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# 12. Plotting

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## 12.1 Introduction to Plotting

Maxima uses an external plotting package to make the plots (see the section on Plotting formats). The plotting functions calculate a set of points and pass them to the plotting package together with a set of commands. That information can be passed to the external program either through a pipe or by calling the program with the name of a file where the data has been saved. The data file is given the name `maxout.interface`, where `interface` is the name of the plotting interface being used (gnuplot, xmaxima, mgnuplot or gnuplot_pipes).

There are options that can be used to save the plot in a graphic format file. In those cases, the file `maxout.interface` will be created and then executed by the external plotting program to save the result in another file; if the name of that graphic file is not given by the options used, the default name `maxplot.format` will be used, where `format` is the format being used.

The `maxout.interface` and `maxplot.format` files (or the plot name given by the options), in the cases when they are used, are created in the directory specified by the system variable `maxima_tempdir`. That location can be changed; by assigning to that variable (or to the environment variable MAXIMA_TEMPDIR) a string that represents a valid directory where Maxima can create new files. The name of the file, or files, created will be shown as the output of the plotting command.

After a plot has been created, the file `maxout.interface` can be executed again with the appropriate external program. If a Maxima plotting command fails to show anything, that file can be inspected to look for possible sources of problems.

Together with the plotting functions described in this chapter, package draw adds other functionalities. Note that some plotting options are named equal in both plotting contexts, but with different syntax; if you want to access the draw information related to these options, you have to type `?? opt`, where `opt` is the name of the option.

Categories: Plotting

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## 12.2 Plotting Formats

There are currently two external plotting programs that Maxima use: Gnuplot and Xmaxima. There are various different formats for those programs, which can be selected with the option `plot_format` (see the Plotting Options section).

The plotting formats are the following:

- gnuplot (default on Windows)

  Used to launch the external program gnuplot, which must be installed in your system. All plotting commands and data are saved into the file `maxout.gnuplot`.

- gnuplot_pipes (default on non-Windows platforms)

  This format is not available in Windows platforms. It is similar to the `gnuplot` format except that the commands are sent to gnuplot through a pipe, while the data are saved into the file `maxout.gnuplot_pipes`. A single gnuplot process is kept open and subsequent plot commands will be sent to the same process, replacing previous plots, unless the gnuplot pipe is closed with the function `gnuplot_close`. When this format is used, the function `gnuplot_replot` can be used to modify a plot that has already displayed on the screen.

  This format is only used to plot to the screen; whenever graphic files are created, the format will be switched automatically to `gnuplot` and the gnuplot commands needed to created the graphic file will be saved in `maxout.gnuplot`.

- mgnuplot

  Mgnuplot is a Tk-based wrapper around gnuplot. It is included in the Maxima distribution. Mgnuplot offers a rudimentary GUI for gnuplot, but has fewer overall features than the plain gnuplot interface. Mgnuplot requires an external gnuplot installation and, in Unix systems, the Tcl/Tk system.

- xmaxima

  Xmaxima is a Tcl/Tk graphical interface for Maxima that can also be used to display plots created when Maxima is run from the console or from other graphical interfaces. To use this format, the xmaxima program, which is distributed together with Maxima, should be installed. If Maxima is being run from xmaxima itself, this format will make the plot functions send the data and commands through the same socket used for the communication between Maxima and Xmaxima. When used from the console or from other interface, the commands and data will be saved in the file `maxout.xmaxima`, and the xmaxima program will be launched with the name of the location of that file as argument.

  In previous versions this format used to be called `openmath`; that old name will still be accepted as a synonym for `xmaxima`.

Categories: Plotting

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## 12.3 Functions and Variables for Plotting

Function: contour_plot (expr, x_range, y_range, options, …)

  It plots the contours (curves of equal value) of expr over the region x_range by y_range. Any additional arguments are treated the same as in `plot3d`.

  This function only works when the plot format is either `gnuplot` or `gnuplot_pipes`. The additional package `implicit_plot` can also be used to plot contours and it works for any format. See `implicit_plot`.

  Examples:

      (%i1) contour_plot (x^2 + y^2, [x, -4, 4], [y, -4, 4])$

  You can add any options accepted by `plot3d`; for instance, the option `legend` with a value of false, to remove the legend. Gnuplot chooses, by default, 3 contours to show. To increase the number of levels, it is necessary to specify a custom gnuplot preamble:

      (%i1) contour_plot (u^3 + v^2, [u, -4, 4], [v, -4, 4],
                    [legend,false],
                    [gnuplot_preamble, "set cntrparam levels 12"])$

  Categories: Plotting

Function: get_plot_option (keyword, index)

  Returns the current default value of the option named keyword. A value of 1 for the index will return the keyword itself, a value of 2 returns the first parameter following the keyword, and so on.

  See also `set_plot_option`, `remove_plot_option` and the section on Plotting Options.

System variable: gnuplot_command

  This variable stores the name of the command used to run the gnuplot program when the plot format is `gnuplot`. Its default value is "wgnuplot" in Windows and "gnuplot" in other systems. If the gnuplot program is not found unless you give its complete path or if you want to try a different version of it, you may change the value of this variable. For instance,

      (%i1) gnuplot_command: "/usr/local/bin/my_gnuplot"$

  Categories: Plotting

System variable: gnuplot_file_args

  When the a graphic file is going to be created using `gnuplot`, this variable is used to specify the way the file name should be passed to gnuplot. Its default value is "~s", which means that the name of the file will be passed directly. The contents of this variable can be changed in order to add options for the gnuplot program, adding those options before the string "~s".

