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LC.Charts
WARNING: LC.Charts v2.5.0.0 requires APL+Win v15.0+

LC.Charts is a freeware for APL+Win Users who are current with their subscription; it allows them to easily and instantly display their APL variables in various types of charts. The license allows any use of LC.Charts: you can even include LC.Charts as part of software you sell: the only restriction is that you are not allowed to sell LC.Charts as such.

Download LC.Charts (7834 Kb) New version 2.5.0.0! (see What's New in this version)

See Sample beautiful math charts created with LC.Charts

Scroll down to see a number of sample charts!

LC.Charts includes:

  • a C# ActiveX DLL (LC.Charts.dll)
  • a User Command file LCCharts.sf including a ]chart User Command

Description

LC.Charts can be used as an ActiveX from APL programs with ⎕wi or through the use of the delivered ]chart user command.
The idea is to make it ultra simple to display APL data in nice charts.

LC.Charts main characteristics are:

  • it is extremely easy to use (i.e. ]chart myVariable)
  • it can be used from any workspace even a clear workspace
  • it is phenomenally fast (draws a scatter plot with 100000 points in 300 milliseconds!)
  • the ]chart command includes 19 options for customization
  • the ActiveX includes 31 properties and 3 methods
  • it supports a crosshair cursor
  • is supports log scale on the Y-axis
  • it supports multiple successive zooms without performance degradation
  • it supports mouse wheel zooming
  • it supports panning
  • it supports copying the chart to the Clipboard and pasting in Emails, Word, etc.
  • it supports saving the image to various formats (png, emf,gif, jpg, tiff, bmp)
  • it supports printing the chart
  • it resizes nicely and smoothly as the form is resized

Requirements

  • .Net Framework 4.0+
  • APL+Win v15.0+

Installation

  1. Click the above Download LC.Charts button to download LCChartsSetup.zip
  2. Unzip the LCChartsSetup.zip file in any folder
  3. Exit all versions of APL+Win loaded on your system (in case you were using a former version of LC.Charts in one of these Sessions)
  4. Right click LCChartsSetup.exe, select Properties and if you see an Unblock button at the bottom right of the Properties window, click it!
  5. Right click LCChartsSetup.exe and select Run as Administrator
    Answer the various installation prompts to install LC.Charts on your system.
  6. When done, load APL and use the following command to set up the LCCharts.sf as your top level User Command file:
         ]ufile {path}\LCCharts
    replacing {path} by the full path name of the folder where you installed LC.Charts
    So, if you installed LC.Charts in the C:\APLWIN15\LCCHARTS folder, you need to use the following command:
         ]ufile C:\APLWIN15\LCCHARTS\LCCharts
    The first LCCHARTS is the folder name and the second one is the User Command File name.

Note: if your User Command Processor is set to use case sensitive commands, you can either:

  • either use ]CHART instead of ]chart
  • or load the TOOLS\UCMDUTIL APL+Win delivered workspace and run CASELESSCMDS function

Important Note:

LC.Charts is delivered as a DLL and a User Command file called LCCHARTS.SF. You should set this file as your top level User Command file.

There is now also a workspace called LCCHARTS.W3 delivered in APL+Win v15.0 format.

It is also highly recommended to read the Getting Started with LC.Charts.doc documentation.

Using LC.Charts with the ]chart3d user command

You can use the ]chart user command from any workspace to produce 3D charts from your APL variables, even from an empty clear workspace

Its syntax is:

      ]chart3d data {/bm=} {/caption=} {/chartcolors=} {/chartsymbols} {/charttypes} {/legend=} {/lm=} {/reflect=} {/risers=} {/rm=} {/spin=} 
              {/symbol=} {/symbolsize=} {/ss} {/title=} {/tm=} {/topmost} {/tr} {/type=} {/version} {/vp=} {/xangle=}
              {/xlabels=} {/xmajstep=} {/xmax=} {/xmin=}
              {/ylabels=} {/ymajstep=} {/ymax=} {/ymin=}
              {/zmajstep=} {/zmax=} {/zmin=}

data must be a vector of numeric vectors.

