Next: Plotting Options, Previous: Plotting Formats, Up: Plotting [Contents][Index]
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
, which works in any graphic format, can also be
used to plot contours but a separate expression must be given for each
contour.
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. By default, Gnuplot chooses and displays 3 contours. To increase the
number of contours, it is necessary to use a custom
gnuplot_preamble
, as in the next example:
(%i1) contour_plot (u^3 + v^2, [u, -4, 4], [v, -4, 4], [legend,false], [gnuplot_preamble, "set cntrparam levels 12"])$
‘Category: Plotting’
This variable stores the name of the command used to run the geomview
program when the plot format is geomview
. Its default value is
"geomview". If the geomview 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) geomview_command: "/usr/local/bin/my_geomview"$
‘Category: Plotting’
Returns the current default value of the option named keyword, which is a list. The optional argument index must be a positive integer which can be used to extract only one element from the list (element 1 is the name of the option).
See also set_plot_option
, remove_plot_option
and the
section on Plotting Options.
This variable stores the name of the command used to run the gnuplot
program when the plot format is gnuplot
. Its default value is
"gnuplot". 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"$
‘Category: Plotting’
When 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 format directive "~s".
‘Category: Plotting’
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_xxx.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
.
‘Category: Plotting’
Displays a plot of a function on the real plane, defined implicitly by
the expression expr. The domain in the plane is defined by
x_range and y_range. Several functions can be represented on
the same plot, giving a list [expr_1, …, expr_n] of
expressions that define them. This function uses the global format
options set up with the set_plot_option
. Additional options can
also be given as extra arguments for the implicit_plot
command.
The method used by implicit_plot
consists of tracking sign
changes on the domain given and it 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])$
‘Category: Plotting’ ‘Category: Share packages’ ‘Category: Package implicit_plot’
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])$
‘Category: Package dynamics’ ‘Category: Plotting’
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.
‘Category: Plotting’
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:
[grid,400,400])$
(%i1) mandelbrot ([iterations, 30], [x, -2, 1], [y, -1.2, 1.2], [grid,400,400])$
‘Category: Package dynamics’ ‘Category: Plotting’
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.
‘Category: Plotting’
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 names 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), [0.6, 0.9, 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) display2d:false$
(%i2) with_stdout ("data.txt", for x:0 thru 10 do print (x, x^2, x^3))$
(%i3) data: read_matrix ("data.txt")$
(%i4) 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.
‘Category: Plotting’
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 points where the function is undefined, as in the next example, which also shows how to change the palette and how to include a color bar that relates colors to 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 each expression and its ranges in a separate list; global ranges for the complete plot are also given after the function definitions.
(%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)-10$ (%i2) expr_2: -5*sin(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3)$ (%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.
‘Category: Plotting’
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
.
‘Category: Plotting’
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.
‘Category: Plotting’
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]]
‘Category: Plotting’
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.
‘Category: Plotting’
Next: Plotting Options, Previous: Plotting Formats, Up: Plotting [Contents][Index]