Scalar fields
A formula that returns a single number at every point in space.
What it is
A scalar field is the simplest and most-wired kind of Fields. Ask it for a value anywhere, at a vertex, a pixel, or a point in a Collections, and it answers with one number.
That number means whatever you decide: a mask from 0 to 1, a height, a density, a displacement strength, an opacity, a temperature. Nothing is stored. The value is computed on demand, point by point, every time something samples the field.
When to use one
Use a scalar field where a parameter should change depending on position.
Masks: fade an effect in over here and leave it alone over there.
Displacement: push a surface out by the field's value, turning noise into mountains and ripples.
Opacity: dissolve an object from one side to the other.
Density: tell a Distance fields & volumes how thick the smoke is at each point.
Any number parameter: wire a field into almost any number slot to make it spatial.
How to use it
Scalar fields come from several places.
Noise for organic, wandering values. Eight algorithms, from classic Perlin and Simplex through Worley and Cell for cracked cellular looks, Manhattan for diamond cells, and Sparse Convolution for scattered impulse grain. Fractal Mode layers octaves over the top: FBM, Turbulence and Ridge, two domain warps, and the Hybrid Multifractal and Heterogeneous Terrain multifractals, which lift ridges above a detail threshold the way real landscape does.
Pattern and Gradient for structured ramps and tiles. Pattern's Voronoi reads back several ways: Cell Random for a flat value per cell, Distance for the reach to the nearest site, Edge Distance for cell walls, and F2 or F3 for the second and third nearest. Output Range swings the whole node between a Unipolar 0 to 1 mask and a Bipolar range centred on zero, which is what displacement that pushes both ways needs.
A Distance fields & volumes, which hands back distance from the surface as a number.
The brightness of a sampled Rasters (images).
An The Expression language, where the result of the formula is the field.
Derive one from a field you already have. Derive runs an operator over its input and hands back the result: Gradient, Edges, Normal, Curvature and Laplacian from a scalar or distance field; Divergence, Curl and Magnitude from a vector field; Hue, Saturation and Luminance from a colour one. Disposition decides the shape of the answer. Replace gives you the operator's result on its own. Capture staples it onto the input as a named channel and keeps both, which is how a field grows into a multi-channel one.
Wire the field into whatever should respond: a displace node, an opacity slot, a material input, or any parameter that should vary across the canvas.
Run a scalar field through a Gradient to turn it into colour. The gradient maps each number to a colour, so a grey mask becomes a full spectrum.
Gotcha
A scalar field carries numbers, not colour. Feed one into a slot expecting colour and you get greyscale, the same number copied into red, green and blue. For real colour, convert through a Gradient or use a Colour fields.
Conversion between field kinds happens automatically where one exists, so a scalar field slots in wherever a number-at-every-point is expected. See Automatic conversion.