Minecraft Density Function

Density Function

Density functions are mathematical expressions mapping coordinates to values, used by noise settings. Java Edition only. The page tracks 26.3 changes (renames/removals marked below).

Definition Format

Registry DENSITY_FUNCTION, data pack path worldgen/density_function (files in data/<namespace>/worldgen/density_function/; tags in tags/worldgen/density_function/).

The file root is either a float constant (range −1000000.0..1000000.0) or an object:

{ "type": "<namespace id>", ... }

Fields expecting a density function accept an ID, a constant number, or an inline density function JSON. Definitions load once at server startup; /reload does not reload them — restart the server.

Marker Functions

• interpolated — interpolates the input per cell (cell size = size_horizontal × 4 / size_vertical × 4).
• flat_cache — caches the input's Y=0 value at cell scale.
• cache_2d — caches the input until the current coordinates change.
• cache_once — caches the input until the next interpolation pass.
• cache_all_in_cell — internally used for final_density; caches per cell in the chunk's memory.
• blend_density — used for blending between old and new chunks.

Univariate Functions

• abs — |x|.
• square — x².
• cube — x³.
• sqrt (26.3) — √x.
• half_negative — x if x > 0, else x/2.
• quarter_negative — x if x > 0, else x/4.
• invert (removed in 26.3) → reciprocal (26.3) — 1/x.
• negate (26.3) — −x.
• squeeze — clamp x to [−1, 1], then x/2 − x³/24.
• log (26.3) — natural logarithm.
• sign (26.3) — −1/0/1 by sign.
• Rounding (26.3): floor, round, ceil, truncate — each with input and optional multiple (rounds to a multiple of the given function's value; default constant 1).

Binary Functions

• add / sub (26.3) / mul / div (26.3) / min / max — two arguments (left/right; older aliases argument1/argument2).

Other Functions

• blend_alpha — 1 in fully-new-chunk regions (chunk blending).
• blend_offset — 0 in fully-new-chunk regions (chunk blending).
• beardifier — adds terrain around structures per their terrain_adaptation; called automatically during generation, no need to declare it.
• old_blended_noise — legacy noise algorithm: xz_scale, y_scale, xz_factor, y_factor (0.001–1000.0), smear_scale_multiplier (1.0–8.0); sampling step = scale × 684.412 per block.
• lerp (26.3) — unclamped linear interpolation first×(1−alpha) + second×alpha.
• noise — samples a noise: noise (ID), xz_scale, y_scale.
• end_islands (removed in 26.3) → end_outer_islands (26.3) — End outer-island noise over XZ (Y unused), range −0.84375..0.5625.
• shifted_noise — like noise but with shifted input coordinates: noise, xz_scale, y_scale, shift_x/shift_y/shift_z density functions.
• range_choice — input, min_inclusive, max_exclusive, when_in_range, when_out_of_range.
• interval_select — input, thresholds (ascending, non-empty), functions (count = thresholds length − 1, ≥2): picks the function for the interval the input falls into.
• shift_a / shift_b / shift — noise sampled at (x/4, 0, z/4) / (z/4, x/4, 0) / (x/4, y/4, z/4), ×4.
• clamp — input, min, max.
• pow (26.3) — base^exponent.
• spline — cubic spline: spline (number or object), coordinate (density function for the coordinate), points (non-empty list of {location, value (number or nested spline), derivative}).
• constant — a constant (value).
• slice (26.3) — removes one dimension: axis (x/y/z), coordinate (fixed value), input.
• gradient (26.3) — maps a clamped coordinate range to an output range: axis, tiling (clamp_to_edge/repeat/mirrored_repeat), from_coordinate, to_coordinate, from_value, to_value.
• distance_to_point (26.3) — distance to a fixed coordinate [x,y,z] with metric = euclidean (√(dx²+dy²+dz²)), euclidean_squared, manhattan, chebyshev.
• y_clamped_gradient (removed in 26.3) — clamps Y (from_y/to_y, −4064..4062) and maps linearly to from_value/to_value.
• find_top_surface — scans from upper_bound (2D density function) down to lower_bound to find the negative-to-positive transition: density, upper_bound, lower_bound, cell_height (>0).

Removed Functions

• slide — old top/bottom slide curves from noise settings (targets outside the offset ranges, smooth transitions of size × size_vertical).
• terrain_shaper_spline — computed terrain shaper splines (offset/factor/jaggedness) from continentalness/erosion/weirdness density functions with min_value/max_value.
• weird_scaled_sampler — scaled/abs'd noise sampling: rarity_value_mapper (type_1: 0.75–2.0, type_2: 0.5–3.0), noise, input.

Source acknowledgment: parts of this page derive from Misode's JSON format documentation.