Density function

This feature is exclusive to Java Edition.

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.

JSON format

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type.
- Other additional fields depend on the value of [String] type, described below.

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

[Double]: A constant number. Value between −1000000.0 and 1000000.0 (both inclusive).

Marker functions

`cache_2d`

^{[until: JE 26.3]} Only computes the input density once per horizontal position.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, cache_2d).
- [String][Double][NBT Compound / JSON Object] argument: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input to be cached.

`cache_all_in_cell`

^{[until: JE 26.3]} Used by the game onto final_density and should not be referenced in data packs.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, cache_all_in_cell).
- [String][Double][NBT Compound / JSON Object] argument: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input to be cached.

`cache_once`

Renamed to cache.^{[upcoming: JE 26.3]} If this density function is referenced twice, it is only computed once per block position.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, cache_once^{[until: JE 26.3]} / cache^{[upcoming: JE 26.3]}).
- [String][Double][NBT Compound / JSON Object] argument^{[until: JE 26.3]} / [Double] input^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input to be cached.

`flat_cache`

^{[until: JE 26.3]} 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.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, flat_cache).
- [String][Double][NBT Compound / JSON Object] argument: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — 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.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, interpolated).
- [String][Double][NBT Compound / JSON Object] argument^{[until: JE 26.3]} / [Double] input^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input to be interpolated.
- [Int] cell_size_xz^{[upcoming: JE 26.3]}: Size in blocks of the interpolation grid cells on the X and Z axes. The number must not be negative.
- [Int] cell_size_y^{[upcoming: JE 26.3]}: Size in blocks of the interpolation grid cells on the Y axis. The number must not be negative.

Noise sampling functions

These density functions are used to sample noises.

`noise`

Samples a noise.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, noise).
- [String] noise: One noise (an [String] ID) — The noise to sample.
- [Double] xz_scale: Scales the X and Z before sampling.
- [Double] y_scale: Scales the Y before sampling.
- [Double] shift_x^{[upcoming: JE 26.3]}: Optional; A domain warp to apply on X. If not specified, no warping will be applied (equivalent to 0).
- [Double] shift_y^{[upcoming: JE 26.3]}: Optional; A domain warp to apply on Y. If not specified, no warping will be applied (equivalent to 0).
- [Double] shift_z^{[upcoming: JE 26.3]}: Optional; A domain warp to apply on Z. If not specified, no warping will be applied (equivalent to 0).

`old_blended_noise`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, old_blended_noise).
- [Double] xz_scale: Value between 0.001 and 1000.0 (both inclusive).
- [Double] y_scale: Value between 0.001 and 1000.0 (both inclusive).
- [Double] xz_factor: Value between 0.001 and 1000.0 (both inclusive).
- [Double] y_factor: Value between 0.001 and 1000.0 (both inclusive).
- [Double] smear_scale_multiplier: Value between 1.0 and 8.0 (both inclusive).

`shift`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, shift).
- [String] argument^{[until: JE 26.3]} / [String] noise^{[upcoming: JE 26.3]}: One noise (an [String] ID) — The noise to sample.

`shift_a`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, shift_a).
- [String] argument^{[until: JE 26.3]} / [String] noise^{[upcoming: JE 26.3]}: One noise (an [String] ID) — The noise to sample.

`shift_b`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, shift_b).
- [String] argument^{[until: JE 26.3]} / [String] noise^{[upcoming: JE 26.3]}: One noise (an [String] ID) — The noise to sample.

`shifted_noise`

^{[until: JE 26.3]} Similar to noise, but first shifts the input coordinates.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, shifted_noise).
- [String] noise: One noise (an [String] ID) — The noise to sample.
- [Double] xz_scale: Scales the X and Z before sampling.
- [Double] y_scale: Scales the Y before sampling.
- [String][Double][NBT Compound / JSON Object] shift_x: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — offset of the position in the X direction.
- [String][Double][NBT Compound / JSON Object] shift_y: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — offset of the position in the Y direction.
- [String][Double][NBT Compound / JSON Object] shift_z: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — offset of the position in the Z direction.

Mathematical density functions

These density functions are used to perform mathematical operations.

`abs`

Calculates the absolute value of the input density function.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, abs).
- [String][Double][NBT Compound / JSON Object] argument^{[until: JE 26.3]} / [Double] input^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input of the calculation.

`add`

Adds two density functions together.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, add).
- [String][Double][NBT Compound / JSON Object] argument1^{[until: JE 26.3]} / [Double] left^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The first input of the calculation.
- [String][Double][NBT Compound / JSON Object] argument2^{[until: JE 26.3]} / [Double] right^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The second input of the calculation.

`ceil`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, ceil).
- [String][Double][NBT Compound / JSON Object] input: Density Function to round.
- [String][Double][NBT Compound / JSON Object] multiple: The output will be rounded to an integer multiple of the value returned by this Density Function. If not specified, defaults to a constant 1.