  Categories: Plotting

System variable: gnuplot_view_args

  This variable is used to parse the argument that will be passed to the gnuplot program when the plot format is `gnuplot`. Its default value is "-persist ~s", where "~s" will be replaced with the name of the file where the gnuplot commands have been written (usually "maxout.gnuplot"). The option `-persist` tells gnuplot to exit after the commands in the file have been executed, without closing the window that displays the plot.

  Those familiar with gnuplot, might want to change the value of this variable. For example, by changing it to:

      (%i1) gnuplot_view_args: "~s -"$

  gnuplot will not be closed after the commands in the file have been executed; thus, the window with the plot will remain, as well as the gnuplot interactive shell where other commands can be issued in order to modify the plot.

  In Windows versions of gnuplot older than 4.6.3 the behavior of "~s -" and "-persist ~s" were the opposite; namely, "-persist ~s" made the plot window and the gnuplot interactive shell remain, while "~s -" closed the gnuplot shell keeping the plot window. Therefore, when older gnuplot versions are used in Windows, it might be necessary to adjust the value of `gnuplot_view_args`.

  Categories: Plotting

Function: implicit_plot (expr, x_range, y_range)
Function: implicit_plot ([expr_1, …, expr_n], x_range, y_range)

  Displays a plot of one or more expressions in implicit form. expr is the expression to be plotted, x_range the range of the horizontal axis and y_range the range of vertical axis. `implicit_plot` respects global setting for the Gnuplot driver set by the set_plot_option function. Options can also be passed to `implicit_plot` function as optional arguments.

  `implicit_plot` works by tracking sign changes on the area given by x_range and y_range and can fail for complicated expressions.

  `load(implicit_plot)` loads this function.

  Example:

      (%i1) load(implicit_plot)$
      (%i2) implicit_plot (x^2 = y^3 - 3*y + 1, [x, -4, 4], [y, -4, 4])$

  Categories: Plotting · Share packages · Package implicit_plot

Function: julia (x, y, ...options...)

  Creates a graphic representation of the Julia set for the complex number (x + i y). The two mandatory parameters x and y must be real. This program is part of the additional package `dynamics`, but that package does not have to be loaded; the first time julia is used, it will be loaded automatically.

  Each pixel in the grid is given a color corresponding to the number of iterations it takes the sequence that starts at that point to move out of the convergence circle of radius 2 centered at the origin. The number of pixels in the grid is controlled by the `grid` plot option (default 30 by 30). The maximum number of iterations is set with the option `iterations`. The program uses its own default palette: magenta,violet, blue, cyan, green, yellow, orange, red, brown and black, but it can be changed by adding an explicit `palette` option in the command.

  The default domain used goes from -2 to 2 in both axes and can be changed with the `x` and `y` options. By default, the two axes are shown with the same scale, unless the option `yx_ratio` is used or the option `same_xy` is disabled. Other general plot options are also accepted.

  The following example shows a region of the Julia set for the number -0.55 + i0.6. The option `color_bar_tics` is used to prevent Gnuplot from adjusting the color box up to 40, in which case the points corresponding the maximum 36 iterations would not be black.

      (%i1) julia (-0.55, 0.6, [iterations, 36], [x, -0.3, 0.2], [y, 0.3, 0.9],
            [grid, 400, 400], [color_bar_tics, 0, 6, 36])$

  Categories: Package dynamics · Plotting

Function: make_transform ([var1, var2, var3], fx, fy, fz)

  Returns a function suitable to be used in the option `transform_xy` of plot3d. The three variables var1, var2, var3 are three dummy variable names, which represent the 3 variables given by the plot3d command (first the two independent variables and then the function that depends on those two variables). The three functions fx, fy, fz must depend only on those 3 variables, and will give the corresponding x, y and z coordinates that should be plotted. There are two transformations defined by default: `polar_to_xy` and `spherical_to_xyz`. See the documentation for those two transformations.

  Categories: Plotting

Function: mandelbrot (options)

  Creates a graphic representation of the Mandelbrot set. This program is part of the additional package `dynamics`, but that package does not have to be loaded; the first time mandelbrot is used, the package will be loaded automatically.

  This program can be called without any arguments, in which case it will use a default value of 9 iterations per point, a grid with dimensions set by the `grid` plot option (default 30 by 30) and a region that extends from -2 to 2 in both axes. The options are all the same that plot2d accepts, plus an option `iterations` to change the number of iterations.

  Each pixel in the grid is given a color corresponding to the number of iterations it takes the sequence starting at zero to move out of the convergence circle of radius 2, centered at the origin. The maximum number of iterations is set by the option `iterations`. The program uses its own default palette: magenta,violet, blue, cyan, green, yellow, orange, red, brown and black, but it can be changed by adding an explicit `palette` option in the command. By default, the two axes are shown with the same scale, unless the option `yx_ratio` is used or the option `same_xy` is disabled.

  Example:

      (%i1) mandelbrot ([iterations, 30], [x, -2, 1], [y, -1.2, 1.2], [grid,400,400])$

  Categories: Package dynamics · Plotting

System function: polar_to_xy

  It can be given as value for the `transform_xy` option of plot3d. Its effect will be to interpret the two independent variables in plot3d as the distance from the z axis and the azimuthal angle (polar coordinates), and transform them into x and y coordinates.

  Categories: Plotting

Function: plot2d (plot, x_range, …, options, …)
Function: plot2d ([plot_1, …, plot_n], …, options, …)
Function: plot2d ([plot_1, …, plot_n], x_range, …, options, …)

  Where plot, plot_1, …, plot_n can be either expressions, function names or a list with the any of the forms: `[discrete, [x1, ..., xn], [y1, ..., yn]]`, `[discrete, [[x1, y1], ..., [xn, ..., yn]]]` or `[parametric, x_expr, y_expr, t_range]`.

  Displays a plot of one or more expressions as a function of one variable or parameter.

