| Data Visualization |
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Using a host of original algorithms developed at Wolfram Research, Mathematica provides powerful functions that automate the process of creating cognitively and aesthetically compelling representations of structured and unstructured data—not only for points, lines and surfaces, but also for graphs and networks.
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ListPlot — plot lists of points
ListLinePlot — plot lines through lists of points
ListLogPlot - ListLogLinearPlot - ListLogLogPlot - ListPolarPlot |
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ListPlot3D — 3D plot from lists of 3D height data
ListPointPlot3D — 3D point scatter plot |
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ListContourPlot, ListDensityPlot — contour and density plots from height values
ListContourPlot3D — 3D contour surfaces from 3D field values |
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ListCurvePathPlot, ListSurfacePlot3D — reconstruct curves and surfaces from points |
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ArrayPlot — plot an array of values or colors
ReliefPlot — plot an array with simulated relief
MatrixPlot — plot values in a matrix |
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DateListPlot, DateListLogPlot — date and time plots |
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Histogram, Histogram3D — create histograms, log histograms, etc. |
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Vector Visualization »
ListStreamPlot - ListStreamDensityPlot - ListVectorPlot - ListVectorPlot3D - ...
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Graph Visualization
GraphPlot — lay out a general graph
LayeredGraphPlot — draw a graph in a layered or hierarchical way
TreePlot — draw a tree structure
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Charting & Information Visualization »
BarChart - PieChart - BubbleChart - BarChart3D - ... |
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Styling Options »
Frame - PlotStyle - Filling - Mesh - ImageSize - ...
Annotation & Combination »
Tooltip - StatusArea - GraphicsGrid - ... |
| Graphics Options & Styling |
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Mathematica provides hundreds of options to control every aspect of the construction and styling of graphics. The options are carefully designed to be both flexible and powerful, and to fit in with Mathematica's sophisticated built-in algorithms for aesthetic optimization.
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Coordinate Ranges »
PlotRange — the range of coordinates to include (All for all points)
Shape & Size »
AspectRatio — ratio of overall height to width (Automatic to use raw coordinate values)
ImageSize — absolute size of the graphic (Small, Large, number of pixels, ...)
Plotting Options »
Joined — whether to join points into lines
Filling — what filling to add under points, curves and surfaces
Mesh — what mesh lines or mesh points to draw
PlotStyle - PlotMarkers - ColorFunction - RegionFunction - ...
Annotation & Appearance »
Tooltip — tooltip specifications for curves or other objects
Frame — whether to draw a frame
Axes - Ticks - PlotLabel - FrameLabel - Background - ...
3D Options »
Boxed — whether to draw a box around the object
RotationAction — whether 3D objects should refit or clip when rotated
BoxRatios - ViewPoint - SphericalRegion - FaceGrids - Lighting - ...
Colors »
ColorData — hundreds of color schemes (gradients, named collections, etc.)
Red - Blue - Blend - Lighter - Darker - Opacity - ... |
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Combining & Modifying Graphics »
Show — overlap graphics or apply new options
GraphicsGrid — lay out graphics in a grid
Epilog - Inset - Manipulate |
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Styling in Text & Notebooks »
ImageSizeMultipliers - BaselinePosition - ... |
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Tweaking Rendering
Antialiasing - ImagePadding - PreserveImageOptions - Method |
| Symbolic Graphics Language |
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Mathematica uses the powerful idea of building up all 2D and 3D graphics from symbolic primitives—which can be manipulated using all standard Mathematica functions, and seamlessly integrated with text, math or tables. Symbolic graphics can also be used as input—and can be made dynamic and interactive.
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Graphics, Graphics3D — overall wrappers for 2D and 3D graphics |
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Basic 2D & 3D Objects »
Point - Line - Polygon - Text - Arrow
Special 2D Objects »
Disk - Circle - Rectangle - Raster
Special 3D Objects »
Sphere - Cuboid - Cylinder - Cone - Tube |
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Directives »
Red - RGBColor - Blend - Opacity - Thickness - Dashing - EdgeForm - ... |
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Sum, Product — symbolic sums and products |
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Coordinates »
Scaled - Offset - ImageScaled
Transformations »
Rotate - Translate - Scale - AffineTransform - ... |
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Compound Constructors »
Inset - GraphicsGroup - GraphicsComplex - GraphicsGrid - ... |
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Dynamic Elements »
Dynamic - Locator - Tooltip - Annotation - Deploy - ... |
| Graphics Importing & Exporting |
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Mathematica can immediately export graphics and animations to online, print and web formats, preserving dynamic annotation when possible. Mathematica also has powerful capabilities for importing graphics, geometry and other formats—immediately translating to a variety of fully integrated symbolic forms.