Here is an example:

      ]chart3d ?6⍴⊂⌽50+10×⍳10 /ty=tower /ti=3D-Tower
tower chart

LC.Charts includes 10 different types of 3D charts.

3D charts can be animated and rotated using the ]spinit user command.

Look at this page for more 3D chart examples.

Using LC.Charts with the ]chart user command

You can use the ]chart user command from any workspace, even an empty clear workspace

Its syntax is:

      ]chart data {/adp} {/caption} {/cf} {/chartcolors=} {/chc} {/legend=} {/pl} {/plangle=} {/plformat=} 
            {/smooth=} {/snofill} {/symb=} {/ssize=} {/title=} {/topmost} {/tr} {/type=} {/version}
            {/xangle=}  {/xmajstep=}{/xmin=} {/xminstep=} {/xmax=} {/xtitle=} {/xtype=}
            {/yangle=} {/ymajstep=} {/ymin=} {/yminstep=} {/ymax=} {/ytitle=} {/ytype=} 
            {/overlay} {/reflect}

data can be an APL variable or an APL expression

Here are some examples (scroll to the bottom of these page to see the corresponding charts):

      ⍝ Draw ?20⍴20
      ]chart ?20⍴20

      ⍝ Same chart with a title and point labels with a 30∘ angle
      ]chart aaa←?20⍴20 /pl /pla=30 /ti=Random Numbers

      ⍝ Same chart with point symbols with a symbol size of 12
      ]chart aaa /pl /pla=30 /ti=Random Numbers /symb=circle /ss=12

      ⍝ Same thing but with more options and a smoothed curve (using a tension of .5)
      ]chart aaa /pl /pla=30 /ymin=0 /xmax=21 /ymax=22 /sy=square /ti=Random Numbers Smoothed /sm=.5

      ⍝ Same thing but with more options and a smoothed curve (using a tension of .9)
      ]chart aaa /pl /pla=30 /ymin=0 /xmax=21 /ymax=22 /sy=square /ti=Random Numbers Smoothed /sm=.9

      ⍝ Draw the content of variable aaa
      aaa←1○.01×⍳1000
      ]chart aaa 

      ⍝ Draw real life data contained in APL matrix SampleData1
      ]chart SampleData1

      ⍝ Same chart with a CrossHair Cursor
      ]chart SampleData1 /chc

You can use the ]chart user command detailed documentation by typing:

      ]chart?
]chart /chartaxistypes
]chart /chartcolors
]chart /chartsymbols
]chart /charttypes
]chart /properties
]chart /methods
]chart /doc=
]chart /version
]chart data {/adp} {/caption} {/cf} {/chartcolors=} {/chc} {/legend=} {/pl} {/plangle=} {/plformat=} 
            {/smooth=} {/snofill} {/symb=} {/ssize=} {/title=} {/topmost} {/tr} {/type=} {/version}
            {/xangle=}  {/xmajstep=}{/xmin=} {/xminstep=} {/xmax=} {/xtitle=} {/xtype=}
            {/yangle=} {/ymajstep=} {/ymin=} {/yminstep=} {/ymax=} {/ytitle=} {/ytype=} 
            {/overlay} {/reflect}