  `plot2d` displays one or several plots in two dimensions. When expressions or function name are used to define the plots, they should all depend on only one variable var and the use of x_range will be mandatory, to provide the name of the variable and its minimum and maximum values; the syntax for x_range is: `[variable, min, max]`.

  A plot can also be defined in the discrete or parametric forms. The discrete form is used to plot a set of points with given coordinates. A discrete plot is defined by a list starting with the keyword discrete, followed by one or two lists of values. If two lists are given, they must have the same length; the first list will be interpreted as the x coordinates of the points to be plotted and the second list as the y coordinates. If only one list is given after the discrete keyword, each element on the list could also be a list with two values that correspond to the x and y coordinates of a point, or it could be a sequence of numerical values which will be plotted at consecutive integer values (1,2,3,...) on the x axis.

  A parametric plot is defined by a list starting with the keyword parametric, followed by two expressions or function names and a range for the parameter. The range for the parameter must be a list with the name of the parameter followed by its minimum and maximum values: `[param, min, max]`. The plot will show the path traced out by the point with coordinates given by the two expressions or functions, as param increases from min to max.

  A range for the vertical axis is an optional argument with the form: `[y, min, max]` (the keyword y is always used for the vertical axis). If that option is used, the plot will show that exact vertical range, independently of the values reached by the plot. If the vertical range is not specified, it will be set up according to the minimum and maximum values of the second coordinate of the plot points.

  All other options should also be lists, starting with a keyword and followed by one or more values. See `plot_options`.

  If there are several plots to be plotted, a legend will be written to identity each of the expressions. The labels that should be used in that legend can be given with the option `legend`. If that option is not used, Maxima will create labels from the expressions or function names.

  Examples:

  Plot of a common function:

      (%i1) plot2d (sin(x), [x, -%pi, %pi])$

  If the function grows too fast, it might be necessary to limit the values in the vertical axis using the `y` option:

      (%i1) plot2d (sec(x), [x, -2, 2], [y, -20, 20])$

  When the plot box is disabled, no labels are created for the axes. In that case, instead of using `xlabel` and `ylabel` to set the names of the axes, it is better to use option `label`, which allows more flexibility. Option `yx_ratio` is used to change the default rectangular shape of the plot; in this example the plot will fill a square.

      (%i1) plot2d ( x^2 - 1, [x, -3, 3], [box, false], grid2d, [yx_ratio, 1],
            [axes, solid], [xtics, -2, 4, 2], [ytics, 2, 2, 6],
            [label, ["x", 2.9, -0.3], ["x^2-1", 0.1, 8]], [title, "A parabola"])$

  A plot with a logarithmic scale in the vertical axis:

      (%i1) plot2d (exp(3*s), [s, -2, 2], logy)$

  Plotting functions by name:

      (%i1) F(x) := x^2 $
      (%i2) :lisp (defun |$g| (x) (m* x x x))
      $g
      (%i2) H(x) := if x < 0 then x^4 - 1 else 1 - x^5 $
      (%i3) plot2d ([F, G, H], [u, -1, 1], [y, -1.5, 1.5])$

  A plot of the butterfly curve, defined parametrically:

      (%i1) r: (exp(cos(t))-2*cos(4*t)-sin(t/12)^5)$
      (%i2) plot2d([parametric, r*sin(t), r*cos(t), [t, -8*%pi, 8*%pi]])$

  Plot of a circle, using its parametric representation, together with the function -|x|. The circle will only look like a circle if the scale in the two axes is the same, which is done with the option `same_xy`.

      (%i1) plot2d([[parametric, cos(t), sin(t), [t,0,2*%pi]], -abs(x)],
               [x, -sqrt(2), sqrt(2)], same_xy)$

  A plot of 200 random numbers between 0 and 9:

      (%i1) plot2d ([discrete, makelist ( random(10), 200)])$

  A plot of a discrete set of points, defining x and y coordinates separately:

      (%i1) plot2d ([discrete, makelist(i*%pi, i, 1, 5), [.6, .9, 0.2, 1.3, 1]])$

  In the next example a table with three columns is saved in a file "data.txt" which is then read and the second and third column are plotted on the two axes:

      (%i1) with_stdout ("data.txt", for x:0 thru 10 do
                                   print (x, x^2, x^3))$
      (%i2) data: read_matrix ("data.txt")$
      (%i3) plot2d ([discrete, transpose(data)[2], transpose(data)[3]],
        [style,points], [point_type,diamond], [color,red])$

  A plot of discrete data points together with a continuous function:

      (%i1) xy: [[10, .6], [20, .9], [30, 1.1], [40, 1.3], [50, 1.4]]$
      (%i2) plot2d([[discrete, xy], 2*%pi*sqrt(l/980)], [l,0,50],
              [style, points, lines], [color, red, blue],
              [point_type, asterisk],
              [legend, "experiment", "theory"],
              [xlabel, "pendulum's length (cm)"],
              [ylabel, "period (s)"])$

  See also the section about Plotting Options.

  Categories: Plotting

Function: plot3d (expr, x_range, y_range, …, options, …)
Function: plot3d ([expr_1, …, expr_n], x_range, y_range, …, options, …)

  Displays a plot of one or more surfaces defined as functions of two variables or in parametric form.

  The functions to be plotted may be specified as expressions or function names. The mouse can be used to rotate the plot looking at the surface from different sides.

