CustomTicksGuide.nb Custom Ticks Guide
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CustomTicks package
Mark A. Caprio, Department of Physics, University of Notre Dame
Version 1.62 (September 30, 2008)
Introduction
Mathematica provides a powerful system for generating graphics but does not provide, in built-in form, the fine
formatting control necessary for the preparation of publication quality figures. The CustomTicks package provides detailed
customization of tick mark placement and formatting. The flexibility achieved matches or exceeds that available with most
commercial scientific plotting software. Linear, logarithmic, and general nonlinear axes are supported. Some tick mark
manipulation functions, for use in graphics programming, are also provided by the CustomTicks package.
The CustomTicks package was developed as part of the LevelScheme system for preparing publication-quality
scientific figures [Comput. Phys. Commun. 171, 107 (2005)], available from http://wnsl.physics.yale.edu/
levelscheme.
Basic use for linear axes
The default tick marks produced by Mathematica's plotting functions are typically not suitable for publication.
Most notably, Mathematica drops trailing zeros after the decimal point in its default tick marks, leading to a series of ticks
of "ragged" lengths (e.g., "0.", "0.5", "1.", …). The tick marks are also often too short to be easily visible. (Note that the
default typewriter-style font used by Mathematica plotting functions is neither aesthetic or appropriate for publication, but
this can easily be remedied by setting $TextStyle={FontFamily->"Times"}.)
It is possible to override the default Mathematica ticks by specifying a list of tick marks, complete with formatting
information, as the value for the Ticks or FrameTicks option (see the Mathematica documentation for basic plotting
options). It is prohibitively tedious to construct such lists by hand. The CustomTicks package provides functions to
automatically construct lists of tick marks, with detailed control over formatting.
LinTicks@ x1, x2D Produces linear tick specifications,
with automatically chosen major and minor tick intervals
LinTicks@ x1,
Produces linear tick specifications, with manually chosen major and minor tick intervals
x2, interval, subdivsD
Tick specification function.
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option name
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default value
TickRange
8−Infinity,
Infinity<
Limits the drawing of ticks
Hand their labelsL to given coordinate range
ShowTickLabels
True
Controls whether or not major tick labels are printed
TickLabelRange
8−Infinity,
Infinity<
Limits printing of major tick labels to given coordinate range
ShowFirst
True
Controls whether or not first major tick label is printed
ShowLast
True
Controls whether or not last major tick label is printed
TickLabelStep
1
Limits printing of major tick labels to
one in every TickLabelStep major ticks
TickLabelStart
0
MajorTickLength
80.01, 0<
Used in conjunction with TickLabelStep
chooses which subset of major tick labels are printed
MinorTickLength
80.005, 0<
MajorTickStyle
8<
List specifying the lengths for the
major ticks Hinto and out of the frame,
as described in the Mathematica documentation for TicksL
List specifying the lengths for the
minor ticks Hinto and out of the frame,
as described in the Mathematica documentation for TicksL
MinorTickStyle
8<
List specifying the line style for the major ticks
DecimalDigits
Automatic
Sets number of digits after decimal
place for major tick labels; if Automatic ,
the maximum number of digits needed for any label is used
ShowMinorTicks
True
ExtraTicks
8<
Controls whether or not the minor ticks are drawn;
mainly for use with LogTicks Hsee belowL
List specifying the line style for the minor ticks
Additional coordinate values at which to insert tick marks
Tick formatting options.
The LinTicks function, in its simplest form, is given a starting and an ending coordinate value as its arguments.
It then generates the same tick marks Mathematica would have for this coordinate range, except that the labels are given
with fixed decimal formatting (e.g., "0.0", "0.5", "1.0", … for the example above) and the tick marks lines are somewhat
longer. Alternatively, arguments may be given to manually specify the coordinate interval between major tick marks and
the number of minor subdivisions. Several further options, listed above, can be specified. These control which tick marks
are drawn, which major ticks have labels, and the formatting of the tick lines and labels. Some examples are shown below.
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Mathematica
ragged labels
LinTicks
neat formatting
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Manual choice
of spacing
Advanced
formatting options
LinTicks@0, 2D LinTicks@0, 2, 1, 5D LinTicks@0, 2, 0.5, 5,
TickLabelStep → 2,
MinorTickStyle → 8Red"Times"}
]
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Plot[
{Log[10,(10^x)^2],Log[10,(10^x)^5]},{x,-1,3},
PlotRange→{{-0.0001,3},{-0.5,4.5}},
FrameTicks→{
LogTicks[10,0,3],
LogTicks[10,-1,5],
None,
None
},
Axes→False,Frame→True,ImageSize→72*3,
BaseStyle→{FontFamily->"Times"}
]
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Automatic ticks for Mathematica plot functions
The functions LinTicks and LogTicks can also be specified as automatic tick generation functions for the
Mathematica plotting functions. This saves you typing the plot range explicitly each time, at least if you do not wish to
specify details such as the number of subdivisions.
Plot[
{Log[10,Cosh[x]],Log[10,Sinh[x]]},{x,0,10},
PlotRange→{{-0.0001,4},{-0.5,2.5}},
FrameTicks→{LinTicks,LogTicks,None,None},
Axes→False,Frame→True,ImageSize→72*3,
BaseStyle→{FontFamily->"Times"}
]
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What if you wish to have tick marks on the top and right as well, but without labels on them? Simply specifying
FrameTicks→{LinTicks,LogTicks} or FrameTicks→{LinTicks,LogTicks,LinTicks,LogTicks}
would unfortunately result in ticks with unsightly and redundant labels. This can be avoided with the CustomTicks StripTickLabels function, as shown below.