⎕wi property        /option         /option abbrev  Description
¯¯¯¯¯¯¯¯¯¯¯¯        ¯¯¯¯¯¯¯         ¯¯¯¯¯¯¯¯¯¯¯¯¯¯  ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
                    /chartaxistypes /charta         Return the possible X-Axis or Y-axis scale types
                    /chartcolors=   /chartc=        Get or set the 22 colors used by LC.CHarts
                    /chartsymbols   /charts         Return the possible point symbols you can use
                    /charttypes     /chartt         Return the possible chart types you can use
                    /doc=           /doc=           Return the documentation for a given property (example: /doc=xSymbol)
                    /methods        /m              Return the LC.Charts available methods
                    /properties     /pr             Return the LC.Charts available properties
                    /tr             /tr             Displays the chart form topmost and at top right of the screen 
                    /version        /v              Return the LC.Charts.dll version number

xAllowDragPoint     /adp            /adp            Allow dragging points and point labels
xCaption            /caption=       /ca=            Set the LC.Charts Form caption
xCurveFill          /cf=            /cf=            Set the curve fill factor (¯99 to 99)
xCrossHairCursor    /chc            /chc            Make the CrossHair Cursor visible
xLegend             /legend=        /le=            Set the legend (comma separated string)         
xOverlay            /overlay        /o              Allows to overlay a chart on another chart
xPointLabels        /pl             /pl             Make the point labels visible (for scatter and curve)
xPointLabelsAngle   /plangle=       /pla=           Set the point labels angle
xPointLabelsFormat  /plformat=      /plf=           Set the point labels format using a .Net format string
                                                    (check: http://www.cheat-sheets.org/saved-copy/msnet-formatting-strings.pdf)
xReflect            /reflect        /r              Sets the xReflect property to 1 so that property changes are immediately reflected on the chart
xSmooth             /smooth=        /sm=            Set the smooth tension factor (0=no smoothing, 1=maximum smoothing)
xSymbol             /symb=          /sy=            Point symbol (one of:      
                                                    circle, default, diamond, hdash, none, plus, square, star, triangle, triangledown, vdash or xcross)
xSymbolFill         /snofill        /sn             Do not fill point symbols
xSymbolSize         /ssize=         /ss=            Set the symbol size (default is 8)          
xTitle              /title=         /ti=            Chart title
xTopMost            /topmost        /to             Forces the chart window to be topmost
xType               /type=          /ty=            Sets the chart type (one of: bar, curve, pie, scatter)
xXAngle             /xangle=        /xa=            Set the X-labels angle (0 to 360)
xXMajorStep         /xmajstep=      /xmaj=          Set the X-Axis major step value
xXMax               /xmax=          /xmax=          Set the X-Axis maximum value
xXMin               /xmin=          /xmin=          Set the X-Axis minimum value
xXMinorStep         /xminstep=      /xmins=         Set the X-Axis minor tickmark step value
xXAxisTitle         /xtitle=        /xti=           Set the X-Axis title
xXAxisType          /xtype=         /xty=           Set the X-Axis scale type (linear, log)
xYAngle             /yangle=        /ya=            Set the Y-labels angle (0 to 360)
xYMajorStep         /ymajstep=      /ymaj=          Set the Y-Axis major tickmarck step value
xYMax               /ymax=          /ymax=          Set the Y-Axis maximum value
xYMin               /ymin=          /ymin=          Set the Y-Axis minimum value
xYMinorStep         /yminstep=      /ymins=         Set the Y-Axis minor tickmarck step value
xYAxisTitle         /ytitle=        /yti=           Set the Y-Axis title
xYAxisType          /ytype=         /yty=           Set the Y-Axis scale type (linear, log)

Notes:
1. You must supply a value for options with are ending with = above
2. The chart title, x-axis title, y-axis title and legend are not shown by default
3. Set the chart title, x-axis title and/or y-axis title to a non empty string to show them
4. Set the /symb= option to one of the possible symbol types to display point symbols
5. Use:  /pl  to display point labels
6. Use:  /sn  to not fill point symbols
7. For pie charts, the supplied data must be a 2-element nested vector with [1]=numeric vector [2]=string vector
8. You can prefix any option value with ⍎ to instruct ]chart to execute the option value
   Example:
   legend←'France,USA'
   ]chart 20 3⍴⍳100 /le=⍎legend

Note: this User Command requires the LC.Charts.dll C# ActiveX DLL to have been propertly registered