  Examples:

  Plot of a function of two variables:

      (%i1) plot3d (u^2 - v^2, [u, -2, 2], [v, -3, 3], [grid, 100, 100],
              [mesh_lines_color,false])$

  Use of the `z` option to limit a function that goes to infinity (in this case the function is minus infinity on the x and y axes); this also shows how to plot with only lines and no shading:

      (%i1) plot3d ( log ( x^2*y^2 ), [x, -2, 2], [y, -2, 2], [z, -8, 4],
               [palette, false], [color, magenta])$

  The infinite values of z can also be avoided by choosing a grid that does not fall on any asymptotes; next example also shows how to change the palette and how to show the color bar that relates the colors used with the values of the z variable:

      (%i1) plot3d (log (x^2*y^2), [x, -2, 2], [y, -2, 2],[grid, 29, 29],
             [palette, [gradient, red, orange, yellow, green]], color_bar,
             [xtics, 1], [ytics, 1], [ztics, 4],[color_bar_tics, 4])$

  Two surfaces in the same plot. Ranges specific to one of the surfaces can be given by placing the expression and the ranges inside a common list; in this example each surface is defined in a domain different from the domain of the complete plot.

      (%i1) plot3d ([[-3*x - y, [x, -2, 2], [y, -2, 2]],
         4*sin(3*(x^2 + y^2))/(x^2 + y^2), [x, -3, 3], [y, -3, 3]],
         [x, -4, 4], [y, -4, 4])$

  Plot of a Klein bottle, defined parametrically:

      (%i1) expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y) + 3.0) - 10.0$
      (%i2) expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y) + 3.0)$
      (%i3) expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))$
      (%i4) plot3d ([expr_1, expr_2, expr_3], [x, -%pi, %pi],
              [y, -%pi, %pi], [grid, 50, 50])$

  Plot of a "spherical harmonic" function, using the predefined transformation, `spherical_to_xyz` to transform from spherical coordinates to rectangular coordinates. See the documentation for `spherical_to_xyz`.

      (%i1) plot3d (sin(2*theta)*cos(phi), [theta, 0, %pi],
              [phi, 0, 2*%pi],
              [transform_xy, spherical_to_xyz], [grid,30,60],
         [legend,false])$

  Use of the pre-defined function `polar_to_xy` to transform from cylindrical to rectangular coordinates. See the documentation for `polar_to_xy`.

      (%i1) plot3d (r^.33*cos(th/3), [r, 0, 1], [th, 0, 6*%pi], [box, false],
         [grid, 12, 80], [transform_xy, polar_to_xy], [legend, false])$

  Plot of a sphere using the transformation from spherical to rectangular coordinates. Option `same_xyz` is used to get the three axes scaled in the same proportion. When transformations are used, it is not convenient to eliminate the mesh lines, because Gnuplot will not show the surface correctly.

      (%i1) plot3d ( 5, [theta, 0, %pi], [phi, 0, 2*%pi], same_xyz,
        [transform_xy, spherical_to_xyz], [mesh_lines_color,blue],
        [palette,[gradient,"#1b1b4e", "#8c8cf8"]], [legend, false])$

  Definition of a function of two-variables using a matrix. Notice the single quote in the definition of the function, to prevent plot3d from failing when it realizes that the matrix will require integer indices.

      (%i1) M: matrix([1, 2, 3, 4], [1, 2, 3, 2], [1, 2, 3, 4], [1, 2, 3, 3])$
      (%i2) f(x, y) := float('M [round(x), round(y)])$
      (%i3) plot3d (f(x,y), [x, 1, 4], [y, 1, 4], [grid, 3, 3], [legend, false])$

  By setting the elevation equal to zero, a surface can be seen as a map in which each color represents a different level.

      (%i1) plot3d (cos (-x^2 + y^3/4), [x, -4, 4], [y, -4, 4], [zlabel, ""],
              [mesh_lines_color, false], [elevation, 0], [azimuth, 0],
              color_bar, [grid, 80, 80], [ztics, false], [color_bar_tics, 1])$

  See also the section about Plotting Options.

  Categories: Plotting

System variable: plot_options

  This option is being kept for compatibility with older versions, but its use is deprecated. To set global plotting options, see their current values or remove options, use `set_plot_option`, `get_plot_option` and `remove_plot_option`.

  Categories: Plotting

Function: remove_plot_option (name)

  Removes the default value of an option. The name of the option must be given.

  See also `set_plot_option`, `get_plot_option` and the section on Plotting Options.

  Categories: Plotting

Function: set_plot_option (option)

  Accepts any of the options listed in the section Plotting Options, and saves them for use in plotting commands. The values of the options set in each plotting command will have precedence, but if those options are not given, the default values set with this function will be used.

  `set_plot_option` evaluates its argument and returns the complete list of options (after modifying the option given). If called without any arguments, it will simply show the list of current default options.

  See also `remove_plot_option`, `get_plot_option` and the section on Plotting Options.

  Example:

  Modification of the `grid` values.

      (%i1) set_plot_option ([grid, 30, 40]);
      (%o1) [[plot_format, gnuplot_pipes], [grid, 30, 40],
      [run_viewer, true], [axes, true], [nticks, 29], [adapt_depth, 5],
      [color, blue, red, green, magenta, black, cyan],
      [point_type, bullet, box, triangle, plus, times, asterisk],
      [palette, [gradient, green, cyan, blue, violet],
      [gradient, magenta, violet, blue, cyan, green, yellow, orange,
      red, brown, black]], [gnuplot_preamble, ], [gnuplot_term, default]]

  Categories: Plotting

System function: spherical_to_xyz

  It can be given as value for the `transform_xy` option of `plot3d`. Its effect will be to interpret the two independent variables and the function in `plot3d` as the spherical coordinates of a point (first, the angle with the z axis, then the angle of the xy projection with the x axis and finally the distance from the origin) and transform them into x, y and z coordinates.

  Categories: Plotting

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## 12.4 Plotting Options

All options consist of a list starting with one of the keywords in this section, followed by one or more values. Some of the options may have different effects in different plotting commands as it will be pointed out in the following list. The options that accept among their possible values true or false, can also be set to true by simply writing their names. For instance, typing logx as an option is equivalent to writing [logx, true].

