Minecraft:Density function

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

JSON format

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type.
  • Other additional fields depend on the value of Template:Nbt, described below.

If the Template:Nbt is constant, a shorthand format is:

• Template:Nbt: A constant number. Value between −1000000.0 and 1000000.0 (both inclusive).

Marker functions

cache_2d

Only computes the input density once per horizontal position.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, cache_2d).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input to be cached.

cache_all_in_cell

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, cache_all_in_cell).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input to be cached.

cache_once

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, cache_once).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input to be cached.

flat_cache

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.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, flat_cache).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input to be cached.

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.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, interpolated).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input to be interpolated.

Mapped density functions

abs

Calculates the absolute value of the input density function.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, abs).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input of the calculation.

cube

Cubes the input (x^3).

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, cube).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input of the calculation.

half_negative

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, half_negative).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input of the calculation.

interval_select

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, interval_select).
  • Template:Nbt: The value to be compared with any given Template:Cd.
  • Template:Nbt: The threshold values to compare Template:Cd with.
    • If the input value is less than the threshold values, the result of Template:Cd will be selected.
    • If the input value is greater than the last threshold value, the last function will be selected.
    • There must be one fewer Template:Cd than Template:Cd.
  • Template:Nbt: The resulting functions (at least two) to be selected from.
    • There must be one more element in Template:Cd than Template:Cd.

invert

Named Template:Cd.Template:Upcoming Inverts the input (1/x).

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, invert).
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — The input of the calculation.

quarter_negative

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, quarter_negative).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input of the calculation.

square

Squares the input. (x^2)

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, square).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input of the calculation.

squeeze

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, squeeze).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The input of the calculation.

Functions with two arguments

add

Adds two density functions together.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, add).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The first input of the calculation.
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The second input of the calculation.

div

Performs division between two arguments.Template:Upcoming

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, div).
  • Template:NbtTemplate:NbtTemplate:Nbt — The left-hand side of the operation.
  • Template:NbtTemplate:NbtTemplate:Nbt — The right-hand side of the operation.

mul

Multiplies two inputs.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, mul).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The first input of the calculation.
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The second input of the calculation.

min

Returns the minimum of two inputs.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, min).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The first input of the calculation.
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The second input of the calculation.

max

Returns the maximum of two inputs.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, max).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The first input of the calculation.
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The second input of the calculation.

sub

Performs subtraction between two arguments.Template:Upcoming

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, sub).
  • Template:NbtTemplate:NbtTemplate:Nbt — The left-hand side of the operation.
  • Template:NbtTemplate:NbtTemplate:Nbt — The right-hand side of the operation.

Other density functions

beardifier

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.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, beardifier).

blend_alpha

Used in vanilla for smooth transition to chunks generated in old versions.Template:Info needed

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, blend_alpha).

blend_density

Used in vanilla for smooth transition to chunks generated in old versions.Template:Info needed

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, blend_density).
  • Template:NbtTemplate:NbtTemplate:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref/density function — The desired density of new chunks.

blend_offset

Used in vanilla for smooth transition to chunks generated in old versions.Template:Info needed

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, blend_offset).

ceil

Rounds the input value to positive infinity.Template:Upcoming

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, ceil).
  • Template:Nbt: The input to round.
  • Template:Nbt: The output will be rounded to an integer multiple of this value. If not specified, it defaults to a constant 1.

clamp

Clamps the input between two values.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, clamp).
  • Template:NbtTemplate:Nbt: One density function (a new Template:NbtTemplate:Nbt density function definition, an Template:NbtID is not allowed here<ref>Template:Cite bug</ref>) — The input to clamp.
  • Template:Nbt: The lower bound. Value between −1000000.0 and 1000000.0 (both inclusive).
  • Template:Nbt: The upper bound. Value between −1000000.0 and 1000000.0 (both inclusive).

constant

A constant value.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, constant).
  • Template:NbtTemplate:Until / Template:NbtTemplate:Upcoming: A constant value. Value between −1000000.0 and 1000000.0 (both inclusive).

end_islands

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.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, end_islands).

find_top_surface

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 Template:Nbt is returned.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, find_top_surface).
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — The density function to scan.
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — The y-level to start the scan at. Usually a 2D density function.
  • Template:Nbt: The y-level to stop the scan.
  • Template:Nbt: The resolution of the scan. E.g. if set to 4, then only every 4th block is checked.

floor

Rounds the input value to negative infinity.Template:Upcoming

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, floor).
  • Template:Nbt: The input to round.
  • Template:Nbt: The output will be rounded to an integer multiple of this value. If not specified, it defaults to a constant 1.

lerp

Performs (unclamped) linear interpolation between two arguments based on an alpha.Template:Upcoming

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, lerp).
  • Template:Nbt: The interpolation factor (e.g. 0 = first, 1 = second). Any value outside of Template:Cd will extrapolate.
  • Template:Nbt: the value at Template:Cd.
  • Template:Nbt: the value at Template:Cd.

negate

Negates the input.Template:Upcoming

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, negate).
  • Template:Nbt: The function to negate.

