Touch Heatmap Tracker: Kernel Density Event Tracking (2D)

Event Stream

Tap rate 6.0 taps/s

Kernel bandwidth σ 3.50 px

Session decay half-life 12 s

Tap Distribution

Live Readouts

Total taps

Peak density

0.00

Screen coverage

0.0%

Marginal peak (x, y)

–

How it works

Mobile-analytics SDKs (Firebase, Amplitude, Hotjar-style session recorders) log every tap as a raw (x, y, t) event. A touch heatmap turns that stream into a continuous surface with 2D kernel density estimation: each tap deposits a Gaussian "splat" on a grid, and overlapping splats sum into hot zones.

For a tap at (x0,y0), grid cell (x,y) gains:
  ΔI(x,y) = A · exp( -((x-x0)² + (y-y0)²) / (2σ²) )

Between ticks the whole grid decays exponentially
(a rolling session window, not infinite memory):
  I(x,y) ← I(x,y) · exp(-λ·dt),   λ = ln(2) / half-life

This 2D counterpart renders the same density field directly as a flat map instead of a 3D-textured phone screen, and adds two analyses a 3D perspective view can't show cleanly:

Isodensity contours — traced with a marching-squares pass over the grid at three density thresholds, the same way a topographic map connects points of equal elevation. Tight nested contours mean a sharply localized hot zone; widely spaced contours mean a broad, diffuse one.
Marginal density profiles — the grid summed along each axis, I_x(x) = Σ_y I(x,y) and I_y(y) = Σ_x I(x,y). Integrating a 2D Gaussian over one axis leaves a 1D Gaussian in the other, so these strips are literally the row/column sums of the same field — they show exactly where taps cluster horizontally and vertically without needing to read the 2D map by eye.

Tap rate — events/second arriving from the simulated user session.
Kernel bandwidth σ — how far a single tap's influence spreads; small σ shows exact touch points, large σ approximates finger/thumb contact area.
Decay half-life — how long a tap keeps contributing before the analytics window "forgets" it.
Realistic vs Uniform — realistic mode samples taps from three weighted UI zones (top search bar, center feed, bottom nav icons); uniform mode is the structureless null model.

Real-world relevance: this is the same aggregation mobile analytics platforms run over millions of raw touch events to answer "where do users actually tap" — informing button placement, nav-bar redesign and dead-zone detection. The 3D counterpart renders the identical density field as a texture on a phone mesh you can orbit around.

Cold Hot Contour Marginal density