Plot option: adapt_depth [adapt_depth, integer]

  Default value: `5`

  The maximum number of splittings used by the adaptive plotting routine.

  Categories: Plotting

Plot option: axes [axes, symbol]

  Default value: `true`

  Where symbol can be either `true`, `false`, `x`, `y` or `solid`. If `false`, no axes are shown; if equal to `x` or `y` only the x or y axis will be shown; if it is equal to `true`, both axes will be shown and `solid` will show the two axes with a solid line, rather than the default broken line. This option does not have any effect in the 3 dimensional plots.

  Categories: Plotting

Plot option: azimuth [azimuth, number]

  Default value: `30`

  A plot3d plot can be thought of as starting with the x and y axis in the horizontal and vertical axis, as in plot2d, and the z axis coming out of the screen. The z axis is then rotated around the x axis through an angle equal to `elevation` and then the new xy plane is rotated around the new z axis through an angle `azimuth`. This option sets the value for the azimuth, in degrees.

  See also `elevation`.

  Categories: Plotting

Plot option: box [box, symbol]

  Default value: `true`

  If set to `true`, a bounding box will be drawn for the plot; if set to `false`, no box will be drawn.

  Categories: Plotting

Plot option: color [color, color_1, …, color_n]

  In 2d plots it defines the color (or colors) for the various curves. In `plot3d`, it defines the colors used for the mesh lines of the surfaces, when no palette is being used.

  If there are more curves or surfaces than colors, the colors will be repeated in sequence. The valid colors are `red`, `green`, `blue`, `magenta`, `cyan`, `yellow`, `orange`, `violet`, `brown`, `gray`, `black`, `white`, or a string starting with the character # and followed by six hexadecimal digits: two for the red component, two for green component and two for the blue component. If the name of a given color is unknown color, black will be used instead.

  Categories: Plotting

Plot option: color_bar [color_bar, symbol]

  Default value: `false` in plot3d, `true` in mandelbrot and julia-

  Where symbol can be either `true` or `false`. If `true`, whenever `plot3d`, `mandelbrot` or `julia` use a palette to represent different values, a box will be shown on the right, showing the corresponding between colors and values.

  Categories: Plotting

Plot option: color_bar_tics [color_bar_tics, x1, x2, x3]

  Defines the values at which a mark and a number will be placed in the color bar. The first number is the initial value, the second the increments and the third is the last value where a mark is placed. The second and third numbers can be omitted. When only one number is given, it will be used as the increment from an initial value that will be chosen automatically.

  Categories: Plotting

Plot option: elevation [elevation, number]

  Default value: `60`

  A plot3d plot can be thought of as starting with the x and y axis in the horizontal and vertical axis, as in plot2d, and the z axis coming out of the screen. The z axis is then rotated around the x axis through an angle equal to `elevation` and then the new xy plane is rotated around the new z axis through an angle `azimuth`. This option sets the value for the azimuth, in degrees.

  See also `azimuth`.

  Categories: Plotting

Plot option: grid [grid, integer, integer]

  Default value: `30`, `30`

  Sets the number of grid points to use in the x- and y-directions for three-dimensional plotting or for the `julia` and `mandelbrot` programs.

  Categories: Plotting

Plot option: grid2d [grid, value]

  Default value: `false`

  Shows a grid of lines on the xy plane. The points where the grid lines are placed are the same points where tics are marked in the x and y axes, which can be controlled with the `xtics` and `ytics` options.

  Categories: Plotting

Plot option: iterations [grid, value]

  Default value: `9`

  Number of iterations made by the programs mandelbrot and julia.

  Categories: Plotting

Plot option: label [label, [string, x, y], …]

  Writes one or several labels in the points with x, y coordinates indicated after each label.

  Categories: Plotting

Plot option: legend [legend, string_1, …, string_n]
Plot option: legend [legend, false]

  It specifies the labels for the plots when various plots are shown. If there are more plots than the number of labels given, they will be repeated. If given the value `false`, no legends will be shown. By default, the names of the expressions or functions will be used, or the words discrete1, discrete2, …, for discrete sets of points.

  Categories: Plotting

Plot option: logx [logx, value]

  Makes the horizontal axes to be scaled logarithmically. It can be either true or false.

  Categories: Plotting

Plot option: logy [logy, value]

  Makes the vertical axes to be scaled logarithmically. It can be either true or false.

  Categories: Plotting

Plot option: mesh_lines_color [mesh_lines_color, color]

  Default value: `black`

  It sets the color used by plot3d to draw the mesh lines, when a palette is being used. It accepts the same colors as for the option `color` (see the list of allowed colors in `color`). It can also be given a value `false` to eliminate completely the mesh lines.

  Categories: Plotting

Plot option: nticks [nticks, integer]

  Default value: `29`

  When plotting functions with `plot2d`, it is gives the initial number of points used by the adaptive plotting routine for plotting functions. When plotting parametric functions with `plot3d`, it sets the number of points that will be shown for the plot.

  Categories: Plotting

Plot option: palette [palette, [palette_1], …, [palette_n]]
Plot option: palette [palette, false]

  It can consist of one palette or a list of several palettes. Each palette is a list with a keyword followed by values. If the keyword is gradient, it should be followed by a list of valid colors.

  If the keyword is hue, saturation or value, it must be followed by 4 numbers. The first three numbers, which must be between 0 and 1, define the hue, saturation and value of a basic color to be assigned to the minimum value of z. The keyword specifies which of the three attributes (hue, saturation or value) will be increased according to the values of z. The last number indicates the increase corresponding to the maximum value of z. That last number can be bigger than 1 or negative; the corresponding values of the modified attribute will be rounded modulo 1.

  Gnuplot only uses the first palette in the list; xmaxima will use the palettes in the list sequentially, when several surfaces are plotted together; if the number of palettes is exhausted, they will be repeated sequentially.

  The color of the mesh lines will be given by the option `mesh_lines_color`. If `palette` is given the value `false`, the surfaces will not be shaded but represented with a mesh of curves only. In that case, the colors of the lines will be determined by the option `color`.

  Categories: Plotting

Plot option: plot_format [plot_format, format]

  Default value: `gnuplot`, in Windows systems, or `gnuplot_pipes` in other systems.

  Where format is one of the following: gnuplot, xmaxima, mgnuplot or gnuplot_pipes.

  It sets the format to be used for plotting.

  Categories: Plotting

Plot option: plot_realpart [plot_realpart, symbol]

  Default value: `false`

  If set to `true`, the functions to be plotted will be considered as complex functions whose real value should be plotted; this is equivalent to plotting `realpart(function)`. If set to `false`, nothing will be plotted when the function does not give a real value. For instance, when `x` is negative, `log(x)` gives a complex value, with real value equal to `log(abs(x))`; if `plot_realpart` were `true`, `log(-5)` would be plotted as `log(5)`, while nothing would be plotted if `plot_realpart` were `false`.

  Categories: Plotting

Plot option: point_type [point_type, type_1, …, type_n]

  In gnuplot, each set of points to be plotted with the style "points" or "linespoints" will be represented with objects taken from this list, in sequential order. If there are more sets of points than objects in this list, they will be repeated sequentially. The possible objects that can be used are: `bullet`, `circle`, `plus`, `times`, `asterisk`, `box`, `square`, `triangle`, `delta`, `wedge`, `nabla`, `diamond`, `lozenge`

  Categories: Plotting

Plot option: pdf_file [pdf_file, file_name]

  Saves the plot into a PDF file with name equal to file_name, rather than showing it in the screen. By default, the file will be created in the directory defined by the variable `maxima_tempdir`, unless file_name contains the character "/", in which case it will be assumed to contain the complete path where the file should be created. The value of `maxima_tempdir` can be changed to save the file in a different directory. When the option `gnuplot_pdf_term_command` is also given, it will be used to set up Gnuplot's PDF terminal; otherwise, Gnuplot's pdfcairo terminal will be used with solid colored lines of width 3, plot size of 17.2 cm by 12.9 cm and font of 18 points.

  Categories: Plotting

Plot option: png_file [png_file, file_name]

  Saves the plot into a PNG graphics file with name equal to file_name, rather than showing it in the screen. By default, the file will be created in the directory defined by the variable `maxima_tempdir`, unless file_name contains the character "/", in which case it will be assumed to contain the complete path where the file should be created. The value of `maxima_tempdir` can be changed to save the file in a different directory. When the option `gnuplot_png_term_command` is also given, it will be used to set up Gnuplot's PNG terminal; otherwise, Gnuplot's pngcairo terminal will be used, with a font of size 12.

  Categories: Plotting

Plot option: ps_file [ps_file, file_name]

  Saves the plot into a Postscript file with name equal to file_name, rather than showing it in the screen. By default, the file will be created in the directory defined by the variable `maxima_tempdir`, unless file_name contains the character "/", in which case it will be assumed to contain the complete path where the file should be created. The value of `maxima_tempdir` can be changed to save the file in a different directory. When the option `gnuplot_ps_term_command` is also given, it will be used to set up Gnuplot's Postscript terminal; otherwise, Gnuplot's postscript terminal will be used with the EPS option, solid colored lines of width 2, plot size of 16.4 cm by 12.3 cm and font of 24 points.

  Categories: Plotting

Plot option: run_viewer [run_viewer, symbol]

  This option is only used when the plot format is `gnuplot` and the terminal is `default` or when the Gnuplot terminal is set to `dumb` (see `gnuplot_term`) and can have a true or false value.

  If the terminal is `default`, a file `maxout.gnuplot` (or other name specified with `gnuplot_out_file`) is created with the gnuplot commands necessary to generate the plot. Option `run_viewer` controls whether or not Gnuplot will be launched to execute those commands and show the plot.

  If the terminal is `default`, gnuplot is run to execute the commands in `maxout.gnuplot`, producing another file `maxplot.txt` (or other name specified with `gnuplot_out_file`). Option `run_viewer` controls whether or not that file, with an ASCII representation of the plot, will be shown in the Maxima or Xmaxima console.

  The default value for this option is true, making the plots to be shown in either the console or a separate graphics window.

  Categories: Plotting

Plot option: same_xy [same_xy , value]

  It can be either true or false. If true, the scales used in the x and y axes will be the same, in either 2d or 3d plots. See also `yx_ratio`.

  Categories: Plotting

Plot option: same_xyz [same_xyz , value]

  It can be either true or false. If true, the scales used in the 3 axes of a 3d plot will be the same.

  Categories: Plotting

Plot option: style [style, type_1, …, type1_n]
Plot option: style [style, [style_1], …, [style_n]]

  The styles that will be used for the various functions or sets of data in a 2d plot. The word style must be followed by one or more styles. If there are more functions and data sets than the styles given, the styles will be repeated. Each style can be either lines for line segments, points for isolated points, linespoints for segments and points, or dots for small isolated dots. Gnuplot accepts also an impulses style.