noise

Samples a noise.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, noise).
  • Template:Nbt: Template:Json ref — The noise to sample.
  • Template:Nbt: Scales the X and Z before sampling.
  • Template:Nbt: Scales the Y before sampling.

old_blended_noise

Samples a legacy noise. Template:Info needed

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, old_blended_noise).
  • Template:Nbt: Value between 0.001 and 1000.0 (both inclusive).
  • Template:Nbt: Value between 0.001 and 1000.0 (both inclusive).
  • Template:Nbt: Value between 0.001 and 1000.0 (both inclusive).
  • Template:Nbt: Value between 0.001 and 1000.0 (both inclusive).
  • Template:Nbt: Value between 1.0 and 8.0 (both inclusive).

range_choice

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, range_choice).
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — The value to compare
  • Template:Nbt: The lower bound of the range. Value between −1000000.0 and 1000000.0 (both inclusive).
  • Template:Nbt: The upper bound of the range. Value between −1000000.0 and 1000000.0 (both inclusive).
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — Used when the input is inside the range.
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — Used when the input is outside the range.

round

Rounds the input value to to the nearest integer (ties round up).Template:Upcoming

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, round).
  • Template:Nbt: The input to round.
  • Template:Nbt: The output will be rounded to an integer multiple of this value. If not specified, it defaults to a constant 1.

shift

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, shift).
  • Template:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref — The noise to sample.

shift_a

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, shift_a).
  • Template:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref — The noise to sample.

shift_b

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

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, shift_b).
  • Template:NbtTemplate:Until / Template:NbtTemplate:Upcoming: Template:Json ref — The noise to sample.

shifted_noise

Similar to noise, but first shifts the input coordinates.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, shifted_noise).
  • Template:Nbt: Template:Json ref — The noise to sample.
  • Template:Nbt: Scales the X and Z before sampling.
  • Template:Nbt: Scales the Y before sampling.
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — offset of the position in the X direction.
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — offset of the position in the Y direction.
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — offset of the position in the Z direction.

spline

Computes a cubic spline.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, spline).
  • Template:NbtTemplate:Nbt: The spline. Can be either a number or an object.
    • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — Input determining the location on the spline.
    • Template:Nbt: (Cannot be empty) List of points of the cubic spline.
      • Template:Nbt: A point of the cubic spline.
        • Template:Nbt: The location of this point.
        • Template:NbtTemplate:Nbt: The value of this point. Can be either a number or a spline object.
        • Template:Nbt: The slope at this point.

truncate

Rounds the input value to 0.Template:Upcoming

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, truncate).
  • Template:Nbt: The input to round.
  • Template:Nbt: The output will be rounded to an integer multiple of this value. If not specified, it defaults to a constant 1.

y_clamped_gradient

Clamps the Y coordinate between from_y and to_y and then linearly maps it to a range.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, y_clamped_gradient).
  • Template:Nbt: The value to be mapped to from_value. Value between −4064 and 4062 (both inclusive).
  • Template:Nbt: The value to be mapped to to_value. Value between −4064 and 4062 (both inclusive).
  • Template:Nbt: The value to map from_y to. Value between −1000000.0 and 1000000.0 (both inclusive).
  • Template:Nbt: The value to map to_y to. Value between −1000000.0 and 1000000.0 (both inclusive).

Removed density functions

slide

Removed in Minecraft:22w12a

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, slide).
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function

The legacy "spline"

Removed in Minecraft:22w11a

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, spline).
  • Template:NbtTemplate:Nbt: The spline. Can be either a number or an object.
    • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function — Input determining the location on the spline.
    • Template:Nbt: (Cannot be empty) List of points of the cubic spline.
      • Template:Nbt: The location of this point.
      • Template:NbtTemplate:Nbt: The value of this point. Can be either a number or a spline object.
      • Template:Nbt: The slope at this point.
  • Template:Nbt: The min value of the output. Value between −1000000.0 and 1000000.0 (both inclusive).
  • Template:Nbt: The max value of the output. Value between −1000000.0 and 1000000.0 (both inclusive).

terrain_shaper_spline

Removed in Minecraft:22w11a

Calculate the spline from the noise settings.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, terrain_shaper_spline).
  • Template:Nbt: Can be offset, factor, orjaggedness.
  • Template:Nbt: The min value of the output. Value between −1000000.0 and 1000000.0 (both inclusive).
  • Template:Nbt: The max value of the output. Value between −1000000.0 and 1000000.0 (both inclusive).
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function
  • Template:NbtTemplate:NbtTemplate:Nbt: Template:Json ref/density function

weird_scaled_sampler

Removed in Minecraft: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.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, weird_scaled_sampler).
  • Template:Nbt: Can be type_1（The minimum scale is 0.75, and the maximum is 2.0）or type_2（The minimum scale is 0.5, and the maximum is 3.0.)
  • Template:Nbt: Template:Json ref — The noise to sample.
  • Template:NbtTemplate:NbtTemplate:Nbt: The input density function. Can be an ID of a density function, or a density function in the form of a JSON object or a constant number.

External links

• Density Function Generator on misode.github.io