By default, colors change with argument from (cyan) to (red) to (cyan):

By default, colors are lighter for complex numbers with larger moduli:

Unknown, symbolic or missing values are shown dark red:

Specify explicit colors for cells:

Plot a ragged array, padding on the right:

Cells with value None are rendered like the background:

Plot a sparse array:

Plot a numeric array:

Add a mesh:

Add a legend:

Turn off the default shading:

Change the color function:

Use shading schemes like ComplexPlot:

Choose a color function and a shading scheme:

By default, the ratio of the height to width for the plot is determined automatically:

Use numerical value to specify the height to width ratio:

Make the height the same as the width with AspectRatio1:

AspectRatioFull adjusts the height and width to tightly fit inside other constructs:

By default, ComplexArrayPlot uses a frame instead of axes:

Use axes instead of a frame:

Use AxesOrigin to specify where the axes intersect:

Turn each axis on individually:

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

Change the style of the axes:

Specify a style for each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

Background is normally visible only around the edges:

The background "shows through" whenever an explicit entry is None:

Background also by default shows through for values outside the plot range:

ClippingStyle overrides background color:

The default is to show values of with values outside the plot range in the background color:

Show values outside the plot range in red:

Show low values in black and high values in red:

By default, complex values are colored by Arg[z] and shaded by Abs[z]:

Turn off the shading based on Abs[z]:

Map modulus values from 0 to 1 onto colors according to Hue:

Use a pure function as the color function:

Use a named color gradient from ColorData:

Specify a shading scheme:

Specify a color function and a shading scheme:

With ColorFunctionScalingTrue, the values are first scaled to lie between 0 and 1:

Use a color function that colors complex values by Re[z], Im[z], Abs[z] or Arg[z]:

By default, values are scaled to lie between 0 to 1 before applying the color function:

Choose to not scale the argument prior to applying the color function:

Some color functions are not cyclic so the colors only change in a small band:

Specify color rules for explicit values:

Specify color rules for patterns:

ColorFunction is used if no color rules apply:

The array can contain symbolic values:

Implement a "default color" by adding a rule for _:

Rules are used in the order given:

By default, data is plotted at integer coordinates:

Specify a range for the data:

Specify a range for the data with a pair of complex numbers:

Specify the bottom-left corner of the data range:

Specify the top-right corner of the data range:

Reverse the order of rows:

The frame ticks give the original row numbers:

Reverse the order of rows and columns:

Reverse the order of columns:

Use Epilog to superimpose other graphics:

Epilog uses the standard Graphics coordinate system:

The graphics can be translucent:

Use MaxPlotPoints to limit the number of elements explicitly plotted in each direction:

Insert mesh lines between all cells:

Insert 1 row mesh line and 3 column mesh lines:

Insert mesh lines around the first 4 columns:

Specify styles for the mesh lines:

Style the mesh lines:

Style the row lines differently than the column lines:

No legend is used by default:

Generate a legend automatically:

PlotLegends automatically picks up a named ColorFunction:

PlotLegends does not pick up a user-defined ColorFunction, but the user can still construct an appropriate legend:

Use Placed to change the location of the legend:

Plot all elements:

Plot values of for which 1≤Abs[z]≤2:

Plot values of for which Abs[z]≤2:

The first two entries in PlotRange specify the range of rows and columns to include:

Use a theme with detailed ticks and a legend:

Move the legend below the plot:

Generate a pure discrete two-dimensional sinusoid:

Compute the two-dimensional Fourier transform:

Display the original data and its Fourier transform. In the second plot, the bright square in row 4 and column 6 (measured from the top-left corner) tells us that the corresponding frequencies are 3 and 5, respectively:

Generate a linear combination of discrete sinusoids:

Identify the component frequencies in the Fourier transform:

Display two-dimensional data and its Fourier transform:

Use ColorRules to threshold a Fourier transform:

Display only the top-left quarter of the Fourier transform:

Model the intensity of light diffracted by a small circular aperture:

Display the diffraction pattern and its Fourier transform:

Create data and modify it by shifting the columns left:

The magnitude of Fourier transforms are graphed, but that does not reveal potentially useful phase information. Observe the extra information in the middle plot:

Note the change in the ComplexArrayPlot and the lack of change in the ArrayPlot of the Fourier transform:

Plot a sparse matrix with complex entries:

Plot a random complex-valued matrix:

Visually verify that the matrix is diagonalized:

Visualize the matrices in a matrix factorization:

Visually compare Kronecker products:

Define a complex valued function with roots at 1, ±^{2π /3}:

Compute the corresponding Newton map:

Compute approximations to the roots of for various starting values:

Display the basins of attraction:

Define a complex-valued function with an infinite number of roots, ,:

Compute the corresponding Newton map:

Note that the roots only have three distinct argument values, and :

Compute approximations to the roots of for various starting values:

Display the basins of attraction, using shading to highlight the dependence on the modulus of the roots:

Define a complex-valued function with roots at 1, ±^{2π /3}:

Newton's method has quadratic convergence, but Halley's method has cubic convergence:

Compute approximations to the roots of for various starting values:

Display the basins of attraction for Halley's method:

Display eigenvalues from a two-parameter family of matrices:

Define a matrix:

Compute its eigenvalues:

The ϵ-pseudospectrum of the matrix is the set of values in the complex plane for which the norm of (m-λ I)^-1 is greater than . Graph the ϵ-pseudospectra for ϵ=1,1/2,1/4,1/8,1/16,1/32 and note the eigenvalues at the white dots:

If the largest eigenvalue is used instead of the norm of (m-λ I)^-1, then argument information can be added:

Create a Toeplitz matrix:

Make a plot similar to an ϵ-pseudospectral plot:

Use a named matrix:

Make a graph similar to a spectral portrait:

Visualize complex cellular automata:

Compute iterates of a complex-valued function:

Display the data on a width of 10:

The iterates appear to converge for a different constant:

Iterates are periodic for carefully chosen constants:

Let be the logistic function with a complex coefficient . Consider the sequence , for . Approximate the values of for which is unbounded and visualize the region:

Highlight Gaussian primes in black:

Plot a Fourier matrix:

Highlight the purely real and purely imaginary entries in black and gray, respectively: