Data Visualization With Mathematica.no 3D Rasterization

8/9/2019 Data Visualization With Mathematica.no 3D Rasterization

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Data Visualization

with

Mathematica

Philadelphia Math + Science Coalitionwww.philaedfund.org/programs/advancing-education/philadelphia-math-science-

coalition

United Way Building

1709 Benjamin Franklin Parkway, Suite 700Philadelphia, PA 19103

March 8, 2010

Edward [email protected]

Goals :

To explore and dynamically interact easily with large real-time data sets visually, graphically, algebraically.Manipulate data and its creative presentation to maximize information transfer utilizing numeric, textual, and/or image representa-

tions.

2 Methods :Import[ ] function allows us to process data from personal files.

Data[ ] functions allow us to manipulate large amounts of real-world data into Mathematica from Wolfram's Integrated

Data Sources (Curated Data Sources).

Notes :With data we have values, not functions. So the data is discrete, not continuous.

In Mathematicathe data can be anything, not just numbers.


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Mathematica

Mathematicafiles are notebooks (.NB).

Each notebook is organized by grouped cells indicated by nested brackets on the right. Cells can be collapsed/expanded.

Almost any type of object can be copied/pasted anywhere or saved as a file.

Ther are numerous types of help: palettes, application (live) documentation, online (live) documentation, support.

The documentation is live and written in Mathematica.

Deployment options:

1. Notebook Player - I can share this interactivity with anyone who does not have Mathematica. User needs to download the

free MathematicaPlayer - www.wolfram.com/products/player. The author needs to publish the notebook (.NB) into a notebook

player (.NBP) file with Wolfram Mathematica Player: Online Conversion - www.wolfram.com/solutions/interactivedeployment/publish

2. Slideshow generator via "Slide Show palette" - dynamic, live - need the free Notebook Player if you do not have Mathemat-

ica.

3. Demonstration - dynamic interactivity with Manipulate[] to create virtual manipulatives that can be hosted at Wolfram's

Demonstrations site - http://demonstrations.wolfram.com4. Can save almost anything (including cell, selections) as static RTF, PDF, HTML, TeX, TXT, PS, XML, package, GIF, JPG,

PNG, TIFF, BMP, WMF, LATEX, MathML

5. Quiz generator.

MathematicaSyntax

Mathematica is symbolic. As in all CAS (Computer Algebrais Systems], the presentation of the mathematical results may some-

times look non "traditional." Sometimes may want TraditionalForm[] or set a system preference to always display tradtional form..

[ ] function

{ } lists and sets( ) grouping

[[ ]] indexing

= assignment

== logical equal

:= function definition

x3 is a "rule," read as x gets 3

Mathematicafunctions are mixed-case and start upper-case.

Do-Loop Construct

2 Data Visualization with Mathematica.03.nb


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? Table

Tableexpr, imax generates a list of imax copies of expr.Tableexpr, i, imax generates a list of the values of exprwhen i runs from 1 to imax.Tableexpr, i, imin, imax starts with i imin.Tableexpr, i, imin, imax, di uses steps di.Tableexpr, i, i1, i2, uses the successive values i1, i2, .Tableexpr, i, imin, imax, j, jmin, jmax, gives a nested list. The list associated with i is outermost.

Table 2 x 1, x, 1, 63, 5, 7, 9, 11, 13

Table x, 2 x, 2 x 5, 2 x4, x, 1, 6

1 2 7 2

2 4 9 32

3 6 11 162

4 8 13 512

5 10 15 1250

6 12 17 2592

Many more such as conditionals (if), user-defined functions.

Can program procedurally, functionally, and/or rule-based.

Built in mathematical algorithm selection is optimally chosen for problem, but can be over-ridden.

Parallel computing - within one CPU across cores and/or across CPUs - this is great for multi-core CPUs, during time-consuming

operations to allow you to do other work on the file.

MathematicaVisualization Capabilities

Looking at some visualization capbabilities. Remember that data is discrete so the Mathematica functions that utilize a mathemati-

cal function can only be used after the data is modeled with a function.

sizeImageNotebook 200;

PlotSinx, x, 0, 2 , ImageSize sizeImageNotebook

1 2 3 4 5 6

1.0

0.5

0.5

1.0

Data Visualization with Mathematica.03.nb 3


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Plot3DSinx y2, x, 3, 3,y, 2, 2, ImageSize sizeImageNotebook

2

0

2 2

1

0

1

2

1.00.50.0

0.5

1.0

ContourPlotSinx y2, x, 3, 3,

y, 2, 2, ImageSize sizeImageNotebook

3 2 1 0 1 2 3

2

1

0

1

2

DiscretePlotPrimek, k, 1, 50, ImageSize sizeImageNotebook

10 20 30 40 50

50

100

150

200

Everything can be changed, decorated, annotated via options (PlotStyle is a graphic option) and directives. This can be easily

accessed from the "Chart Element Schemes" and the "Color Schemes"palettes.

Hover cursor over any point to be shown the data value in the tooltip.



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data1 ListPlotTooltip3, 4, 5,PlotStyle PointSize0.025, Red,ImageSize sizeImageNotebook

0.5 1.0 1.5 2.0 2.5 3.0

3.5

4.0

4.5

5.0

data2 ListLinePlot3, 4, 5,PlotStyle Dashed, Magenta, ImageSize sizeImageNotebook

0.5 1.0 1.5 2.0 2.5 3.0

3.5

4.0

4.5

5.0

Can combine many graphs:

Showdata1, data2

0.5 1.0 1.5 2.0 2.5 3.0

3.5

4.0

4.5

5.0



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ListLinePlotAccumulateRandomReal 1, 1, 250,ColorFunction "Rainbow", Filling Axis,

ImageSize sizeImageNotebook

50 100 150 200 250

5

10

15

starData TableCosk 2 Pi 7, Sink 2 Pi 7, k, 0, 21, 31 0

cos

7 sin

7 sin 3

14 cos 3

14

sin 14

cos 14

sin

14 cos

14

sin 3 14

cos 3 14

cos

7 sin

7

1 0

NstarData

1. 0.0.900969 0.433884

0.62349 0.781831

0.222521 0.974928

0.222521 0.974928

0.62349 0.781831

0.900969 0.433884

1. 0.

ListLinePlotTooltipstarData, Frame True,Axes False, ImageSize sizeImageNotebook

0.5 0.0 0.5 1.01.0

0.5

0.0

0.5

1.0



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ParametricPlotSin2 u, Sin3 u,u, 0, 2 Pi, ImageSize sizeImageNotebook

1.0 0.5 0.5 1.0

1.0

0.5

0.5

1.0

ParametricPlotr^2 Sqrtt Cost, Sint,t, 0, 3 Pi 2, r, 1, 2, ImageSize sizeImageNotebook

6 4 2 0 2

4

2

0

2

4



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ParametricPlot3D

t Cost10

, t Sint

10,

t

10,

t, 6 , 6

,

ImageSize sizeImageNotebook,

PlotStyle Thick, Red

1

0

1

1

0

1

1

0

1

ParametricPlot3D1.16^ v Cosv 1 Cosu, 1.16^ v Sinv 1 Cosu, 2 1.16^ v 1 Sinu,

u, 0, 2 Pi, v, 15, 6, Mesh None, PlotStyle Opacity0.6,PlotRange All, PlotPoints 25, ImageSize sizeImageNotebook

PolarPlotSin5 t, t, 0, , ImageSize sizeImageNotebook

0.5 0.5

0.5

0.5

1.0



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ReliefPlotTablei Sini^2 j^2, i, 4, 4, .03, j, 4, 4, .03,ColorFunction "SunsetColors", ImageSize sizeImageNotebook

GraphPlotTablei Modi^2, 102, i, 0, 102

A 100-node random graph with 1% of possible edges filled in:



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GraphPlotRandomChoice0.01, 0.99 1, 0, 100, 100

Layered graphs.

LayeredGraphPlot1 2, 1 3, 2 3, 1 4, 2 4, 1 5,VertexLabeling True, ImageSize sizeImageNotebook

1

2

3 4

5



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LayeredGraphPlot"John" "plants", "lion" "John", "tiger" "John",

"tiger" "deer", "lion" "deer", "deer" "plants",

"mosquito" "lion", "frog" "mosquito", "mosquito" "tiger",

"John" "cow", "cow" "plants", "mosquito" "deer","mosquito" "John", "snake" "frog", "vulture" "snake",

Left, VertexLabeling True, ImageSize 700

Johnlion

tiger deer

mosquitofrog

cow

snakevulture

And many more:

ListPlot, DateListPlot, ListLogPlot,

RegionPlot, RegionPlot3D, DensityPlot, ListDensityPlot, ContourPlot, ArrayPlot, RegionPlot, StreamPlot, VectorPlot, StreamDensi-

tyPlot, VectordensityPlot,

StreamPlot VectorPlot StreamDensityPlot VectorDensityPlot

RevolutionPlot3D, ParametricPlot3D, TreePlot

Import [ ] and Fitting Model to Data

Import and Export can handle not only tabular data, but also data corresponding to graphics, sounds, expressions and even

whole documents. Import and Export can often deduce the appropriate format for data simply by looking at the extension of the

file name for the file in which the data is being stored. "Exporting Graphics and Sounds" and "Importing and Exporting Files" discuss

in more detail how Import and Export work. Note that you can also use Import and Export to manipulate raw files of binary

data.



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$ImportFormats

3DS, ACO, AIFF, ApacheLog, AU, AVI, Base64, Binary, Bit, BMP, Byte, BYU, BZIP2, CDED, CDF, Character16, Character8,Complex128, Complex256, Complex64, CSV, CUR, DBF, DICOM, DIF, Directory, DXF, EDF, ExpressionML, FASTA, FITS,

FLAC, GenBank, GeoTIFF, GIF, Graph6, GTOPO30, GZIP, HarwellBoeing, HDF, HDF5, HTML, ICO, Integer128, Integer16,

Integer24, Integer32, Integer64, Integer8, JPEG, JPEG2000, JVX, LaTeX, List, LWO, MAT, MathML, MBOX, MDB, MGF,

MMCIF, MOL, MOL2, MPS, MTP, MTX, MX, NB, NetCDF, NOFF, OBJ, ODS, OFF, Package, PBM, PCX, PDB, PDF,

PGM, PLY, PNG, PNM, PPM, PXR, QuickTime, RawBitmap, Real128, Real32, Real64, RIB, RSS, RTF, SCT, SDF, SDTS,

SDTSDEM, SHP, SMILES, SND, SP3, Sparse6, STL, String, SXC, Table, TAR, TerminatedString, Text, TGA, TIFF, TIGER,

TSV, UnsignedInteger128, UnsignedInteger16, UnsignedInteger24, UnsignedInteger32, UnsignedInteger64, UnsignedInteger8,