`clamp`

Clamps the input between two values.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, clamp).
- [String][Double][NBT Compound / JSON Object] input: One density function — The input to clamp.
- [Double] min: The lower bound. Value between −1000000.0 and 1000000.0 (both inclusive).
- [Double] max: The upper bound. Value between −1000000.0 and 1000000.0 (both inclusive).

`constant`

A constant value.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, constant).
- [Double] argument^{[until: JE 26.3]} / [Double] value^{[upcoming: JE 26.3]}: A constant value. Value between −1000000.0 and 1000000.0 (both inclusive).

`cube`

Cubes the input (x^3).

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, cube).
- [String][Double][NBT Compound / JSON Object] argument^{[until: JE 26.3]} / [Double] input^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input of the calculation.

`div`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, div).
- [String][Double][NBT Compound / JSON Object] left — The left-hand side of the operation.
- [String][Double][NBT Compound / JSON Object] right — The right-hand side of the operation.

`floor`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, floor).
- [String][Double][NBT Compound / JSON Object] input: Density Function to round.
- [String][Double][NBT Compound / JSON Object] multiple: The output will be rounded to an integer multiple of the value returned by this Density Function. If not specified, defaults to a constant 1.

`invert`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, invert^{[until: JE 26.3]} / reciprocal^{[upcoming: JE 26.3]}).
- [String][Double][NBT Compound / JSON Object] argument: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input of the calculation.

`log`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, log).
- [String][Double][NBT Compound / JSON Object] input: Density Function for which to compute the natural logarithm.

`mul`

Multiplies two inputs.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, mul).
- [String][Double][NBT Compound / JSON Object] argument1^{[until: JE 26.3]} / [Double] left^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The first input of the calculation.
- [String][Double][NBT Compound / JSON Object] argument2^{[until: JE 26.3]} / [Double] right^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The second input of the calculation.

`min`

Returns the minimum of two inputs.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, min).
- [String][Double][NBT Compound / JSON Object] argument1^{[until: JE 26.3]} / [Double] left^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The first input of the calculation.
- [String][Double][NBT Compound / JSON Object] argument2^{[until: JE 26.3]} / [Double] right^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The second input of the calculation.

`max`

Returns the maximum of two inputs.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, max).
- [String][Double][NBT Compound / JSON Object] argument1^{[until: JE 26.3]} / [Double] left^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The first input of the calculation.
- [String][Double][NBT Compound / JSON Object] argument2^{[until: JE 26.3]} / [Double] right^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The second input of the calculation.

`negate`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, negate).
- [String][Double][NBT Compound / JSON Object] input: Density Function to negate.

`pow`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, pow).
- [String][Double][NBT Compound / JSON Object] base: the base value (Density Function).
- [String][Double][NBT Compound / JSON Object] exponent: the exponent (Density Function).

`round`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, round).
- [String][Double][NBT Compound / JSON Object] input: Density Function to round.
- [String][Double][NBT Compound / JSON Object] multiple: The output will be rounded to an integer multiple of the value returned by this Density Function. If not specified, defaults to a constant 1.

`sub`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, sub).
- [String][Double][NBT Compound / JSON Object] left — The left-hand side of the operation.
- [String][Double][NBT Compound / JSON Object] right — The right-hand side of the operation.

`sign`

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]}

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, sign).
- [String][Double][NBT Compound / JSON Object] input: Density Function for which to compute the sign.

`sqrt`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, sqrt).
- [String][Double][NBT Compound / JSON Object] input: Density Function for which to compute the square root.

`square`

Squares the input. (x^2)

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, square).
- [String][Double][NBT Compound / JSON Object] argument^{[until: JE 26.3]} / [Double] input^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input of the calculation.

`truncate`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, truncate).
- [String][Double][NBT Compound / JSON Object] input: Density Function to round.
- [String][Double][NBT Compound / JSON Object] multiple: The output will be rounded to an integer multiple of the value returned by this Density Function. If not specified, defaults to a constant 1.

Mapped density functions

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

`gradient`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, gradient).
- [String] axis: x, y. or z: The axis over which to define the gradient .
- [String] tiling: How the density function handles values outside the specified coordinate range. 3 options:
  - clamp_to_edge: outside the gradient boundaries, the value at the nearest boundary will be used.
  - repeat: The gradient will be repeated outside its boundaries.
  - mirrored_repeat: The gradient will be repeated as such that odd repetitions are mirrored, ensuring continuity between repetitions.
- [Int] from_coordinate^{[upcoming: JE 26.3]}: The coordinate at which the gradient starts.
- [Int] to_coordinate: The coordinate at which the gradient ends. It must not equal from_coordinate.
- [Float] from_value: The value at which the gradient starts.
- [Float] to_value: The value at which the gradient ends.

`lerp`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, lerp).
- [String][Double][NBT Compound / JSON Object] alpha: Density function representing the interpolation factor (e.g. 0 = first, 1 = second). Any value outside of [0; 1] will extrapolate.
- [String][Double][NBT Compound / JSON Object] first: Density Function to use at alpha=0.
- [String][Double][NBT Compound / JSON Object] second: Density Function to use at alpha=1.