Plot[
{Log[10,Cosh[x]],Log[10,Sinh[x]]},{x,0,10},
PlotRange→{{-0.0001,4},{-0.5,2.5}},
FrameTicks→
{LinTicks,LogTicks,StripTickLabels[LinTicks],StripTickLabels[LogTicks]},
Axes→False,Frame→True,ImageSize→72*3,
BaseStyle→{FontFamily->"Times"}
]
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If you are doing many such plots, it is easiest to set the necessary options as the default options for Plot.
SetOptions[Plot,Axes→False,Frame→True,FrameTicks→
{LinTicks,LogTicks,StripTickLabels[LinTicks],StripTickLabels[LogTicks]},Bas
eStyle→{FontFamily→"Times"}];
GraphicsGrid[{{Plot[Log[10,x^2],{x,0,10}],Plot[Log[10,x^-2],{x,0,10}]}}]
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Advanced customization
option name
default value
TickLabelFunction
Automatic
Function used to generate major tick labels
Hfirst argument is the numerical coordinate, second
argument is the LinTicks default formatted labelL;
Automatic gives the default label
TickPreTransformation
Identity
Function to be applied to tick coordinates,
before range tests and label generation
TickPostTransformation Identity
Function to be applied to tick coordinates,
after range tests and label generation
MinorTickIndexTransfo
rmation
Function to be applied to
minor tick indices Horiginally 1, 2, …,
subdivs -1L before minor tick coordinate is obtained by
linear interpolation between major tick positions
MinorTickIndexRange
Identity
81, Infinity<
Limits drawing of minor ticks to those with
indices Hbefore tranformationL in given range
Advanced customization options.
LinTicks accepts several options for advanced customization, allowing fully customizable labels and general
nonlinear axis scales. The option TickLabelFunction is used to specify the function to be used to construct tick
labels (see the Mathematica documentation for Function for information on defining functions). The label function is
given as arguments both the raw numerical tick coordinate and the LinTicks default formatted label, so it can work with
whichever is more convenient. The label function may be used for simple tasks, such as attaching a prefix or suffix to the
usual default label, or for more sophisticated formatting. In the following example, tick values are formatted as rational
multiples of p.
LinTicks[0,2*Pi,Pi/2,4,TickLabelFunction→(Rationalize[#/Pi]*Pi&)]
1
0
-1
0
p
ÅÅÅÅÅ
2
3p
ÅÅÅÅÅÅÅÅÅÅ
2
p
2p
Nonlinear axes are constructed using the coordinate transformation functions. For instance, the LogTicks function
provided by the CustomTicks package is actually implemented as a special case of LinTicks, with transformed minor
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tick positions. A simplified version (base 10 logarithm only) is given below for illustration.
Log10Ticks[p1_Integer,p2_Integer,Opts___?OptionQ]:=LinTicks[
p1,p2,1,9,
TickLabelFunction→(DisplayForm[SuperscriptBox[10,IntegerPart[#]]]&),
MinorTickIndexTransformation→(Log[10,#+1]*9&),
Opts
];
LinTicks@
Produces major and minor ticks at the specified coordinate values
majorticklist, minorticklistD
Form of tick specification function for ticks at arbitrary locations.
Ticks may be placed at arbitrary coordinate locations by using the most flexible
form of LinTicks, in which all major and minor tick coordinates are specified explicitly in two lists. All the usual coordinate-transformation and customization options
described above (except MinorTickIndexRange) are still applicable.
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Manual choice of tick coordinates
LinTicks@80,1,2,3,5<,Range@0.1,0.9,0.1DD
Tick mark programming utilities
LimitTickRange@8 x1, x2 <, ticksD Selects those tick mark with coordinates in the range specified;
approximate equality testing is used to avoid dropping ticks at the ends of the
interval due to roundoff ; ticks must be specifies as lists rather than bare numbers
TransformTicks@
Applies the specified transformation functions to the tick coordinates and tick lengths,
coordfcn, lengthfcn, ticksD respectively; ticks must be specified with an explicit pair of in and out lengths
StripTickLabels@ ticksD Removes any text labels from ticks;
ticks must be specified as lists rather than bare numbers
AugmentTicks@ labelfcn , Upgrades all tick specifications to full specifications, complete with labels,
8 l1, l2 <, stylelist, ticksD lengths into and out of the frame Hdefault 0 for outL, and style directives
AugmentAxisTickOptions@ Given a list of tick options Hthemselves lists of tick specificationsL for several axes,
numaxes, tickoptionsD
replaces any None entries with null lists and
appends additional null lists as needed to make numaxes entries;
a value None for tickoptions is replaced by a list of null lists
TickQ@ xD Tests whether or not x is a valid tick mark specificiation
TickListQ@ xD Tests whether or not x is a list of valid tick mark specificiations
Tick manipulation utilities.
Several utility functions for tick mark manipulation and testing are provided. These are mainly intended for use in
graphics programming rather than for direct use by someone wishing to specify tick marks. They are used internally by the
LevelScheme figure preparation system.
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FractionDigits@ xD Returns the number of digits to the right of the point in the decimal representation of x
Decimal digit counting function.
FractionDigits determines the number of digits to the right of the point in the decimal representation of a
number. It is of use in constructing fixed-point tick labels. It will, naturally, return large values, determined by Mathematica's Precision, for some numbers, such as non-terminating rationals. It accepts the option FractionDigitsBase,
by default 10, for work with non-decimal representations. Some examples follow:
FractionDigits@100D
FractionDigits@1.25D
FractionDigits@1 ê 3D
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© Copyright 2008, Mark A. Caprio.
Version 1.62
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