Interactive plots that explore themselves: axis folding and data grouping

30 minutes · For anyone who wants to use MathJet’s interactive visualization features. Basic plotting experience helps.

This is where MathJet’s visualization story stops sounding like every other charting library’s. Data grouping lets you drag along an axis to define value ranges — called axis data groups — that organize data points by their coordinate values. Each group carries a toggle button that switches it between “expanded” and “collapsed.” Axis folding is what happens when you collapse a group: the axis condenses, the group’s value range is removed from the display, all data points within it disappear, and the remaining data spreads out to fill the freed screen space — without filtering or modifying the underlying data. Create groups over sparse regions, collapse them, and the dense regions suddenly have room to breathe. These are patented MathJet capabilities, not styling on top of standard plot widgets. Along the way you’ll also see axis selection — dragging along an axis line to pick out every data point whose coordinate falls in the dragged range — the natural first step for creating a data group. By the end of the tutorial you’ll have used these features on a real dataset and seen structure you would have missed in a fixed-scale plot.

What you’ll learn

• How axis selection lets you drag along an axis line to select every data point whose coordinate in that dimension falls in the dragged range — a fast alternative to rectangle selection when you’re slicing by one variable, and the natural entry point for data grouping
• How to create an axis data group from an axis selection — a persistent, named value range on the axis with a marker line and a toggle button
• How collapsing an axis data group produces axis folding: the value range is removed from the axis, data points within it are hidden, and the remaining data spreads into the freed space — all without modifying the underlying data
• How axis data groups can be created on multiple axes and can form hierarchical structures when their value ranges overlap
• How collapsed groups handle null data points on line and surface graphs — with options for discontinuity, bridging, or overlapped display
• How to use selection in plots to drive downstream cell formulas (e.g., compute statistics on the selected subset only)

What you’ll need

• MathJet installed (download)
• Tutorial 1 completed, or basic familiarity with creating a plot in MathJet
• A dataset with a wide dynamic range. The provided measurements.csv works well. Bring your own if you have one with more dramatic scale variation — the bigger the gaps in the data, the more dramatic the folding effect.
• No prior knowledge of axis folding required — the tutorial introduces it from scratch

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Step 1: Load the sample data and create a scatter plot

Download measurements.csv and save it somewhere you’ll find it. The file has four columns — sample_id, condition, measurement_value, and timestamp — with one header row and 100 data rows.

Launch MathJet and insert a worksheet (File → New → Worksheet). Drag measurements.csv onto the worksheet — MathJet populates columns A through D.

Now create a scatter plot of measurement values over time. Select columns C and D (click the column-C header, drag across D), then insert a chart: Insert → Chart → Scatter Graph → 2D Scatter (or use the Insert Chart tool button and pick 2D Scatter Graph from the pane). A scatter plot appears inside the worksheet with timestamp on the x-axis and measurement_value on the y-axis. One hundred points spread across the chart area.

On a standard linear axis, the entire value range gets equal visual space — whether a region has twenty data points or zero. Sparse stretches waste screen area that could make dense clusters easier to read. This tutorial’s core workflow — select a range, group it, collapse it — fixes that.

Step 2: Select a value range with axis selection

Move the mouse cursor toward the y-axis line on the left side of the chart. As you approach the axis, a small axis selection icon appears next to the cursor, signaling that axis selection mode is active.

Click and drag along the y-axis, selecting a range of measurement values — try the range from roughly 25 to 65 (the dense middle band where most data points cluster). As you drag, a semi-transparent rectangle extends along the axis, and every data point whose y-coordinate falls within that range highlights dynamically. Markers at the top and bottom of the rectangle show the exact boundary values. Release the mouse button.

A context menu appears automatically after the selection. For now, click away from the menu to dismiss it — you’ll use it in the next step.

This is axis selection — a fast way to slice data by one dimension. Unlike rectangle selection (which selects by screen position), axis selection picks every point whose coordinate value in that axis dimension falls in the dragged range. The same gesture works on the x-axis: drag along the x-axis line to select all points within a time range.

Step 3: Create an axis data group

Repeat the axis selection from Step 2: drag along the y-axis to select a value range. This time, when the context menu appears, choose Create Axis Data Group.

An axis data group appears on the chart. It has two visual elements:

• A marker line parallel to the y-axis, spanning the group’s value range. Click this line to toggle the selection of all data points within the range.
• A toggle button at one end of the marker line. This is the expand/collapse control — the heart of axis folding.

The group is initially in the expanded state — all data points are visible, the axis is unmodified. Click the marker line to select or deselect the data points within the range. The group is persistent: it survives chart resizing, data updates, and workspace saves.

Step 4: Collapse the group — axis folding

Click the toggle button on the axis data group you just created.

The axis folds. Three things happen at once:

1. The group’s value range is removed from the axis. The y-axis tick labels skip directly from the value below the group’s range to the value above it — the intervening range is gone from the display.
2. All data points whose y-coordinates fall within the collapsed range disappear from the chart.
3. A dashed line appears at the fold point, marking where the axis was condensed.

The remaining data points — those above and below the collapsed range — spread out to fill the freed screen space. Points that were squeezed together at the extremes now have more room, making their structure easier to read.

Click the toggle button again. The group expands: the axis restores its full range, the hidden data points reappear, and the dashed line vanishes. This is purely a visual-layer operation — the data values in the worksheet haven’t changed, any formulas referencing them still compute the same results, and you can toggle back and forth freely.

How this differs from zooming and filtering. Zooming picks one scale and applies it everywhere — you see more detail in one region but lose the others entirely. Filtering removes data points from the visible set, which changes statistics and derived items. Axis folding does neither: it removes a value range from the axis while keeping the data intact. The hidden points aren’t filtered — they’re behind the fold, and one click brings them back.

Step 5: Create groups on multiple axes

The axis data group workflow is repeatable across any active chart axis. Try creating a second group, this time on the x-axis.

Drag along the x-axis to select a time range — pick a stretch in the middle where measurements are sparse. When the context menu appears, choose Create Axis Data Group. A marker line and toggle button appear on the x-axis.

Now collapse both groups (click both toggle buttons). The chart folds on two dimensions simultaneously: the y-axis skips the collapsed value range, the x-axis skips the collapsed time range, and only the data points outside both collapsed regions remain visible. The effect is dramatic — what was a sparse, hard-to-read cloud becomes a focused view of the data you care about.

Hierarchical groups. If you create a new axis data group whose value range overlaps an existing group on the same axis, MathJet automatically generates a child group for the intersecting range. The result is a hierarchy: the parent group spans the full original range, and the child group spans only the overlap. Each has its own toggle button, so you can collapse the parent (hiding everything in its range) or just the child (hiding only the overlap). FIG. 2D in the patent drawings illustrates this with groups on both X and Y axes.

Step 6: Handling collapsed data in line graphs

Axis folding on scatter plots is straightforward — collapsed data points simply disappear. On line graphs, collapsing a group introduces a subtlety: the hidden data points create a gap in the connected line. MathJet calls these null data points and offers three ways to handle them.

To see this in action, create a line graph from the same data (or switch the scatter plot to a line graph via Plot → Graph Type). Create an axis data group on the x-axis that covers a range in the middle of the timeline, then collapse it.

The three handling options (accessible via the group’s context menu or properties) are:

1. Treat as missing (default) — null data points are considered absent. The line is interrupted at both edges of the collapsed range, creating a visible discontinuity. This makes the fold obvious.
2. Connect across the gap — the line segments immediately before and after the collapsed range are connected with a straight line, bridging the gap for visual continuity. The fold is marked by the dashed line on the axis, but the graph line itself is unbroken.
3. Show as overlapped — the null data points and their connecting line segments are displayed at their original positions, overlapping with the axis fold. This preserves the full original line shape even in the collapsed state, at the cost of visual clutter at the fold boundary.

The same three options apply to surface graphs in 3D charts — axis data groups and axis folding work on all three axes of a 3D Cartesian coordinate system.

Step 7: Explore data in the Graph Companion

Open the Graph Companion window: View → Graph Companion or the corresponding toolbar button. A spreadsheet-style table appears showing the numerical values behind every graph in the chart.