USGSDEM, UUE, VCF, WAV, Wave64, WDX, XBM, XHTML, XHTMLMathML, XLS, XML, XPORT, XYZ, ZIP

$ExportFormats

3DS, ACO, AIFF, AU, AVI, Base64, Binary, Bit, BMP, Byte, BYU, BZIP2, CDF, Character16, Character8, Complex128,Complex256, Complex64, CSV, DICOM, DIF, DXF, EMF, EPS, ExpressionML, FASTA, FITS, FLAC, FLV, GIF, Graph6,

GZIP, HarwellBoeing, HDF, HDF5, HTML, Integer128, Integer16, Integer24, Integer32, Integer64, Integer8, JPEG,

JPEG2000, JVX, List, LWO, MAT, MathML, Maya, MGF, MIDI, MOL, MOL2, MTX, MX, NB, NetCDF, NOFF, OBJ,

OFF, Package, PBM, PCX, PDB, PDF, PGM, PLY, PNG, PNM, POV, PPM, PXR, RawBitmap, Real128, Real32, Real64,

RIB, RTF, SCT, SDF, SND, Sparse6, STL, String, SVG, SWF, Table, TAR, TerminatedString, TeX, Text, TGA, TIFF, TSV,

UnsignedInteger128, UnsignedInteger16, UnsignedInteger24, UnsignedInteger32, UnsignedInteger64, UnsignedInteger8,

UUE, VRML, WAV, Wave64, WDX, WMF, X3D, XBM, XHTML, XHTMLMathML, XLS, XML, XYZ, ZIP, ZPR

? Import

Import"file" imports data from a file, returning a complete Mathematica version of it.Import"file", elements imports the specified elements from a file.Import"http:url", and Import"ftp:url", imports from any accessible URL.

?Fit

Fitdata, funs, vars finds a least-squares fit toa list of data as a linear combination of the functions funs of variables vars.

? FindFit

FindFitdata, expr, pars, vars finds numerical values of the parameters pars that make exprgive abest fit to data as a function of vars. The data can have the form x1, y1, , f1, x2, y2, , f2, ,where the number of coordinates x, y, is equal to the number of variables in the list vars. The

data can also be of the form

f

1, f

2,

, with a single coordinate assumed to take values 1, 2, .

FindFitdata, expr, cons, pars, vars finds a best fit subject to the parameter constraints cons.

$DataDirectory ToFileNameNotebookDirectory, "Data";



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$DataDirectory

J:\presentations\Data Visualization with Mathematica\Data\

AppendTo$Path, $DataDirectory;$Path

C:\Program Files\Wolfram Research\Mathematica\7.0\SystemFiles\Links,C:\Documents and Settings\Ed\Application Data\Mathematica\Kernel,

C:\Documents and Settings\Ed\Application Data\Mathematica\Autoload,

C:\Documents and Settings\Ed\Application Data\Mathematica\Applications,

C:\Documents and Settings\All Users\Application Data\Mathematica\Kernel,

C:\Documents and Settings\All Users\Application Data\Mathematica\Autoload,

C:\Documents and Settings\All Users\Application Data\Mathematica\Applications, .,

C:\Documents and Settings\Ed, C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\Packages,

C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\LegacyPackages,

C:\Program Files\Wolfram Research\Mathematica\7.0\SystemFiles\Autoload,

C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\Autoload,

C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\Applications,

C:\Program Files\Wolfram Research\Mathematica\7.0\AddOns\ExtraPackages,

C:\Program Files\Wolfram Research\Mathematica\7.0\SystemFiles\Kernel\Packages,

C:\Program Files\Wolfram Research\Mathematica\7.0\Documentation\English\System,

J:\presentations\Data Visualization with Mathematica\Data\

Fitting a model to a series of (x,y) data values:

dataLinear Import"data.xls", "Data", 1;dataPlotLinear

ListPlotTooltipdataLinear, PlotStyle PointSize0.02, Green

2 4 6 8 10

30

40

50

Fit the data to the model a x b.



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Clear a, b;fitLinear FindFitdataLinear, a x b, a, b, x

a 4.61415, b 8.924

Display the fit function together with the data.

ShowdataPlotLinear,Plota x b . fitLinear, x, 0, 10, PlotStyle Red

2 4 6 8 10

30

40

50

Fitting non-linear data.

dataNoisy Import

"noisydata.xls",

"Data", 1

;

dataNoisyPlot ListPlotdataNoisy

1 2 3 4 5 6

1.0

0.5

0.5

1.0

Fit the data to the model sinx sin x.

fit FindFitdataNoisy, Sin x Sin x, , , , , x 0.00718779, 1.00277, 1.41681, 0.999737



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Display the fit function together with the data.

ShowdataNoisyPlot,Plot Sin x Sin x . fit, x, 0, 6.3, PlotStyle Red

1 2 3 4 5 6

1.0

0.5

0.5

1.0

The next example fits a nonlinear model to some astronomical data.

This imports a data file consisting of timing residuals for the pulsar PSR1257+12 spanning a three-year period (kindly supplied by

Alex Wolszczan).

dataPulsar Import"pulsar1257.dat", "Table";Display the pulsar data:

dataPulsar

0.687021 0.0188495

0.719811 0.335115

0.730804 0.52507

0.796315 0.257191

0.845486 2.15298

0.861925 2.10726

0.952068 2.59551

0.95484 2.62171

0.973977 2.32315

0.976714 2.22064

1.20073 0.568935



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. .

1.30188 0.488403

1.30455 0.494481

1.31002 0.469674

1.39201 1.94947

1.39477 1.97185

1.44655 0.0107999

1.44664 0.00668151.55317 0.0770058

1.55587 0.128978

1.59684 2.46479

1.59966 2.52511

1.63513 1.86379

1.67874 0.689795

1.68151 0.815304

1.6897 1.12602

1.70062 1.37461

1.71974 1.37764

1.76346 0.223993

1.76619 0.155781

1.80171 0.231833

1.80456 0.218089

1.80735 0.19759

1.82358 0.02412

1.82634 0.0089064

1.8509 0.22583

1.85364 0.222086

1.86456 0.150962

1.88094 0.176626

1.88366 0.253788

1.90829 1.07285

1.91101 1.16397

1.91379 1.24854

1.91918 1.40647

1.92192 1.469481.96838 1.15017

1.99029 0.019696

2.06935 1.89477

2.12112 1.7299

2.13467 2.39416

2.15652 2.67063

2.15925 2.63692

2.18661 1.47038

2.19189 1.12811

2.19464 0.939938

2.26282 1.63623



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. .

2.30105 0.467178

2.3038 0.370373

2.30653 0.27104

2.30923 0.185139

2.31196 0.100059

2.31473 0.0191635

2.31741 0.06136372.32012 0.135984

2.32288 0.193437

2.32562 0.262972

2.33105 0.3573

2.3336 0.386537

2.38549 0.108196

2.3882 0.0782136

2.41802 0.0979297

2.41909 0.116686

2.4208 0.139112

2.49979 1.2944

2.50256 1.23173

2.55708 1.44589

2.55979 1.583872.57344 2.143

2.57619 2.21118

2.66331 1.77407

2.66602 1.93837

2.72048 2.01038

2.7232 1.85777

2.75059 0.0428941

2.75592 0.405188

2.75867 0.595059

2.78859 1.85679

2.79134 1.89844

2.83763 0.804781

2.84038 0.68503

2.87312 0.49313

2.87584 0.550665

2.91669 0.564317

2.96028 0.154039

2.96302 0.17036

3.02575 1.16419

3.02851 1.17307

3.08589 0.619972

3.08867 0.764877

3.12139 2.11591

3.1706 0.76415

3.17332 0.576337



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3.23625 2.80614

3.2389 2.80191

3.26894 1.70996

3.2717 1.52628

3.27441 1.34718

3.27716 1.15426

3.27988 0.958417

3.2826 0.752647

3.28539 0.542753

3.28809 0.337932

3.29353 0.0750401

3.29624 0.274558

3.299 0.47054

3.30172 0.667524

3.30445 0.851145

3.30719 1.02325

3.31267 1.34591

3.3154 1.48888

3.31809 1.61345

3.32085 1.73499

3.3263 1.919163.32906 1.9923

3.33182 2.04945

3.33455 2.09106

3.38369 0.774774

3.38643 0.647009

3.43013 0.938914

3.4312 0.951182

3.43291 0.967501

3.47933 0.531234

3.48206 0.479443

3.52028 0.222164

3.54214 0.516191

3.54486 0.560826

3.55033 0.649746

3.55852 0.771456

3.56671 0.857604

3.56947 0.87025

3.57219 0.882395

3.57496 0.889598

3.58044 0.873126

3.58584 0.832191

3.5886 0.800181

3.5914 0.757595

3.59404 0.708435

3.59676 0.654172



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3.59952 0.585253

3.60227 0.513836

3.60496 0.43218

3.60775 0.345518

3.6241 0.303461

3.62692 0.430591

3.63231 0.679269

3.63502 0.809463

3.63778 0.929009

3.64049 1.05495

3.64323 1.18237

3.64596 1.30095

3.65144 1.5187

3.65414 1.6279

3.65689 1.70974

3.65962 1.79757

3.66236 1.87084

3.6651 1.93

3.71426 0.703003

3.71701 0.515862

3.76086 2.36768

3.76342 2.46275

dataPulsarPlot

ListPlotdataPulsar, AspectRatio 12

, PlotStyle Red

1.5 2.0 2.5 3.0 3.5

2

1

1

2

3

Here is the nonlinear model we will use for the fit.

+ cos(t ) + cos(t ) + sin(t ) + sin(t )

This computes the regression using nondefault starting values for the parameters.

params FindFit

dataPulsar,

Sin t Cos t Sin t Cos t ,, 1, , 1, , 1, , 0, , 23.31, , 34.64, , 0, t

0.46115, 1.33261, 1.29803, 0.209533, 23.3869, 34.5111, 0.0769581

This plot shows the quality of the nonlinear fit.



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ShowPlot Sin t Cos t Sin t Cos t . params,t, 0.68, 3.76,

dataPulsarPlot

1.5 2.0 2.5 3.0 3.5

2

1

1

2

xxxxData[] - Curated Data Sources - Integrated Data Sources - What Kind of Data Collections?

xxxxData functions :An efficient load-on-demand mechanism makes hundreds of gigabytes of carefully curated and continually updated data immedi-

ately available inside Mathematica for use in computations. This data, curated at Wolfram Research, can be accessed and pro-

cessed in a coherent way.

These data functions cover:

math, science, politics, geography, finance, ...

Examples include:

LatticeData,

WeatherData,

Physical and chemical data: ElementData, ChemicalData, IsotopeData, ParticleData,

Earth and astronomical data: WeatherData, GeodesyData, CityData, CountryData, GeoDistance, AstronomicalData,

Life science data: GenomeData, GenomeLookup, SequenceAlignment, ProteinData,

Finance and economic data: FinancialData, CountryData,

Mathematical data: FiniteGroupData, GraphData, KnotData, LatticeData, PolyhedronData,

Linguistic data: DictionaryLookup, WordData, ExampleData,

ProteinData"prot" gives the reference amino acid sequence for the protein prot.ProteinData"prot", "property" gives the value of the specified property for the protein prot.



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What Kind of Data and Meta-Data within Collection?

? ElementData

ElementData"name", "property" gives the value of the specified property for the chemical element "name".ElementDatan, "property" gives the specified property for the nth chemical element.

List the ElementData[] collections:

ElementDataHydrogen, Helium, Lithium, Beryllium, Boron, Carbon, Nitrogen, Oxygen, Fluorine, Neon, Sodium, Magnesium, Aluminum, Silicon,

Phosphorus, Sulfur, Chlorine, Argon, Potassium, Calcium, Scandium, Titanium, Vanadium, Chromium, Manganese, Iron,

Cobalt, Nickel, Copper, Zinc, Gallium, Germanium, Arsenic, Selenium, Bromine, Krypton, Rubidium, Strontium, Yttrium,

Zirconium, Niobium, Molybdenum, Technetium, Ruthenium, Rhodium, Palladium, Silver, Cadmium, Indium, Tin, Antimony,

Tellurium, Iodine, Xenon, Cesium, Barium, Lanthanum, Cerium, Praseodymium, Neodymium, Promethium, Samarium,

Europium, Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium, Ytterbium, Lutetium, Hafnium, Tantalum, Tungsten,

Rhenium, Osmium, Iridium, Platinum, Gold, Mercury, Thallium, Lead, Bismuth, Polonium, Astatine, Radon, Francium, Radium,

Actinium, Thorium, Protactinium, Uranium, Neptunium, Plutonium, Americium, Curium, Berkelium, Californium, Einsteinium,

Fermium, Mendelevium, Nobelium, Lawrencium, Rutherfordium, Dubnium, Seaborgium, Bohrium, Hassium, Meitnerium,

Darmstadtium, Roentgenium, Ununbium, Ununtrium, Ununquadium, Ununpentium, Ununhexium, Ununseptium, Ununoctium

ElementData1Hydrogen

LengthElementData118

ElementData"Properties"Abbreviation, AbsoluteBoilingPoint, AbsoluteMeltingPoint, AdiabaticIndex, AllotropeNames, AllotropicMultiplicities, AlternateNames,

AlternateStandardNames, AtomicNumber, AtomicRadius, AtomicWeight, Block, BoilingPoint, BrinellHardness, BulkModulus,

CASNumber, Color, CommonCompoundNames, CovalentRadius, CriticalPressure, CriticalTemperature, CrustAbundance,

CrystalStructure, CuriePoint, DecayMode, Density, DiscoveryCountries, DiscoveryYear, ElectricalConductivity, ElectricalType,

ElectronAffinity, ElectronConfiguration, ElectronConfigurationString, Electronegativity, ElectronShellConfiguration,

FusionHeat, GasAtomicMultiplicities, Group, HalfLife, HumanAbundance, IconColor, IonizationEnergies, IsotopeAbundances,

KnownIsotopes, LatticeAngles, LatticeConstants, Lifetime, LiquidDensity, MagneticType, MassMagneticSusceptibility,

MeltingPoint, Memberships, MeteoriteAbundance, MohsHardness, MolarMagneticSusceptibility, MolarVolume, Name,

NeelPoint, NeutronCrossSection, NeutronMassAbsorption, OceanAbundance, Period, Phase, PoissonRatio, QuantumNumbers,

Radioactive, RefractiveIndex, Resistivity, ShearModulus, SolarAbundance, SoundSpeed, SpaceGroupName, SpaceGroupNumber,

SpecificHeat, StableIsotopes, StandardName, SuperconductingPoint, ThermalConductivity, ThermalExpansion, UniverseAbundance,

Valence, VanDerWaalsRadius, VaporizationHeat, VickersHardness, VolumeMagneticSusceptibility, YoungModulus

ElementData can be indexed by full name, number, or abbreviation:



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ElementData"Hydrogen", "MeltingPoint"259.14

ElementData1, "MeltingPoint"259.14

ElementData"H", "MeltingPoint"259.14

What are the units of Hydrogen's MeltingPoint?

ElementData"H", "MeltingPoint", "Units"DegreesCelsius

ElementData"H", "MeltingPoint", "UnitsNotation"C

Sample Visualization Development

? ListLinePlot

ListLinePloty1, y2, plots a line through a list of values, assumed to correspond to x coordinates 1, 2, .ListLinePlotx1, y1, x2, y2, plots a line through specific x and y positions.ListLinePlotlist1, list2, plots several lines.

TableElementDataz, "MeltingPoint", z, 1, 118259.14, , 180.54, 1287., 2075., 3550., 210.1, 218.3, 219.6, 248.59, 97.72, 650., 660.32, 1414., 44.2, 115.21, 101.5, 189.3,

63.38, 842., 1541., 1668., 1910., 1907., 1246., 1538., 1495., 1455., 1084.62, 419.53, 29.76, 938.3, 817., 221., 7.3, 157.36,

39.31, 777., 1526., 1855., 2477., 2623., 2157., 2334., 1964., 1554.9, 961.78, 321.07, 156.6, 231.93, 630.63, 449.51, 113.7, 111.8,

28.44, 727., 920., 798., 931., 1021., 1.1 10

3

, 1072., 822., 1313., 1356., 1412., 1474., 1497., 1545., 819., 1663., 2233., 3017.,3422., 3186., 3033., 2466., 1768.3, 1064.18, 38.83, 304., 327.46, 271.3, 254., 302., 71., , 7.0 102, 1050., 1750., 1572.,

1135., 644., 640., 1176., 1345., 1050., 900., 860., 1527., 827., 827., 1627., , , , , , , , , , , , , , ,



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ListLinePlotTableElementDataz, "MeltingPoint", z, 1, 118

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? ListPlot

ListPloty1, y2, plots points corresponding to a list of values, assumed to correspond to x coordinates 1, 2, .ListPlotx1, y1, x2, y2, plots a list of points with specified x and y coordinates.ListPlotlist1, list2, plots several lists of points.

ListPlotTableElementDataz, "MeltingPoint", z, 1, 118

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TableElementDataz, "MeltingPoint", z, 118259.14, , 180.54, 1287., 2075., 3550., 210.1, 218.3, 219.6, 248.59, 97.72, 650., 660.32, 1414., 44.2, 115.21, 101.5, 189.3,

63.38, 842., 1541., 1668., 1910., 1907., 1246., 1538., 1495., 1455., 1084.62, 419.53, 29.76, 938.3, 817., 221., 7.3, 157.36,

39.31, 777., 1526., 1855., 2477., 2623., 2157., 2334., 1964., 1554.9, 961.78, 321.07, 156.6, 231.93, 630.63, 449.51, 113.7, 111.8,

28.44, 727., 920., 798., 931., 1021., 1.1 103, 1072., 822., 1313., 1356., 1412., 1474., 1497., 1545., 819., 1663., 2233., 3017.,

3422., 3186., 3033., 2466., 1768.3, 1064.18, 38.83, 304., 327.46, 271.3, 254., 302., 71., , 7.0 102, 1050., 1750., 1572.,

1135., 644., 640., 1176., 1345., 1050., 900., 860., 1527., 827., 827., 1627., , , , , , , , , , , , , , ,

dataMeltingPointElement

TableElementDataz, "MeltingPoint", ElementDataz, z, 118



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259.14 Hydrogen

Helium

180.54 Lithium

1287. Beryllium

2075. Boron

3550. Carbon

210.1 Nitrogen

218.3 Oxygen

219.6 Fluorine

248.59 Neon

97.72 Sodium

650. Magnesium

660.32 Aluminum

1414. Silicon

44.2 Phosphorus

115.21 Sulfur

101.5 Chlorine

189.3 Argon

63.38 Potassium

842. Calcium

1541. Scandium

1668. Titanium

1910. Vanadium

1907. Chromium

1246. Manganese

1538. Iron

1495. Cobalt

1455. Nickel

1084.62 Copper

419.53 Zinc

29.76 Gallium

938.3 Germanium

817. Arsenic

221. Selenium

7.3 Bromine

157.36 Krypton



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39.31 Rubidium

777. Strontium

1526. Yttrium

1855. Zirconium

2477. Niobium

2623. Molybdenum

2157. Technetium

2334. Ruthenium

1964. Rhodium

1554.9 Palladium

961.78 Silver

321.07 Cadmium

156.6 Indium

231.93 Tin

630.63 Antimony

449.51 Tellurium

113.7 Iodine

111.8 Xenon

28.44 Cesium

727. Barium

920. Lanthanum798. Cerium

931. Praseodymium

1021. Neodymium

1.1 103 Promethium

1072. Samarium

822. Europium

1313. Gadolinium

1356. Terbium

1412. Dysprosium

1474. Holmium

1497. Erbium

1545. Thulium

819. Ytterbium

1663. Lutetium

2233. Hafnium

3017. Tantalum

3422. Tungsten

3186. Rhenium

3033. Osmium

2466. Iridium

1768.3 Platinum

1064.18 Gold

38.83 Mercury

304. Thallium

327.46 Lead



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271.3 Bismuth

254. Polonium

302. Astatine

71. Radon

Francium

7.0 102 Radium

1050. Actinium

1750. Thorium

1572. Protactinium

1135. Uranium

644. Neptunium

640. Plutonium

1176. Americium

1345. Curium

1050. Berkelium

900. Californium

860. Einsteinium

1527. Fermium

827. Mendelevium

827. Nobelium

1627. Lawrencium Rutherfordium

Dubnium

Seaborgium

Bohrium

Hassium

Meitnerium

Darmstadtium

Roentgenium

Ununbium

Ununtrium

Ununquadium

Ununpentium

Ununhexium

Ununseptium

Ununoctium

? Dimensions

Dimensionsexpr gives a list of the dimensions of expr.Dimensionsexpr, n gives a list of the dimensions of exprdown to level n.

DimensionsdataMeltingPointElement

118, 2

LengthdataMeltingPointElement118



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dataMeltingPointElement1259.14, Hydrogen

dataMeltingPointElement12Hydrogen

ListLinePlotTableElementDataz, "MeltingPoint", z, 1, 118

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ListLinePlotTooltipTableElementDataz, "MeltingPoint", z, 1, 118,PlotLabel "Melting Point vs Atomic Number",

AxesLabel "Atomic\nNumber", "Melting\nPoint C",LabelStyle DirectiveBlue, Bold, GridLines Automatic

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Melting

Point C

Melting Point vs Atomic Number

dataMpBp TableElementDataz, "MeltingPoint",ElementDataz, "BoilingPoint", z, 1, 118;



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ListLinePlotdataMpBp

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ListPlotdataMpBp

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The data points can have tool tips with information when the mouse hovers over a data point.

? Tooltip

Tooltipexpr, label displays label as a tooltip while the mouse pointer is in the area where expr is displayed.



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ListPlotTooltipdataMpBp

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ElementData"Properties"

Abbreviation, AbsoluteBoilingPoint, AbsoluteMeltingPoint, AdiabaticIndex, AllotropeNames, AllotropicMultiplicities, AlternateNames,AlternateStandardNames, AtomicNumber, AtomicRadius, AtomicWeight, Block, BoilingPoint, BrinellHardness, BulkModulus,

CASNumber, Color, CommonCompoundNames, CovalentRadius, CriticalPressure, CriticalTemperature, CrustAbundance,

CrystalStructure, CuriePoint, DecayMode, Density, DiscoveryCountries, DiscoveryYear, ElectricalConductivity, ElectricalType,

ElectronAffinity, ElectronConfiguration, ElectronConfigurationString, Electronegativity, ElectronShellConfiguration,

FusionHeat, GasAtomicMultiplicities, Group, HalfLife, HumanAbundance, IconColor, IonizationEnergies, IsotopeAbundances,

KnownIsotopes, LatticeAngles, LatticeConstants, Lifetime, LiquidDensity, MagneticType, MassMagneticSusceptibility,

MeltingPoint, Memberships, MeteoriteAbundance, MohsHardness, MolarMagneticSusceptibility, MolarVolume, Name,

NeelPoint, NeutronCrossSection, NeutronMassAbsorption, OceanAbundance, Period, Phase, PoissonRatio, QuantumNumbers,

Radioactive, RefractiveIndex, Resistivity, ShearModulus, SolarAbundance, SoundSpeed, SpaceGroupName, SpaceGroupNumber,

SpecificHeat, StableIsotopes, StandardName, SuperconductingPoint, ThermalConductivity, ThermalExpansion, UniverseAbundance,

Valence, VanDerWaalsRadius, VaporizationHeat, VickersHardness, VolumeMagneticSusceptibility, YoungModulus

dataMpBp2 TableElementDataz, "MeltingPoint",ElementDataz, "BoilingPoint", z, 1, 118

259.14 252.87

268.93

180.54 1342.

1287. 2470.

2075. 4000.

3550. 4027.

210.1 195.79



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. .

219.6 188.12

248.59 246.08

97.72 883.

650. 1090.

660.32 2519.

1414. 2.9 103

44.2 280.5115.21 444.72

101.5 34.04

189.3 185.8

63.38 759.

842. 1484.

1541. 2830.

1668. 3287.

1910. 3407.

1907. 2671.

1246. 2061.

1538. 2861.

1495. 2927.

1455. 2913.

1084.62 2927.

419.53 907.

29.76 2204.

938.3 2820.

817. 614.

221. 685.

7.3 59.

157.36 153.22

39.31 688.

777. 1382.

1526. 3345.

1855. 4409.

2477. 4744.

2623. 4639.2157. 4265.

2334. 4150.

1964. 3695.

1554.9 2963.

961.78 2162.

321.07 767.

156.6 2072.

231.93 2602.

630.63 1587.

449.51 988.

113.7 184.3



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. .

28.44 671.

727. 1870.

920. 3464.

798. 3360.

931. 3290.

1021. 3.1 103

1.1 103 3.0 103

1072. 1803.

822. 1527.

1313. 3250.

1356. 3230.

1412. 2567.

1474. 2700.

1497. 2868.

1545. 1950.

819. 1196.

1663. 3402.

2233. 4603.

3017. 5458.

3422. 5555.

3186. 5596.

3033. 5012.

2466. 4428.

1768.3 3825.

1064.18 2856.

38.83 356.73

304. 1473.

327.46 1749.

271.3 1564.

254. 962.

302.

71. 61.7

7.0 102

1737.1050. 3200.

1750. 4820.

1572. 4000.

1135. 3927.

644. 4.0 103

640. 3230.

1176. 2011.

1345. 3110.

1050.

900.

860.



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1527.

827.

827.

1627.

Creating a Dynamic Interactive Manipulative to Huge Data Set

ManipulateplotTypeTable

ElementDataz, prop1, ElementDataz, prop2, z, 1, 118,plotType, ListPlot, ListLinePlot,

ListLogPlot, ListLogLinearPlot,prop1, ElementData"Properties",prop2, ElementData"Properties"



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plotType ListPlot ListLinePlot ListLogPlot ListLogLinearPlot

prop1 AtomicNumber

prop2 AtomicRadius

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Capabilities - Only the Beginning

Plot the closing prices for Google stock since its initial public offering on August 19, 2004.

DateListPlotTooltipFinancialData"GOOG", "August 19 2004", Joined True

2005 2006 2007 2008 2009 2010

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This creates a plot comparing the closing stock price over the year 2006 for three companies: General Electric, Akamai, and

Microsoft.



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DateListPlotTooltipFinancialData"GE", "2006", FinancialData"AKAM", "2006",

FinancialData"MSFT", "2006", Joined True

2006 2007 2008 2009 2010

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AstronomicalData"Earth", "Image"

TooltipAstronomicalData, "Image",AstronomicalData, "Name" & AstronomicalData"Planet"

Make a graphic of solar system orbit paths with tooltips displaying images of each planet.



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Graphics3DLightGray, TooltipAstronomicalData, "OrbitPath",AstronomicalData, "Image" &

AstronomicalData"Planet", Background Black

Varying distance of planets from Earth in 2009:

AstronomicalData"Earth", "Distance", "Units"Meters

DateListPlotTooltipTableDateList2009, 1, i, AstronomicalData,

"Distance", DateList2009, 1, i, i, 1, 365.25, 10, & "Mercury", "Venus", "Mars", "Jupiter", "Saturn",

Joined True, GridLines Automatic

Jan Apr Jul Oct Jan

0

5.0 1011

1.0 1012

1.5 1012



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ProteinData"SP1", "MoleculePlot"

Import a PDB file.

Import"ExampleData1PPT.pdb"Import a PDB file by setting various options.

Import"ExampleData1PPT.pdb", "PDB", Background GrayLevel0.15,ImageSize Medium, "Rendering" "Wireframe"

Get the title of this PDB file.

Import"ExampleData1PPT.pdb", "PDB", "Title"XRAY ANALYSIS 1.4ANGSTROMS RESOLUTION OF

AVIAN PANCREATIC POLYPEPTIDE. SMALL GLOBULARPROTEIN HORMONE

Get the name of the organism referenced in this file.

Import"ExampleData1PPT.pdb","PDB", "Organism", "DepositionDate"

MOL_ID 1, ORGANISM_SCIENTIFIC MELEAGRIS GALLOPAVO, 1981, 1, 16, 0, 0, 0.

Import the residue sequence.

Import"ExampleData1PPT.pdb", "Residues" Gly Pro Ser Gln Pro Thr Tyr Pro Gly Asp Asp Ala Pro Val Glu Asp Leu Ile Arg Phe Tyr Asp Asn Leu Gln Gl

Import a 3D molecule model as a ball-and-stick model.

Import"ExampleDataaspirin.mol"

Show the bonds of the same molecule using spacefilling rendering.

Import"ExampleDataaspirin.mol", "Rendering" "Spacefilling"



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Import a 3D molecule model as a wireframe model.

Import"ExampleDataaspirin.mol", "Rendering" "Wireframe"

When importing a molfile that contains a 2 D representation of a molecule, Mathematica automatically renders it as a

chemical structure diagram.

Import "ExampleDatafluoxetine.mol"

This gives the atom types and their 2D coordinates for the structure diagram.

Import"ExampleDatafluoxetine.mol","VertexTypes", "VertexCoordinates"

C C O C C C C

98.28, 75.86 98.28, 7.24 25.86, 117.59 170.69, 117.59 171.03, 48.97 26.21, 48.97 46.21, 75.86 242.4

This creates a molfile from the previous output.

molstr

ExportString , "MOL", "VertexTypes", "VertexCoordinates"



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Created by Wolfram Mathematica 7.0 : www.wolfram.com

22 0 0 0 0 999 V2000

0.9828 0.7586 0.0000 C 0 0 0 0 0 0 0 0 0

0.9828 0.0724 0.0000 C 0 0 0 0 0 0 0 0 0

0.2586 1.1759 0.0000 O 0 0 0 0 0 0 0 0 0

1.7069 1.1759 0.0000 C 0 0 0 0 0 0 0 0 0

1.7103 0.4897 0.0000 C 0 0 0 0 0 0 0 0 0

0.2621 0.4897 0.0000 C 0 0 0 0 0 0 0 0 0

0.4621 0.7586 0.0000 C 0 0 0 0 0 0 0 0 0

2.4241 0.7621 0.0000 C 0 0 0 0 0 0 0 0 0

1.7103 1.3241 0.0000 C 0 0 0 0 0 0 0 0 0

0.2621 1.3241 0.0000 C 0 0 0 0 0 0 0 0 0

0.4621 0.0724 0.0000 C 0 0 0 0 0 0 0 0 0

1.1828 1.1759 0.0000 C 0 0 0 0 0 0 0 0 0

3.1483 1.1793 0.0000 N 0 0 0 0 0 0 0 0 0

0.9828 1.7414 0.0000 C 0 0 0 0 0 0 0 0 0

1.1793 0.4897 0.0000 C 0 0 0 0 0 0 0 0 0

1.9035 0.7586 0.0000 C 0 0 0 0 0 0 0 0 0

3.8690 0.7621 0.0000 C 0 0 0 0 0 0 0 0 0

1.9035 0.0759 0.0000 C 0 0 0 0 0 0 0 0 0

2.6241 0.4931 0.0000 C 0 0 0 0 0 0 0 0 0

3.4000 0.8690 0.0000 F 0 0 0 0 0 0 0 0 0

2.9724 0.0966 0.0000 F 0 0 0 0 0 0 0 0 0

2.2172 1.1621 0.0000 F 0 0 0 0 0 0 0 0 0

M END



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ImportStringmolstr, "MOL", "VertexTypes"C, C, O, C, C, C, C, C, C, C, C, C, N, C, C, C, C, C, C, F, F, F

ImportStringmolstr, "MOL", "VertexCoordinates"98.28 75.86

98.28 7.24

25.86 117.59

170.69 117.59

171.03 48.97

26.21 48.97

46.21 75.86

242.41 76.21

171.03 132.41

26.21 132.41

46.21 7.24

118.28 117.59

314.83 117.93

98.28 174.14

117.93 48.97

190.35 75.86

386.9 76.21

190.35 7.59

262.41 49.31

340. 86.9

297.24 9.66

221.72 116.21

Initializations

sizeImageNotebook 200;
