in a checker plot.

For documentation of the remaining arguments see checkerplot.

DomainColoring.domaincolorshader(
    w :: Complex;
    abs = false,
    grid = false,
    color = true,
    all = false,
    box = nothing,
)

Takes a complex value w and shades it as in a domain coloring.

For documentation of the remaining arguments see domaincolor.

DomainColoring.renderimage(
    f :: "Complex -> Complex",
    shader :: "Complex -> Color",
    limits = (-1, 1, -1, 1),
    pixels = (720, 720),
)

Arguments

• f is the complex function to turn into an image.

• shader is the shader function to compute a pixel.

• limits are the limits of the rectangle to render, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

• pixels is the size of the output in pixels, respectively, the number of pixels along the real and imaginary axis, taking the same for both if only one number is provided.

DomainColoring.renderimage!(
    out :: Matrix{<: Color},
    f :: "Complex -> Complex",
    shader :: "Complex -> Color",
    limits = (-1, 1, -1, 1),
)

Arguments

• out is the output image buffer.

• f is the complex function to turn into an image.

• shader is the shader function to compute a pixel.

• limits are the limits of the rectangle to render, in the format (minRe, maxRe, minIm, maxIm), if one or two numbers are provided instead they are take symmetric along the real and imaginary axis.

DomainColoring.sawplotshader(
    w :: Complex;
    real = false,
    imag = false,
    rect = false,
    angle = false,
    abs = false,
    polar = false,
    color = false,
    box = nothing,
)

Takes a complex value w and shades it as in a saw plot.

For documentation of the remaining arguments see sawplot.

DomainColoring.shadedplot(
    f :: "Complex -> Complex",
    shader :: "Complex -> Color",
    limits = (-1, 1, -1, 1),
    pixels = (720, 720);
    kwargs...
)

Takes a complex function f and a shader and produces a plot.

For documentation of the remaining arguments see renderimage.

Keyword arguments are passed to the backend.

DomainColoring.shadedplot(
    f :: "Complex -> Complex",
    shader :: "Complex -> Color",
    limits = (-1, 1, -1, 1),
    pixels = (720, 720);
    kwargs...
)

Takes a complex function f and a shader and produces a plot.

For documentation of the remaining arguments see renderimage.

Keyword arguments are passed to the backend.

DomainColoring.@shadedplot(basename, shaderkwargs, shader)

Macro emitting implementations of basename and basename! in a similar fashion to the other plotting routines in this library, see for instance domaincolor and domaincolor!.

shaderkwargs is a named tuple setting keyword arguments used in the expression shader. The result of shader should be a function Complex -> Color and is used to shade the resulting plot.

See the source for examples.