Click a data point in the chart. The corresponding row in the Graph Companion table highlights — and the table auto-scrolls to bring it into view if it was off-screen. Now try the reverse: click a cell in the Graph Companion table, and the matching data point highlights on the chart. This is bidirectional selection sync — the chart and the table are two views of the same data, always in agreement.

Click the marker line of an axis data group to select all data points in that group’s range. The Graph Companion highlights every corresponding row at once — useful for scanning the numerical values of the data you’re about to fold away (or keep).

Try using the Filter text box at the top of the Graph Companion window. Type a value range — the matching rows highlight in both the table and the chart.

Step 8: Drive a worksheet formula from a chart selection

The interactive features you’ve been using aren’t just for looking at data — they can feed computation. Here’s a concrete example: computing statistics on only the data points currently selected in the chart.

Use axis selection (drag along the y-axis) to select a value range. The selected points highlight on the chart. Now click a cell in the worksheet — say F1 — and type a label like Selected Mean. In F2, enter a formula that references the selection. The key insight is that MathJet’s selection state is accessible to the formula engine: the chart selection defines which data points are active, and aggregate functions respect that scope.

Edit a few data values in column C (measurement_value) while the selection is active. The formula in F2 updates to reflect the new values — limited to the selected subset. Change the chart selection by dragging a different range, and F2 recomputes again.

This is the payoff of MathJet’s fused architecture: chart interaction, cell formulas, and the data store all share state. A selection made with the mouse on the chart is not a separate concept from a range reference in a formula — they compose.

What you’ve learned

• Axis selection slices data by dragging along an axis line — faster than rectangle selection when you’re working with one dimension, and the natural first step for creating axis data groups.
• Axis data groups define a named value range on an axis, marked by a line parallel to the axis and a toggle button. Clicking the marker line selects or deselects data points in the range.
• Axis folding is what happens when you collapse an axis data group: the value range is removed from the axis, data points within it are hidden, a dashed line marks the fold, and the remaining data spreads to fill the freed space. Click again to expand — a patented MathJet capability.
• Groups can be created on multiple axes and can form hierarchical structures when their value ranges overlap — parent groups contain child groups for the intersecting ranges.
• On line and surface graphs, null data points in collapsed groups can be treated as missing (discontinuity), connected across the gap, or shown overlapped — three options for different analytical needs.
• The Graph Companion window provides bidirectional selection sync between a spreadsheet-style table and the chart, with integrated filtering.
• Chart selections can drive worksheet formulas, closing the loop between visual exploration and computation.

Next steps

The interactive features in this tutorial compose naturally with the analytics covered in Tutorial 7: Graph analytics — characteristics and dependent graphs. Graph characteristics tables update when you change a selection or apply a filter; curve fits recalculate when the visible data changes. If you want to analyze the structure you just uncovered, that’s the next tutorial.

For the full reference on every selection method (polygonal, freeform, axis, Quick Find), see the Selecting reference. For filtering operations that complement axis folding, see the Filtering reference.

Troubleshooting

The axis selection icon doesn’t appear when I move the cursor near the axis. Make sure the chart has focus (click inside the chart area first). The axis selection icon appears when the cursor is close to the axis line itself — not the tick labels or the plot area. Move the cursor slowly toward the axis line and watch for the icon to appear.

Collapsing a group doesn’t seem to change the chart. Collapsing a group removes its value range from the axis and hides data points within it. If the group’s range contains no data points (e.g., you selected an empty region of the axis), collapsing it still condenses the axis but no points disappear — the visual effect may be subtle. For the most dramatic result, create a group over a range that contains data points, then collapse it.

I created overlapping groups and now there are extra child groups. When a new axis data group’s range overlaps an existing group, MathJet automatically creates a child group for the intersection. This is intentional — it lets you collapse the overlap independently. If you didn’t want the hierarchy, undo (Ctrl+Z) and create the new group with a non-overlapping range, or delete the unwanted child group.

Graph Companion window is empty. The Graph Companion shows data for the most recently clicked chart. Click inside the chart to make it active, and the Graph Companion will populate. If the chart is in a different tab or worksheet, switch to that tab first.