  Each of the styles can be enclosed inside a list with some additional parameters. lines accepts one or two numbers: the width of the line and an integer that identifies a color. The default color codes are: 1: blue, 2: red, 3: magenta, 4: orange, 5: brown, 6: lime and 7: aqua. If you use Gnuplot with a terminal different than X11, those colors might be different; for example, if you use the option [gnuplot_term, ps], color index 4 will correspond to black, instead of orange.

  points accepts one two or three parameters; the first parameter is the radius of the points, the second parameter is an integer that selects the color, using the same code used for lines and the third parameter is currently used only by Gnuplot and it corresponds to several objects instead of points. The default types of objects are: 1: filled circles, 2: open circles, 3: plus signs, 4: x, 5: *, 6: filled squares, 7: open squares, 8: filled triangles, 9: open triangles, 10: filled inverted triangles, 11: open inverted triangles, 12: filled lozenges and 13: open lozenges.

  linesdots accepts up to four parameters: line width, points radius, color and type of object to replace the points.

  See also `color` and `point_type`.

  Categories: Plotting

Plot option: svg_file [svg_file, file_name]

  Saves the plot into an SVG file with name equal to file_name, rather than showing it in the screen. By default, the file will be created in the directory defined by the variable `maxima_tempdir`, unless file_name contains the character "/", in which case it will be assumed to contain the complete path where the file should be created. The value of `maxima_tempdir` can be changed to save the file in a different directory. When the option `gnuplot_svg_term_command` is also given, it will be used to set up Gnuplot's SVG terminal; otherwise, Gnuplot's svg terminal will be used with font of 14 points.

  Categories: Plotting

Plot option: t [t, min, max]

  Default range for parametric plots.

  Categories: Plotting

Plot option: title [title, text]

  Defines a title that will be written at the top of the plot.

  Categories: Plotting

Plot option: transform_xy [transform_xy, symbol]

  Where symbol is either `false` or the result obtained by using the function `transform_xy`. If different from `false`, it will be used to transform the 3 coordinates in plot3d.

  See `make_transform`, `polar_to_xy` and `spherical_to_xyz`.

  Categories: Plotting

Plot option: x [x, min, max]

  When used as the first option in a `plot2d` command (or any of the first two in `plot3d`), it indicates that the first independent variable is x and it sets its range. It can also be used again after the first option (or after the second option in plot3d) to define the effective horizontal domain that will be shown in the plot.

  Categories: Plotting

Plot option: xlabel [xlabel, string]

  Specifies the string that will label the first axis; if this option is not used, that label will be the name of the independent variable, when plotting functions with `plot2d` or `implicit_plot`, or the name of the first variable, when plotting surfaces with `plot3d` or contours with `contour_plot`, or the first expression in the case of a parametric plot. It can not be used with `set_plot_option`.

  Categories: Plotting

Plot option: xtics [xtics, x1, x2, x3]

  Defines the values at which a mark and a number will be placed in the x axis. The first number is the initial value, the second the increments and the third is the last value where a mark is placed. The second and third numbers can be omitted. When only one number is given, it will be used as the increment from an initial value that will be chosen automatically

  Categories: Plotting

Plot option: xy_scale [xy_scale, sx, sy]

  In a 2d plot, it defines the ratio of the total size of the Window to the size that will be used for the plot. The two numbers given as arguments are the scale factors for the x and y axes.

  Categories: Plotting

Plot option: y [y, min, max]

  When used as one of the first two options in `plot3d`, it indicates that one of the independent variables is y and it sets its range. Otherwise, it defines the effective domain of the second variable that will be shown in the plot.

  Categories: Plotting

Plot option: ylabel [ylabel, string]

  Specifies the string that will label the second axis; if this option is not used, that label will be "y", when plotting functions with `plot2d` or `implicit_plot`, or the name of the second variable, when plotting surfaces with `plot3d` or contours with `contour_plot`, or the second expression in the case of a parametric plot. It can not be used with `set_plot_option`.

  Categories: Plotting

Plot option: ytics [ytics, y1, y2, y3]

  Defines the values at which a mark and a number will be placed in the y axis. The first number is the initial value, the second the increments and the third is the last value where a mark is placed. The second and third numbers can be omitted. When only one number is given, it will be used as the increment from an initial value that will be chosen automatically

  Categories: Plotting

Plot option: yx_ratio [yx_ratio, r]

  In a 2d plot, the ratio between the vertical and the horizontal sides of the rectangle used to make the plot. See also `same_xy`.

  Categories: Plotting

Plot option: z [z, min, max]

  Used in `plot3d` to set the effective range of values of z that will be shown in the plot.

  Categories: Plotting

Plot option: zlabel [zlabel, string]

  Specifies the string that will label the third axis, when using `plot3d`. If this option is not used, that label will be "z", when plotting surfaces, or the third expression in the case of a parametric plot. It can not be used with `set_plot_option` and it will be ignored by `plot2d` and `implicit_plot`.

  Categories: Plotting

Plot option: zmin [zmin, z]

  In 3d plots, the value of z that will be at the bottom of the plot box.

  Categories: Plotting

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## 12.5 Gnuplot Options

There are several plot options specific to gnuplot. All of them consist of a keyword (the name of the option), followed by a string that should be a valid gnuplot command, to be passed directly to gnuplot. In most cases, there exist a corresponding plotting option that will produce a similar result and whose use is more recommended than the gnuplot specific option.

Plot option: gnuplot_term [gnuplot_term, terminal_name]

  Sets the output terminal type for gnuplot. The argument terminal_name can be a string or one of the following 3 special symbols

  - default (default value)

    Gnuplot output is displayed in a separate graphical window and the gnuplot terminal used will be specified by the value of the option `gnuplot_default_term_command`.

  - dumb

    Gnuplot output is saved to a file `maxout.gnuplot` using "ASCII art" approximation to graphics. If the option `gnuplot_out_file` is set to filename, the plot will be saved there, instead of the default `maxout.gnuplot`. The settings for the "dumb" terminal of Gnuplot are given by the value of option `gnuplot_dumb_term_command`. If option `run_viewer` is set to true and the plot_format is `gnuplot` that ASCII representation will also be shown in the Maxima or Xmaxima console.

