DomainColoringToy

checkerplot(
    f :: "Complex -> Complex",
    limits = (-1, 1, -1, 1);
    pixels = (480, 480),
    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 as an interactive GLMakie 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 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. If either is :auto, the viewport resolution is used.

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 = (480, 480),
    abs = false,
    grid = false,
    color = true,
    all = false,
    box = nothing,
    kwargs...
)

Takes a complex function and produces its domain coloring plot as an interactive GLMakie 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 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. If either is :auto, the viewport resolution is used.

• 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 sigma. base changes the base of the logarithm, as before. transform is the function applied to the magnitude (m -> log(base, m) by default), and sigma 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 = (480, 480),
    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 as an interactive GLMakie plot.

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 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. If either is :auto, the viewport resolution is used.

• 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 = (480, 480),
    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 as an interactive GLMakie 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 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. If either is :auto, the viewport resolution is used.

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 = (480, 480),
    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 as an interactive GLMakie plot.

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 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. If either is :auto, the viewport resolution is used.

• 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.

DomainColoringToy.shadedplot(
    f :: "Complex -> Complex",
    shader :: "Complex -> Color",
    limits = (-1, 1, -1, 1),
    pixels = (480, 480);
    kwargs...
)

Takes a complex function and a shader and produces a GLMakie plot with auto updating.

Arguments

• f is the complex function to plot.

• shader is the shader function to compute a pixel.

• limits are the initial limits of the 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.

• 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. If either is :auto, the viewport resolution is used.

Keyword arguments are passed to GLMakie.

DomainColoringToy.@shadedplot(
    basename,
    shaderkwargs,
    shader
)

Macro emitting an implementation of fname in a similar fashion to the other plotting routines in this library, see for instance 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.