Example:
    ]chart 1○.1×⍳10000 /xmin=0 /xmax=1000
    ]chart ?20⍴20 /ty=bar
    ]chart (10 20 30)('Oranges' 'Bananas' 'Lemons') /ty=pie
    aaa←20 3⍴0
    aaa[;1]←⍳20
    aaa[;2]←((⍳20)*.5)+.1ׯ6+?20⍴6
    aaa[;3]←⌽((⍳20)*.5)+.1ׯ6+?20⍴6
    ]chart aaa /pl /pla=0 /plf=G3 /xmax=21 /sy=square /ss=10 /ti=My Sample Chart

And, of course, you can use the ]chart user command under program control using ⎕ucmd']chart ...'

Using LC.Charts as an ActiveX object

You first need to create an instance of the ActiveX object:

      'ff'⎕wi'*Create' 'LC.Charts.Chart'
ff

The C# chart form is not shown by default.

You can then simply use the xData property to send the data you want to plot and use the XShow method to display the form:

      ]uload SampleData1

      'ff'⎕wi'*xData'SampleData1
      'ff'⎕wi'*XShow'
Charting an APL matrix variable

So this is very simple.

Of course, you could also have set a number of properties before calling the XShow method to customize your chart (not that, if you set properties after the xData property, you need to call the XRedraw method for your changes to be taken in account):

      'ff'⎕wi'*xCaption' 'Charting my SampleData1 APL Matrix'
      'ff'⎕wi'*xLegend' 'Curve 1' 'Curve 2' 'Curve 3'
      'ff'⎕wi'*xLegendVisible'1
      'ff'⎕wi'*xXMax'4
      'ff'⎕wi'*xYMax'1.1
      'ff'⎕wi'*xCrossHairCursor'1
      'ff'⎕wi'*XRedraw'
Customizing an already drawn chart

The available properties, methods and events are:

      100 TELPRINT⊃'ff'⎕wi'*properties'
apldata       properties        xLegendBorder       xTitleFont         xY2AxisMagAuto
children      self              xLegendFont         xTitleVisible      xY2AxisTitle
class         state             xLegendPosition     xTopMost           xY2AxisTitleFont
clsid         suppress          xLegendPositions    xType              xY2MajorStep
data          unicodebstr       xLegendVisible      xUseY2Axis         xY2Max
def           version           xLineColor          xVersion           xY2Min
description   xAllowDragPoint   xLineStyle          xWhere             xY2MinorStep
errorcode     xAllowZoom        xLineStyles         xXAngle            xYAngle
errormessage  xAxisColor        xLineWidth          xXAxisFormat       xYAxisAtX
events        xCaption          xMagAuto            xXAxisLabelsFont   xYAxisFormat
instance      xChartAxisTypes   xOutsideColor       xXAxisMagAuto      xYAxisLabelsFont
interface     xChartColors      xOverlay            xXAxisTitle        xYAxisMagAuto
links         xChartSymbols     xPointLabels        xXAxisTitleFont    xYAxisTitle
methods       xChartTypes       xPointLabelsAngle   xXAxisType         xYAxisTitleFont
modified      xCrossHairCursor  xPointLabelsFormat  xXMajorStep        xYAxisType
modifystop    xCurveFill        xReflect            xXMax              xYMajorStep
name          xData             xSmooth             xXMin              xYMax
obj           xFontsScaled      xSymbol             xXMinorStep        xYMin
opened        xHandle           xSymbolFill         xXTitleVisible     xYMinorStep
pending       xInsideColor      xSymbolSize         xY2AxisFormat      xYTitleVisible
progid        xLegend           xTitle              xY2AxisLabelsFont

      100 TELPRINT⊃'ff'⎕wi'*methods'
Close      Send                 XEuroDollarRates       XSmoothDoc        XXMajorStepDoc
Create     Set                  XGetScalingFactor      XSymbolDoc        XXMaxDoc
Defer      SetLinks             XHandleDoc             XSymbolFillDoc    XXMinDoc
Delete     XAddText             XLegendDoc             XSymbolSizeDoc    XXMinorStepDoc
EnumEnd    XAllowDragPointDoc   XLegendVisibleDoc      XTitleDoc         XXTitleVisibleDoc
EnumNext   XCaptionDoc          XLocalizeTo            XTitleVisibleDoc  XYAngleDoc
EnumStart  XChartAxisTypesDoc   XLocalizeToDoc         XTopMostDoc       XYAxisAtXDoc
Event      XChartColorsDoc      XOverlayDoc            XTypeDoc          XYAxisTitleDoc
Exec       XChartSymbolsDoc     XPointLabelsAngleDoc   XVersionDoc       XYAxisTypeDoc
Info       XChartTypesDoc       XPointLabelsDoc        XWait             XYMaxDoc
Modify     XClose               XPointLabelsFormatDoc  XWhereDoc         XYMinDoc
New        XCrossHairCursorDoc  XRedraw                XXAngleDoc        XYTitleVisibleDoc
Open       XCurveFillDoc        XReflectDoc            XXAxisTitleDoc
Ref        XDataDoc             XShow                  XXAxisTypeDoc

     100 TELPRINT⊃'ff'⎕wi'*events'
Action  Close  Delete  Modified  Open  Reopen  Send

Recommended Use

It is recommended that you use LC.Charts with the ]chart user command rather than as an ActiveX.

The main reason is that there is much less to type to get your chart on the screen as you want it when using ]chart than when using the ActiveX.

However, to keep the ]chart simple enough, not all the LC.Charts properties have been added as ]chart command options. And over time more properties and methods may be added to the ActiveX and probably not to the ]chart command to keep it simple.

Examples

Here are a series of examples, using LC.Charts:

Simple chart of an APL matrix variable

      SampleData3←30 3⍴0
      SampleData3[;1]←⍳30
      SampleData3[;2]←(⍳30)+.1×?30⍴40
      SampleData3[;3]←⌽(⍳30)+.1×?30⍴40

      ]chart SampleData3
Simple chart of an APL matrix variable

Adding point symbols (may use: circle, default, square, diamond, hdash, none, plus, square, star, triangle, triangledown, vdash or xcross):

      ]chart SampleData3 /sy=square
Chart with point symbols

Setting the point symbol size

      ]chart SampleData3 /sy=circle /ss=6
Chart with point symbols

Smoothing the curves

      ]chart SampleData3 /sy=circle /ss=6 /sm=.5
Smoothing the curves

Using different smoothing tensions (choose between 0=no tension and 1=maximum tension):

      ]chart SampleData3 /sy=circle /ss=6 /sm=1
Using different smoothing tension

Adding point labels

      ]chart SampleData3 /sy=circle /pl
Adding point labels

Changing point label orientation (any angle between 0 and 360) and format (use .Net Framework number formats)

      ]chart SampleData3 /sy=triangle /pl /pla=90 /plf=#.0
Changing point label orientation and format

Changing the X-Axis and Y-Axis maximum values

      ]chart SampleData3 /sy=triangle /pl /pla=90 /plf=#.0 /lv /xmax=31 /ymax=40
Changing the X-Axis and Y-Axis maximum values

You can also change the X-Axis and Y-Axis minimym values with /xmin= and /ymin=

Draw a pie chart

      ]chart (10 20 30 40)('Oranges' 'Bananas' 'Apples' 'Lemons') /ty=pie /lv
Draw a pie chart

For pie charts, you need to supply a 2-element nested vector with the values and the labels. The /lv option means: make the legend visible.

Draw a bar chart

      ]chart ?20⍴20 /ty=bar
Draw a bar chart

/ty stands for type of chart.

Draw a side by side bar chart

      SampleData4←20 3⍴0
      SampleData4[;1]←⍳20 
      SampleData4[;2]←?20⍴100
      SampleData4[;3]←SampleData4[;2]+¯10+?20⍴20  ⍝ add noise

      ]chart SampleData4 /ty=bar /xmin=0 /xmax=21 /ymax=102
Draw a side by side bar chart

When supplying a APL matrix variable to the LC.Charts object for drawing, whether as a bar chart or a curve chart, your matrix must contain:

  • X-coordinates (abscissas) in the 1st column
  • Y-coordinates of the various bars or curves in the other columns.

Scatter plot with Point Labels

      ]uload SampleData5

      ]chart (SampleData5[;3 4])(SampleData5[;2]) /ty=scatter /pl /ss=5 /xmax=6 /ymax=140 /ti=Mortality vs Population Growth (2010) /yti=Mortality (under-5 per 1000) /xti=Population Growth (in %)
Scatter plot with Point Labels

Notes: data downloaded from http://data.worldbank.org/topic/climate-change
There seems to be a relation between Mortality under 5 per 1000 capita and the Population Growth!

Zooming more to explore low Population Growth and Low Mortality

Let's zoom in for more details

      ]chart (SampleData5[;3 4])(SampleData5[;2]) /ty=scatter /pl /ss=5 /xmax=6 /ymax=140 /ti=Mortality vs Population Growth (2010) /yti=Mortality (under-5 per 1000) /xti=Population Growth (in %)
Scatter plot with Point Labels

Zooming even more and using the context menu for maybe printing or copying to clipboard

      ]chart (SampleData5[;3 4])(SampleData5[;2]) /ty=scatter /pl /ss=5 /xmax=6 /ymax=140 /ti=Mortality vs Population Growth (2010) /yti=Mortality (under-5 per 1000) /xti=Population Growth (in %)
Scatter plot with Point Labels

More examples with real data and with more ]chart options

The delivered LCCHARTS.SF UCMD file includes some data downloaded from the World Bank.

      ]uload worlddata Countries DataItems WorldDataEvolution

      ⍝ The available data are:

      ]data
  1 Agricultural land (km2)                                        12 Electricity prod. coal based (% of total)
  2 Agricultural land (%)                                          13 Electricity prod. hydroelectric based (% of total)
  3 Population growth (annual %)                                   14 Electricity prod. natural gas based (% of total)
  4 Population (total)                                             15 Electricity prod. nuclear based (% of total)
  5 Urban population growth (annual %)                             16 Electricity prod. oil based (% of total)
  6 Urban population                                               17 Electricity prod. (kWh)
  7 Urban population (% of total)                                  18 Electricity prod. renewable sources (kWh)
  8 Cereal yield (kg/ha)                                           19 Electricity prod. renewable sources, not hydro (kWh)
  9 Population in cities > 1 million (% of total pop.)             20 Electricity prod. renewable sources, not hydro (% of total)
 10 Mortality rate under-5 (per 1000 live births)                  21 Energy use (kt of oil equivalent)
 11 GDP (current US$)                                              22 Energy use (kg of oil equivalent per capita)

      ⍝ The available countries are:

      ]countries
  1 Australia          4 Switzerland        7 Finland           10 Greece            13 Japan             16 Sweden
  2 Austria            5 Denmark            8 France            11 Ireland           14 Netherlands       17 Turkey
  3 Canada             6 Spain              9 United Kingdom    12 Italy             15 Portugal          18 United States

      ⍝ The WorldDataEvolution function extracts data from the <worlddata>
      ⍝ variable and structure it so that it can be plotted with ]chart
      ⍝ The left argument is an <data> number
      ⍝ The right argument is one or more <country> numbers

      ⍴10 WorldDataEvolution 3 8 10 16 17 18
52 7

      5↑[1]10 WorldDataEvolution 3 8 10 16 17 18
 Mortality rate under-5 (per 1000 live births) Canada France Greece Sweden Turkey United States
                                          1962   30.5   25.7   52.7   18.6  239.6          28.9
                                          1963   29.4   24.5   51.1   17.9  232.3          28.3
                                          1964   28.2   23.4   49.4   17.1  225.3          27.7
                                          1965   27.1   22.3   47.7   16.3  218.5          27.1
      ...       

So let's draw some charts

      data←10 WorldDataEvolution 3 8 10 16 17 18
      legend←Countries[3 8 10 16 17 18]
      legend
 Canada France Greece Sweden Turkey United States

      ]chart 1 0↓data /le=⍎legend /ti=⍎⎕first data[1;1] /sy=square /ss=5 /xa=30 /xmaj=1
Mortality under 5 since 1962

Note the use of the ⍎ prefix in some options: it allows you to get the option value by excuting some APL expression. This makes the ]chart command very flexible and dynamic.

In this chart we used a point symbol of square a point symbol size of 5 pixels, an X-Axis labels angle of 30° and an X-Axis major tick step of 1. Note that the ]chart command chooses by itself what labels to display on the X-Axis.

For example, if we make the chart wider, we get:

Mortality under 5 since 1962

and if we make it narrower:

Mortality under 5 since 1962

At any time you can query the available choices for some properties:

      ]chart /chartsymbols
 circle default diamond hdash none plus square star triangle triangledown vdash xcross

      ]chart /charttypes
 bar curve pie scatter

      ]chart /chartaxistypes
 date dateasordinal exponent linear linearasordinal log ordinal text

      ]chart /chartcolors
 0 0 255  255 0 0  0 255 0  0 0 43  255 26 184  255 211 0  0 87 0  131 131 255  158 79 70  0 255 193  0 131 149  0 0 123  149 211 79  246 158 219  211 17 255  123 26 105
       246 17 96  255 193 131  35 35 8  140 167 123  246 131 8  131 114 0

Animated Graphics

It is easily possible to create animated graphics: it is a perfect way to see how data changes over time.

The WorldDataAnimation function in the LCCHARTS User Command file can do that.

Let's plot 2 data variables against each other and see their evolution from 1962 to 2012:

      ]uload WorldDataAnimation

      ⎕vr'WorldDataAnimation'
    ∇ items WorldDataAnimation countries;allcountries;bool;dataItems;data1;data2;i;x;y;z;⎕io
[1]   ⍝∇ items WorldDataAnimation countries -- Shows an animation of world cross data evolution from 1961 to 2012
[2]   ⍝∇ items ←→ an integer scalar (see ]data to see possible choices)
[3]   ⍝∇ countries ←→ '' for a selection of 11 countries
[4]   ⍝∇           or a vector of country numbers (see ]countries to see possible choices)
[5]   ⍝∇ Requires: (F) Countries DataItems
[6]   ⍝∇           (V) worlddata (source: data downloaded from http://data.worldbank.org/topic/climate-change)
[7]   ⍝∇ ELE6jan15
[8]
[9]   ⎕io←1
[10]  dataItems←DataItems[items]
[11]  allcountries←Countries
[12]  :if 0∊⍴countries ⋄ countries←1 3 5 6 8 9 10 13 16 17 18 ⋄ :endif
[13]  bool←1,(⍳⍴allcountries)∊countries
[14]  (data1 data2)←⊂[2 3]bool/[2]worlddata[items;;]
[15]
[16]  z←'ff'⎕wi'*Create' 'LC.Charts.Chart'
[17]  z←'ff'⎕wi'*XShow'
[18]  z←'ff'⎕wi'*xXMin'(⌊/,1 0↓0 1↓0 ¯2↓data1)
[19]  z←'ff'⎕wi'*xXMax'(1.1×⌈/,1 0↓0 1↓0 ¯2↓data1)
[20]  z←'ff'⎕wi'*xYMin'(⌊/,1 0↓0 1↓0 ¯2↓data2)
[21]  z←'ff'⎕wi'*xYMax'(1.05×⌈/,1 0↓0 1↓0 ¯2↓data2)
[22]  z←'ff'⎕wi'*xSymbol' 'square'
[23]  z←'ff'⎕wi'*xSymbolSize'8
[24]  z←'ff'⎕wi'*xType' 'scatter'
[25]  z←'ff'⎕wi'*xXAxisTitle'(1⊃dataItems)
[26]  z←'ff'⎕wi'*xYAxisTitle'(2⊃dataItems)
[27]  :for i :in 1↓¯2↓⍳2⊃⍴data1
[28]      x←1↓data1[;i]
[29]      y←1↓data2[;i]
[30]      z←'ff'⎕wi'*xData'(x,[1.5]y)(1↓data1[;1])
[31]      z←'ff'⎕wi'*xPointLabels'1
[32]      z←'ff'⎕wi'*xTitle'(⍕data1[1;i])
[33]      z←'ff'⎕wi'*XRedraw'
[34]      z←⎕dl.1
[35]  :endfor
[36]
    ∇

