Maxima can pass raw gnuplot directives to the plotting backend through gnuplot_preamble, enabling fine control over plot aesthetics. This approach is especially useful for scientific figures where borders, ticks, grids, labels, legends, numeric formatting, and sampling density must be standardized.

What gnuplot_preamble Does

The option gnuplot_preamble injects a single string of gnuplot commands into the generated plotting script. The content of this string must be valid gnuplot syntax (not Maxima syntax). Typical uses include:

• controlling borders and line widths,
• configuring major and minor ticks,
• placing and styling the legend (key),
• setting grids and zero axes,
• improving curve smoothness via sampling,
• formatting axis numbers,
• adjusting margins to prevent label clipping.

Basic Structure and Minimal Example

The general pattern is to include [gnuplot_preamble, “…”] among the plotting options, writing all gnuplot commands inside one string and separating them with semicolons.

plot2d(
    expr,
    [x, xmin, xmax],
    [plot_format, gnuplot],
    [gnuplot_preamble,
     "gnuplot command 1;
      gnuplot command 2;
      gnuplot command 3;"]
);

A minimal working example with a smooth curve and clean framing is:

k1 : 1.0$
k2 : 0.5$
w  : 1.0$

y : exp(w*t)*(k2*t + k1)$

plot2d(
    y,
    [t, -2, 2],
    [plot_format, gnuplot],
    [xlabel, "t"],
    [ylabel, "y(t)"],
    [legend, "y(t)=exp(w*t)*(k2*t+k1)"],
    [gnuplot_preamble,
     "set border 31 lw 2;
      set tics out nomirror scale 1.2;
      set grid;
      set samples 1000;"]
);

Meaning of Common gnuplot Directives

The commands below are commonly used to achieve a “premium” scientific look; they are written exactly as gnuplot expects.

• Border framing:

  • set border 31 lw 2; draws all four borders with line width 2.

• Major ticks:

  • set tics out nomirror scale 1.2; places ticks outward, prevents mirrored ticks, and scales tick length.

• Minor ticks:

  • set mxtics 2; and set mytics 2; add minor ticks between major ticks on each axis.

• Label fonts:

  • set xlabel 'Time, t' font ',18';
  • set ylabel 'y(t)' font ',18';

• Legend box (key):

  • set key top left box opaque font ',14'; positions the legend, adds a boxed frame, and uses an opaque background.

• Grid:

  • set grid xtics ytics mxtics mytics back lw 1; draws major and minor grid lines behind the data.

• tics formatting:

  • set xtics 5 font 'Times New Roman,20';
  • set ytics 0.5 font 'Times New Roman,20'; This sets the major tick intervals and fonts for each axis.
  • set xtics start,increment,end; This syntax allows for custom tick placement at specified intervals.

• Zero axis:

  • set zeroaxis lw 1.2; draws the $x=0$ and/or $y=0$ reference axis (as supported).

• Sampling density:

  • set samples 1200; increases point sampling for smoother curves.

• Number formatting:

  • set format x '%.1f';
  • set format y '%.2f';

• Margins:

  • set lmargin 10;
  • set rmargin 4;
  • set tmargin 3;
  • set bmargin 4;

Premium Scientific Example and Reusable Template

The following example combines the most useful directives into one consistent style while avoiding terminal-specific commands.

k1 : 1.0$
k2 : 0.5$
w  : 1.0$

y : exp(w*t)*(k2*t + k1)$

plot2d(
    y,
    [t, -2, 2],
    [plot_format, gnuplot],
    [xlabel, "Time, t"],
    [ylabel, "y(t)"],
    [legend, "y(t)=exp(w*t)*(k2*t+k1)"],
    [style, [lines, 4]],
    [gnuplot_preamble,
     "set border 31 lw 2.2;
      set tics out nomirror scale 1.3;
      set mxtics 2;
      set mytics 2;
      set xtics font 'Times New Roman,20';
      set ytics font 'Times New Roman,20';
      set xlabel 'Time, t' font ',18';
      set ylabel 'y(t)' font ',18';
      set key top left box opaque font ',14';
      set grid xtics ytics mxtics mytics back lw 1;
      set zeroaxis lw 1.2;
      set samples 1500;
      set format x '%.1f';
      set format y '%.2f';
      set lmargin 10;
      set rmargin 4;
      set tmargin 3;
      set bmargin 4;"]
);