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Export — export static or animated graphics, or geometry data
Import — import from files and URLs as images, animations, graphics primitives, etc. |
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Raster Image Formats »
"GIF" - "JPEG" - "TIFF" - "PNG" - "BMP" - "PICT" - "WMF" - "SCT" - ...
Vector Graphics Formats »
"SVG" - "WMF" - "EPS" - "DXF" - ...
3D Geometry & Modeling Formats »
"PLY" - "OFF" - "OBJ" - "X3D" - "Maya" - "POV" - "LWO" - "STL" - ...
Multimedia Formats »
"AVI" - "FLV" - "QuickTime" - "SWF"
Web & Document Formats »
"HTML" - "XHTML" - "PDF" - ... |
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Scientific & Medical Data Formats »
"HDF" - "CDF" - "FITS" - "DICOM" - "EDF" - "XYZ" - ...
Geospatial Formats »
"USGSDEM" - "GTOPO30" - "CDED" - "SDTS" - ... |
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Options
ImageSize - ImageResolution - Background
Common Data Elements
"Graphics" — graphics object that displays as the image
"Data" — array of numbers or lists giving numerical color values
"RGBData" — array of RGBColor objects
"Rules" — rules for all elements |
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Interactive Notebook Operations
Copy, Paste — exchange graphics with external programs
Cell - ConvertTo — make a copied graphic evaluatable
Save Selection As — save graphics in any format
Open, Insert - Picture— open, insert from a graphics file |
| Function Visualization |
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Long the standard for high-quality function and surface visualization, Mathematica incorporates a host of original numeric, symbolic and geometric algorithms that automate the immediate creation of highly aesthetic and technically correct 2D and 3D visualizations.
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Plot — curves of one or more functions f (x)
LogPlot - LogLinearPlot - LogLogPlot
DiscretePlot — plot discrete sequences f (n) |
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Plot3D — 3D surfaces of one or more functions f (x, y) |
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ContourPlot — contour plot for a function f (x, y) or curve f (x, y)=c
ContourPlot3D — 3D contour plot for a function f (x, y, z) or surface f (x, y, z)=c |
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DensityPlot — density plot for a function f (x, y) |
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ParametricPlot — 2D parametric curves or regions
ParametricPlot3D — 3D parametric curves or surfaces
PolarPlot - RevolutionPlot3D - SphericalPlot3D |
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RegionPlot — 2D regions defined by inequalities
RegionPlot3D — 3D regions defined by inequalities |
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Vector Visualization »
StreamPlot - StreamDensityPlot - VectorPlot - VectorPlot3D - ... |
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Styling Options »
Frame - PlotStyle - Filling - Mesh - ImageSize - ...
Annotation & Combination »
Tooltip - StatusArea - GraphicsGrid - ... |
| Dynamic Visualization |
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Building on Mathematica's integrated symbolic architecture it becomes easy to introduce powerful dynamic behavior into any aspect of visualization. Single Mathematica symbolic functions are all it takes to set up full interactive parameter explorations, animations, dynamic annotation or drill-down information viewers.
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Manipulate — dynamically manipulate parameters in graphics
Animate — animate as a function of one or more parameters
ListAnimate — animate a list of graphics or other objects |
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TabView — make any list of objects be selectable with tabs
SlideView — view any list of objects as a sequence of slides
FlipView — flip between displaying two or more objects
MenuView - OpenerView - PopupView |
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Tooltip — attach any tooltip to any object
Mouseover — specify what to show when the mouse is over an object
StatusArea — put a string in the window status area
Annotation — attach a general annotation to an object
PopupWindow — attach a popup window to any object
Button - Speak - EmitSound |
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Locator — an object to move around in a graphic
Slider - Slider2D - ColorSlider - LocatorPane - ClickPane - ControllerState |
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ControlActive — specify "preview" settings when controls are active |
| Graphics Interactivity & Drawing |
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Mathematica's unified symbolic graphics architecture makes possible powerful mixing of programmatic graphics generation with interactive editing and control. The Mathematica Drawing Tools palette makes it straightforward to modify existing plots or illustrations—or to create free-form ones from scratch.