      ⍝ Plot 9=Population in Cities > 1 million (% of total population)
      ⍝ against 4=Population (total)

      9 4 WorldDataAnimation ''

I have captured 2 frames from the animation: state in year 1969 and state in 2012:

Cross Tab Animation of 2 Variables (year 1969) Cross Tab Animation of 2 Variables (year 2012)

Doing such animated graphs can teach a lot.

Needing little code to display spectacular charts

      ]uload Butterfly

      ⎕vr'Butterfly'
    ∇ Butterfly;t;v;x;y;In;To;⎕io
[1]   ⍝∇ Butterfly -- Draws a Butterly using LC.Charts.dll
[2]   ⍝∇ ELE3jan15
[3]   ⎕io←1
[4]   ⎕ucmd']uload In To /quiet'
[5]   t←0 To(21×○1)In 2000
[6]   v←((1○t÷12)*5)+(*2○t)-2×2○4×t
[7]   x←v×1○t
[8]   y←v×2○t
[9]   ⎕ucmd']chart x,[1.5]y /ti=Butterfly'
    ∇

      Butterfly
Draw a Butterfly with only maths!

The above Butterfly APL function uses some maths cartesian equation to draw this nice Butterly with LC.Charts.

Animated Charts

LC.Charts is so fast that you can animate a chart to show the evolution of one or more curves over time and the animation you get is perfectly fluid. The Lissajous APL function below demonstrates how to do this. Of course you won't see the animation on this Web page, but try it when you have downloaded LC.Charts. It is a suprisingly smooth animation!

      ]uload Lissajous

      ⎕vr'Lissajous'
    ∇ Lissajous n;a;b;c;i;n;t;x;y;z;In;To;d
[1]   ⍝∇ Lissajous n -- Demonstrates how to draw animated curves with LC.Charts
[2]   ⍝∇ ELE3jan15
[3]   ⎕ucmd']uload In To /quiet'
[4]   (c d)←n
[5]   t←0 To(2×○1)In 4000
[6]   a←1 To c In 400
[7]   b←1 To d In 400
[8]   z←'ff'⎕wi'*Create' 'LC.Charts.Chart'('*∆t't)('*xTitle' 'Lissajous Curve')('xXMin'¯1)('*xXMax'1)
[9]   z←'ff'⎕wi'*XShow'
[10]  :for i :in⍳⍴a
[11]      x←1○a[i]×t
[12]      y←1○b[i]×t
[13]      'ff'⎕wi'*xData'(x,[1.5]y)
[14]      z←⎕dl.01
[15]  :endfor
    ∇

      Lissajous 1 2
Animating a curve!
      Lissajous 3 4
Animating a curve!
      Lissajous 19 20
Animating a curve!

Enjoy and please Email me a copy of some of the charts you create with LC.Charts!