Past the density ceiling, the only real options are aggregating, sampling, or splitting into smaller panels

What it is

Once density crosses the limit there are exactly three legitimate exits: aggregate (bin points into hexes or squares and encode counts), sample (take a principled subset), or facet (split one dense chart into several sparse, category-partitioned charts). What the three share is changing the data or layout before drawing; their shared dark alternative is brute-forcing with tinier marks and heavier transparency — palliatives that mask the symptom without solving the overload.

Why it happens

Each route trades something away and preserves something else, which sets its use case: aggregation swaps individual identity for the density distribution — point-level information is gone, the distribution's shape stays whole, right for "where is it dense" questions; sampling keeps individual form but imports sampling error — the method must be disclosed or readers will treat the sample as the population; faceting preserves individuals and group structure at the cost of canvas area — right for between-group comparison. The selection criterion is simply what the task needs: distribution → aggregate, individual identity → sample, group comparison → facet. All three work only when honest — aggregate colour scales, sampling rates, and faceting groupings must all be labelled.

Where it stops holding

Aggregation granularity is a new free parameter: bins too large flatten the structure, bins too small rebuild the occlusion — expect to try two or three sizes. Sampling is dangerous in anomaly-hunting tasks — anomalies are exactly the points most likely to be sampled away; those tasks should switch to aggregate-plus-highlight or full-data faceting. Facet count has its own ceiling: too many panels and the cross-panel comparison cost overtakes the density gain, returning to the small-multiples shared-order rules.

Applying it

• Try aggregation first for overloaded scatters: hexagonal binning with a count colour scale on a sequential palette, labelled "count per bin."
• When individuals must survive, use systematic sampling and state the rate ("random 10% sample"); eyeballed sampling is banned.
• For grouped comparison, switch to facets with shared coordinates and a shared order.
• Verification: after treatment, readers must complete the original task (find anomalies, compare distributions, read trends) and be able to say how the data was processed — both together mean the treatment qualifies.

Related

• Same group: U5.06.1 One chart's mark count is limited by overlap and occlusion · U5.06.3 The density ceiling shifts with final size and resolution · U5.06.4 High-density charts keep overall shape and lose individual readability · U5.06.5 Solve density in data processing, not by shrinking marks
• Nearby: U4.01.2 Too many categories means grouping or aggregation · U5.04.4 Side-by-side charts need a shared order for cross-chart comparison
• Search terms: hexbin · sampling plot · small multiples facet