Mathematica - Wolfram uses mouseover tooltips to convey additional information in most graphics...

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��As in many areas of functionality, apparent similarities in visualization capabilities between Maple and Mathematica are only skin deep.

◼ Mathematica automates more of the graphic creation to give more accurate or more understandable results in more cases.

◼ Mathematica automates more sensible aesthetic choices for professional-looking results.

◼ Mathematica supports a wider range of visualization routines.

◼ Mathematica visualizations make use of dynamic elements for richer electronic presentation.

◼ Mathematica visualizations support a greater range of inputs.

��Most Mathematica routines use adaptive resampling to achieve smooth results even where functions are rapidly changing. Most Maple visualizations do not. Without it, Maple is unable to trace the smooth circular perimeter of this plot:

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Comparison of Graphics Capabilities between Mathematica 10 and Maple 18 | 1

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Notice also that the Mathematica 3D images are rendered using perspective. Maple’s use no perspective and appear as if viewed from an infinite distance, giving a slightly unnatural look.

The default choice for Maple is not to include axes for either scale or orientation, which can make plots hard to interpret unless the user manually adds them.

Maple can only automate sensible plot ranges for data with outliers in 2D. In this 3D example, we generate a table of values for a curved surface with one strong outlier. Mathematica’s automatic plot range preserves most of the interesting detail in the image at the expense of the outlier.


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��However, all useful detail in the Maple plot is lost in order to include the single outlier.

Mathematica

Mathematica automatically detects many kinds of branch cuts and discontinuities in function plots.


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��Maple incorrectly joins up the branch cut to make the function appear continuous.

Note: The output of the Maple plot has been manually rotated, as the default viewpoint obscured the key feature.


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Mathematica

Mathematica automatically detects many kinds of discontinuity.

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��In implicit plotting and contour plotting, Maple’s lack of automatic adaptive resampling results in poor smoothness.


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In the following example, notice how the only indication of relative contour values in Maple are the subtle color differences on the thin contour lines. The color filling between contours in Mathematica makes it easier to perceive the areas of low and high values, and automatic tooltips allow the user to see specific contour values.


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In 3D contour plotting, Maple’s lack of adaptive sampling combined with a low sample rate yields extremely rough results.


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��Maple provides graph plotting, but defaults to much more primitive algorithms. In this example, notice how Mathematica manages to avoid any edge crossings and has managed to use the canvas area more evenly. The Maple plot of the same data is confusing. This is made much worse by the default choice of Maple to label vertices. This fairly small set of data is already too large to fit all vertex labels without overlaps, making them unreadable. Instead, Mathematica has provided mouseover tooltips to label vertices by default.

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��Both Mathematica and Maple provide standard statistical charts, but in this example we see that Maple’s choice to use many of the same defaults as a function plot (1:1 aspect ratio, x axis inside the image) make the image harder to interpret since x axis tick labels appear on top of key features.

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Mathematica uses mouseover tooltips to convey additional information in most graphics types. In this case, mousing over the last dataset shows the following information.

��Maple does not use tooltips in any graphics. The graduated color scheme used by Maple conveys no addi-tional meaning and is there only for questionable aesthetic appeal.


��Once again, Maple’s less sophisticated approach and lack of adaptive resampling produces a plot which is much rougher than Mathematica’s.

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��Maple graphics cannot contain interactive elements. Individual elements in a Mathematica graphic (lines, points, polygons, etc.) can be given mouseover effects, tooltips (containing formatted text, typeset content, or graphics), or be made into buttons to execute arbitrary Mathematica programs. Mathematica graphics can also be made to update themselves automatically (even if a program is currently being executed) in response to external data feeds, the time, or the state of other calculations.

For example, the following code creates a bar chart where hovering over the bar with the mouse reveals a tooltip containing the photograph that the bar refers to.

Mathematica

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��Mesh lines are an important feature for interpretation of scientific visualizations. Mathematica automates meshes for maximum readability and allows arbitrary user control of meshes in most visualizations.

For example, in this plot of data, Mathematica chooses to use 15 mesh lines in each dimension, even though the data is sampled at 450×450 points.

Mathematica

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��In contrast, Maple places a mesh line for each row and column of the data, making them unreadable as the lines join and interfere with each other.

Note: The output of the Maple plot has been manually rotated, as the default viewpoint obscured the key feature.


��Often the ideal style choices are different for small and large datasets. Mathematica automatically applies these choices. For example, in this data plot, Mathematica’s larger choice of point size makes the points easier to see, especially on the axes.

Mathematica

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However, when there are many points, Mathematica automatically uses smaller points than Maple, allowing more detail to be seen and avoiding unnecessary point overlap.


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Both Mathematica and Maple use polygon edges to improve the appearance of bar charts.


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Mathematica�Most Mathematica 3D visualization routines give optional arbitrary control over mesh lines. Maple provides only rectangular mesh lines or contours. For example, here Mathematica is instructed to place meshes at isolines in distance from {0,0,0}.

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��In Maple the region over which visualizations can be created is always either rectangular or one in which the second independent variable is an interval that is a function of the first variable. Mathematica visualizations can be created over any region, specified implicitly or explicitly, or by using geometric constructs or arbitrary meshes. The following visualizations would be very hard to create in Maple.

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��Maple requires you to prepare all data as numeric values. It will also entirely fail if a single value is non-numeric (e.g. a NaN value in your data).


��Maple has no direct way to produce any of the following visualization types.

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Maple provides no facility for rendering data or functions as sound within a report. Mathematica documents can contain generated waveform sounds or MIDI instrumental sounds.

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��◼ Images have been copied using a screen capture tool to preserve pixel-level screen rendering. Printing

this document will not represent the resolution that printing from the original application would achieve.

◼ Except where stated, all comparisons use default options. Both systems allow manual control over plot details and in some cases, with sufficient work, a user may override some of the Maple deficiencies described in this comparison.


Mathematica - Wolfram uses mouseover tooltips to convey additional information in most graphics...

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