Density function

Density functions make up mathematical expressions to obtain a number from a position, stored as JSON files within a data pack in the path data/<namespace>/worldgen/density_function. They are referenced from the noise router in noise settings.

A density function can be a constant number or an object.

If the [String] type is constant, a shorthand format is:

Only computes the input density once per horizontal position.

Used by the game onto final_density and should not be referenced in data packs.

If this density function is referenced twice, it is only computed once per block position.

Calculate the value per 4×4 column (Value at each block in one column is the same). And it is calculated only once per column, at Y=0. Used often in combination with interpolated.

Interpolates at each block in one cell based on the input density function value of some cells around. The size of each cell is size_horizontal * 4 and size_vertical * 4. Used often in combination with flat_cache.

These density functions are used to sample noises.

Samples a noise.

Samples a legacy noise. ​^{[more information needed]}

Samples a noise at (x/4, y/4, z/4), then multiplies it by 4.

Samples a noise at (x/4, 0, z/4), then multiplies it by 4.

Samples a noise at (z/4, x/4, 0), then multiplies it by 4.

Similar to noise, but first shifts the input coordinates.

These density functions are used to perform mathematical operations.

Calculates the absolute value of the input density function.

Adds two density functions together.

Rounds the input value to positive infinity.​^{[upcoming: JE 26.3]}

Clamps the input between two values.

A constant value.

Cubes the input (x^3).

Performs division between two arguments.​^{[upcoming: JE 26.3]}

Rounds the input value to negative infinity.​^{[upcoming: JE 26.3]}

Renamed to reciprocal.​^{[upcoming: JE 26.3]} Inverts the input (1/x).

Computes the natural logarithm of the given input.​^{[upcoming: JE 26.3]}

Multiplies two inputs.

Returns the minimum of two inputs.

Returns the maximum of two inputs.

Negates the input.​^{[upcoming: JE 26.3]}

Raises the given base value to an exponent.​^{[upcoming: JE 26.3]}

Rounds the input value to to the nearest integer (ties round up).​^{[upcoming: JE 26.3]}

Performs subtraction between two arguments.​^{[upcoming: JE 26.3]}

Computes the sign of the given input. If positive, it returns as 1. If the input is 0, it returns 0. If negative, it returns as -1.​^{[upcoming: JE 26.3]}

Computes the square root of the given input.​^{[upcoming: JE 26.3]}

Squares the input. (x^2)

Rounds the input value to 0.​^{[upcoming: JE 26.3]}

These density functions map a set of values onto another set of values.

Clamps the given coordinate and maps the gradient to a range.​^{[upcoming: JE 26.3]}

Performs (unclamped) linear interpolation between two arguments based on an alpha.​^{[upcoming: JE 26.3]} The returned value is: first*(1-alpha) + second*alpha

First clamps the input between −1 and 1, then transforms it using x/2 - x*x*x/24.

Computes a cubic spline.

Replaced with gradient.​^{[upcoming: JE 26.3]}

Clamps the Y coordinate between from_y and to_y and then linearly maps it to a range.​^{[until: JE 26.3]}

These density functions are used to apply "if-then" logic.

If the input is negative, returns half of the input. Otherwise returns the input. (x < 0 ? x/2 : x)

Selects between a number of density functions based on an input density function and a set of threshold values.

If the input is negative, returns a quarter of the input. Otherwise returns the input. (x < 0 ? x/4 : x)

Computes the input value, and depending on that result returns one of two other density functions. Basically an if-then-else statement.

Adds beards for structures (see the terrain_adaptation field in structures). Its value is added to the final_density in noise setting by the game. Should not be referenced in data packs.

Used in vanilla for smooth transition to chunks generated in old versions.​^{[more information needed]}

Used in vanilla for smooth transition to chunks generated in old versions.​^{[more information needed]}

Used in vanilla for smooth transition to chunks generated in old versions.​^{[more information needed]}

Computes the distance to a fixed point using the specified distance function.​^{[upcoming: JE 26.3]}

Renamed to end_outer_islands.​^{[upcoming: JE 26.3]} Samples at current position using a noise algorithm used for end islands. Its minimum value is −0.84375 and its maximum value is 0.5625.

Scans through a column of an input density and returns the topmost y-level that is above 0. If no such position exists within the bounds, the [Int] lower_bound is returned.

Removes a dimension from the input domain by taking a "slice" along an axis with a specific coordinate (e.g. with the axis equaling y and the coordinate of 0, a slice will be taken along the XZ plane, with all values sampled at y=0).​^{[upcoming: JE 26.3]}

Removed in 22w12a

Removed in 22w11a

Removed in 22w11a

Calculate the spline from the noise settings.

Removed in 26.2-snap5

According to the input value, scales and enhances (or weakens) some regions of the specified noise, and then returns the absolute value.

Java Edition
1.18.2			pre1				Added density functions: abs, add, beardifier, blend_alpha, blend_density, blend_offset, cache_2d, cache_all_in_cell, cache_once, clamp, constant, cube, end_islands, flat_cache, half_negative, interpolated, max, min, mul, noise, old_blended_noise, quarter_negative, range_choice, shift, shift_a, shift_b, shifted_noise, slide, square, squeeze, terrain_shaper_spline, weird_scaled_sampler, and y_clamped_gradient.
			pre2				Added density function spline.
1.19			22w11a				Removed density function terrain_shaper_spline.
							Removed min_value and max_value fields in spline.
			22w12a				Removed density function slide. Instead a combination of add, mul, and y_clamped_gradient is used to achieve the same result.
							Added fields to old_blended_noise density function: xz_scale, y_scale, xz_factor, y_factor, and smear_scale_multiplier.
1.21.9			25w31a				Added density functions minecraft:find_top_surface and minecraft:invert.
26.2			snap1				Density function minecraft:clamp can now take a density function ID as an input.
			snap5				Added density function minecraft:interval_select.
							Removed density function minecraft:weird_scale_sampler. Its functionality has been replaced with interval_select.
Upcoming Java Edition
26.3			snap4				Added the following density functions: ceil div floor negate lerp round sub truncate
							invert has been renamed to reciprocal.
							Numerous argument fields in density functions have been renamed.
			snap6				Added the following density functions: distance_to_point log pow sign slice sqrt
							end_islands has been renamed to end_outer_islands.
							y_clamped_gradient has been replaced with gradient.
			snap7				Density functions are no longer evaluated with double-precision floating point values, but instead with single-precision.

Issues relating to "Density function" are maintained on the bug tracker. Issues should be reported and viewed there.

• Density Function Generator on misode.github.io