  - ps

    Gnuplot generates commands in the PostScript page description language. If the option `gnuplot_out_file` is set to filename, gnuplot writes the PostScript commands to filename. Otherwise, it is saved as `maxplot.ps` file. The settings for this terminal of are given by the value of option `gnuplot_dumb_term_command`.

  - A string representing any valid gnuplot term specification

    Gnuplot can generate output in many other graphical formats such as png, jpeg, svg etc. To use those formats, option `gnuplot_term` can be set to any supported gnuplot term name (for example symbol) or even a full gnuplot term specification with any valid options (string). For example `[gnuplot_term, png]` creates output in PNG (Portable Network Graphics) format while `[gnuplot_term, "png size 1000,1000"]` creates PNG of 1000 x 1000 pixels size. If the option `gnuplot_out_file` is set to filename, gnuplot writes the output to filename. Otherwise, it is saved as `maxplot.term` file, where term is gnuplot terminal name.

  Categories: Plotting

Plot option: gnuplot_out_file [gnuplot_out_file, file_name]

  It can be used to replace the default name for the file that contains the commands that will interpreted by gnuplot, when the terminal is set to `default`, or to replace the default name of the graphic file that gnuplot creates, when the terminal is different from `default`. If it contains one or more slashes, "/", the name of the file will be left as it is; otherwise, it will be appended to the path of the temporary directory. The complete name of the files created by the plotting commands is always sent as output of those commands so they can be seen if the command is ended by semi-colon.

  When used in conjunction with the `gnuplot_term` option, it can be used to save the plot in a file, in one of the graphic formats supported by Gnuplot. To create PNG, PDF, Postscript or SVG, it is easier to use options `png_file`, `pdf_file`, `ps_file`, or `svg_file`.

  Categories: Plotting

Plot option: gnuplot_pm3d [gnuplot_pm3d, value]

  With a value of `false`, it can be used to disable the use of PM3D mode, which is enabled by default.

  Categories: Plotting

Plot option: gnuplot_preamble [gnuplot_preamble, string]

  This option inserts gnuplot commands before any other commands sent to Gnuplot. Any valid gnuplot commands may be used. Multiple commands should be separated with a semi-colon. See also `gnuplot_postamble`.

  Categories: Plotting

Plot option: gnuplot_postamble [gnuplot_postamble, string]

  This option inserts gnuplot commands after other commands sent to Gnuplot and right before the plot command is sent. Any valid gnuplot commands may be used. Multiple commands should be separated with a semi-colon. See also `gnuplot_preamble`.

  Categories: Plotting

Plot option: gnuplot_default_term_command

  [gnuplot_default_term_command, command]

  The gnuplot command to set the terminal type for the default terminal. It this option is not set, the command used will be: `"set term wxt size 640,480 font \",12\"; set term pop"`.

  Categories: Plotting

Plot option: gnuplot_dumb_term_command

  [gnuplot_dumb_term_command, command]

  The gnuplot command to set the terminal type for the dumb terminal. It this option is not set, the command used will be: `"set term dumb 79 22"`, which makes the text output 79 characters by 22 characters.

  Categories: Plotting

Plot option: gnuplot_pdf_term_command [gnuplot_pdf_term_command, command]

  The gnuplot command to set the terminal type for the PDF terminal. It this option is not set, the command used will be: `"set term pdfcairo color solid lw 3 size 17.2 cm, 12.9 cm font \",18\""`. See the gnuplot documentation for more information.

  Categories: Plotting

Plot option: gnuplot_png_term_command [gnuplot_png_term_command, command]

  The gnuplot command to set the terminal type for the PNG terminal. It this option is not set, the command used will be: `"set term pngcairo font \",12\""`. See the gnuplot documentation for more information.

  Categories: Plotting

Plot option: gnuplot_ps_term_command [gnuplot_ps_term_command, command]

  The gnuplot command to set the terminal type for the PostScript terminal. It this option is not set, the command used will be: `"set term postscript eps color solid lw 2 size 16.4 cm, 12.3 cm font \",24\""`. See the gnuplot documentation for `set term postscript` for more information.

  Categories: Plotting

Plot option: gnuplot_svg_term_command [gnuplot_svg_term_command, command]

  The gnuplot command to set the terminal type for the SVG terminal. It this option is not set, the command used will be: `"set term svg font \",14\""`. See the gnuplot documentation for more information.

  Categories: Plotting

Plot option: gnuplot_curve_titles

  This is an obsolete option that has been replaced `legend` described above.

  Categories: Plotting

Plot option: gnuplot_curve_styles

  This is an obsolete option that has been replaced by `style`.

  Categories: Plotting

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## 12.6 Gnuplot_pipes Format Functions

Function: gnuplot_start ()

  Opens the pipe to gnuplot used for plotting with the `gnuplot_pipes` format. Is not necessary to manually open the pipe before plotting.

  Categories: Plotting

Function: gnuplot_close ()

  Closes the pipe to gnuplot which is used with the `gnuplot_pipes` format.

  Categories: Plotting

Function: gnuplot_restart ()

  Closes the pipe to gnuplot which is used with the `gnuplot_pipes` format and opens a new pipe.

  Categories: Plotting

Function: gnuplot_replot ()
Function: gnuplot_replot (s)

  Updates the gnuplot window. If `gnuplot_replot` is called with a gnuplot command in a string s, then `s` is sent to gnuplot before reploting the window.

  Categories: Plotting

Function: gnuplot_reset ()

  Resets the state of gnuplot used with the `gnuplot_pipes` format To update the gnuplot window call `gnuplot_replot` after `gnuplot_reset`.

  Categories: Plotting

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