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Direct Interactive Drawing & Editing
Ctrl+1 — create a new empty graphic
Ctrl+D — bring up the Drawing Tools palette
Multi-click — select subparts of groups and insets
Shift+Drag — resize changing aspect ratio
Ctrl+G — bring up the Graphics Inspector |
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Programmatic Interactive Graphics »
Manipulate — create a complete framework for interactive graphics
Locator — interactively movable control point 
LocatorPane - ClickPane - EventHandler - ... |
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Interactive 3D Control »
Drag — rotate a 3D graphic
Shift+Drag — zoom |
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Imported Graphics
Cell > Convert To > StandardForm — make a copied graphic evaluatable |
| Computational Geometry |
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Mathematica's strengths in algebraic computation and graphics as well as numerics combine to bring unprecedented flexibility and power to geometric computation. Making extensive use of original algorithms developed at Wolfram Research, Mathematica's ability to represent and manipulate geometry symbolically allows it for the first time to fully integrate generation, analysis and rendering of geometrical structures.
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Nearest — find nearest points in any number of dimensions with any metric
NearestFunction — a function created to repeatedly find nearest points |
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Reduce — symbolically reduce real, complex and integer geometry descriptions
CylindricalDecomposition, GroebnerBasis — real, complex decompositions |
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RegionPlot, RegionPlot3D — plot regions defined by inequalities
Integrate, NIntegrate — find areas and volumes of geometric regions
Minimize, NMinimize — globally minimize over geometric regions
LinearProgramming — minimize over finite or infinite polyhedral regions |
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FindShortestTour - FindCurvePath - FindClusters
ListCurvePathPlot, ListSurfacePlot3D — reconstruct curves and surfaces |
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GraphPlot, GraphPlot3D — 2D, 3D graph layout |
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PolyhedronData — geometrical and structural data on regular polyhedra
KnotData - LatticeData - GraphData |
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Geometric Transformations »
RotationTransform - AffineTransform - TransformationMatrix - ... |
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Geometry Formats »
"DXF" - "PLY" - "BYU" - "X3D" - "STL" - ... |
| Sound and Sonification |
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Mathematica supports state-of-the-art sound generation, providing both arbitrary waveform synthesis from functions and data, and symbolic note-based MIDI-style sound synthesis. It also supports translation of arbitrary text, math, programs and graphics to speech.
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Play — play a function by taking it as the waveform for a sound
ListPlay — play a list of amplitude values |
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Sound Primitives
Sound — sound wrapper with timing information
SoundNote — music-like sound note
SampledSoundList — sampled sound from a list of data |
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EmitSound — emit a symbolically specified sound
Beep — generate a beep |
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Import, Export — import and export sounds
"MIDI" — music-oriented note format
"WAV", "AU", "FLAC", ... — sampled sounds |
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SystemDialogInput — use your computer system to record a sound for input |
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Expressions to Speech
Speak — speak a representation of any Mathematica expression
SpokenString — give the text for a spoken representation of an expression |
| New in 7.0: Visualization & Graphics |
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Building on Mathematica's unique base of visualization and graphics capabilities, Mathematica 7 adds several important new areas. Emphasizing integration and automation, Mathematica 7 introduces built-in vector visualization, automated dynamic charting and fully general splines and NURBS.
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New Vector Visualization Functions »
StreamPlot — make a stream plot from a vector field function
VectorPlot — plot vectors from a vector field function
StreamDensityPlot — superimpose plots of vector and scalar field functions
ListVectorPlot - VectorPlot3D - LineIntegralConvolutionPlot
New Visualization Functions
DiscretePlot — plot discrete sequences specified by formulas
DateListLogPlot - ListCurvePathPlot - FindCurvePath |
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New Charting Functions »
BarChart - PieChart - BubbleChart - RectangleChart - Histogram - ...
BarChart3D - PieChart3D - BubbleChart3D - Histogram3D - ...
Palettes - Chart Element Schemes — extensive styling options for charts |
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New Graphics Objects »
Cone - Tube - BSplineCurve - BSplineSurface - BezierCurve - ...
New Graphics Styling Features
CapForm - JoinForm - RoundingRadius - ... |
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Fully General Splines »
BezierCurve — 2D or 3D composite Bézier curves of any degree
BSplineCurve — 2D or 3D B-spline (NURBS) curves of any degree
BSplineSurface — B-spline (NURBS) surfaces of any degree
SplineDegree - SplineKnots - SplineWeights - SplineClosed - ... |
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New Sonification Functions
Speak - SpokenString - ... |
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PieChart — 
BubbleChart — 
SectorChart — 
PieChart3D — 
BubbleChart3D — 
SectorChart3D — 
Histogram3D — 