Density Plot

A bivariate function as a heatmap (Wolfram's DensityPlot), rendered by <notatio-density-plot>. The expression is sampled on an n×n grid — the same sampling <notatio-contour-plot> uses — and each sample is shaded on a sequential ramp running from a cool low end to the theme's accent. Cells overlap by a hairline so no seams show between them; a non-finite sample leaves its cell unpainted.

Where a contour plot shows where the level sets are, a density plot shows how much there is everywhere — the two pair naturally over the same field.

Function densities

#A trig field

source

<notatio-density-plot expr="Sin(x) * Cos(y)" xrange="-3.14,3.14" yrange="-3.14,3.14" />

#A saddle, with a colour bar

legend adds a colour bar labelled with the sampled extremes.

source

<notatio-density-plot expr="x^2 - y^2" xrange="-3,3" yrange="-3,3" legend label="x² − y²" />

#Interference

n raises the sampling resolution — the ramp is quantised by the cell grid, so a finer grid reads as a smoother image.

source

<notatio-density-plot expr="Sin(x * y)" xrange="-4,4" yrange="-4,4" n="80" legend />

#A pinned colour scale

zrange pins the colour scale instead of using the sampled min and max, so several plots can be compared on one scale.

source

<notatio-density-plot expr="x^2 + y^2" xrange="-3,3" yrange="-3,3" zrange="0,30" legend x-label="x" y-label="y" />

List densities

data (a JSON 2-D array) shades a pre-sampled grid directly — no expression evaluation (Wolfram's ListDensityPlot). Row 0 is the smallest y, so it sits at the bottom of the frame.

#A pre-sampled grid

source

<notatio-density-plot data="[[0,1,2,3],[1,2,3,4],[2,3,4,5],[3,4,5,6]]" legend />

Roadmap

• Bilinear interpolation between samples, for a genuinely continuous ramp.
• A diverging ramp for signed fields, keyed on zero.
• Contour lines overlaid on the density, as ContourPlot and DensityPlot combine in Wolfram.