`squeeze`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, squeeze).
- [String][Double][NBT Compound / JSON Object] argument^{[until: JE 26.3]} / [Double] input^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input of the calculation.

`spline`

Computes a cubic spline.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, spline).
- [Float][NBT Compound / JSON Object] spline: The spline. Can be either a number or an object.
  - [String][Double][NBT Compound / JSON Object] coordinate: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — Input determining the location on the spline.
  - [NBT List / JSON Array] points: (Cannot be empty) List of points of the cubic spline.
    - [NBT Compound / JSON Object]: A point of the cubic spline.
      - [Float] location: The location of this point.
      - [Float][NBT Compound / JSON Object] value: The value of this point. Can be either a number or a spline object.
      - [Float] derivative: The slope at this point.

`y_clamped_gradient`

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]}

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, y_clamped_gradient).
- [Int] from_y: The value to be mapped to from_value. Value between −4064 and 4062 (both inclusive).
- [Int] to_y: The value to be mapped to to_value. Value between −4064 and 4062 (both inclusive).
- [Double] from_value: The value to map from_y to. Value between −1000000.0 and 1000000.0 (both inclusive).
- [Double] to_value: The value to map to_y to. Value between −1000000.0 and 1000000.0 (both inclusive).

Conditional density functions

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

`half_negative`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, half_negative).
- [String][Double][NBT Compound / JSON Object] argument^{[until: JE 26.3]} / [Double] input^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — 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.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, interval_select).
- [String][Double][NBT Compound / JSON Object] input: Density Function to be compared with any given thresholds.
- [NBT List / JSON Array] thresholds: (List of Floats) The threshold values to compare input with.
  - If the input value is less than the threshold values, the result of functions[i] 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 thresholds than functions.
- [NBT List / JSON Array] functions: The resulting functions (at least two) to be selected from.
  - There must be one more element in functions than thresholds.

`quarter_negative`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, quarter_negative).
- [String][Double][NBT Compound / JSON Object] argument^{[until: JE 26.3]} / [Double] input^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The input of the calculation.

`range_choice`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, range_choice).
- [String][Double][NBT Compound / JSON Object] input: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The value to compare
- [Double] min_inclusive: The lower bound of the range. Value between −1000000.0 and 1000000.0 (both inclusive).
- [Double] max_exclusive: The upper bound of the range. Value between −1000000.0 and 1000000.0 (both inclusive).
- [String][Double][NBT Compound / JSON Object] when_in_range: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — Used when the input is inside the range.
- [String][Double][NBT Compound / JSON Object] when_out_of_range: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — Used when the input is outside the range.

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.

[NBT Compound / JSON Object]: Root object.
- [String] type: 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.^{[more information needed]}

[NBT Compound / JSON Object]: Root object.
- [String] type: 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.^{[more information needed]}

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, blend_density).
- [String][Double][NBT Compound / JSON Object] argument^{[until: JE 26.3]} / [Double] input^{[upcoming: JE 26.3]}: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The desired density of new chunks.

`blend_offset`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, blend_offset).

`distance_to_point`

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

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, distance_to_point).
- [Int Array] point: [x, y, z]; the point to compute distance to
- [String] metric:
  - [String] euclidean: (i.e. sqrt(dx^2 + dy^2 + dz^2))
  - [String] euclidean_squared: (i.e. dx^2 + dy^2 + dz^2)
  - [String] manhattan: (i.e. abs(dx) + abs(dy) + abs(dz))
  - [String] chebyshev: (i.e. max(abs(dx), abs(dy), abs(dz)))

`end_islands`

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.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, end_islands^{[until: JE 26.3]} / end_outer_islands^{[upcoming: JE 26.3]}).

`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 [Int] lower_bound is returned.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, find_top_surface).
- [String][Double][NBT Compound / JSON Object] density: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The density function to scan.
- [String][Double][NBT Compound / JSON Object] upper_bound: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — The y-level to start the scan at. Usually a 2D density function.
- [Int] lower_bound: The y-level to stop the scan.
- [Int] cell_height: The resolution of the scan. E.g. if set to 4, then only every 4th block is checked.

`ore_vein`

^{[upcoming: JE 26.3]}

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, ore_vein).
- [String] ore_block: The ore block to place.
- [String] raw_ore_block: The raw ore block to place.
- [String] filler_block: The filler block to place.
- [Float] raw_ore_chance: The probability for a raw ore block to be placed instead of an ore block. Value between 0 and 1 (inclusive).
- [Int] density: The probability for the ore vein to replace a block. If the value is 0 or lower, no block will be replaced.
- [Int] richness: The probability for an ore block or a raw ore block to be placed, as opposed to filler_block. If the value is 0 or lower, all blocks will be the filler block. If the value is 1 or greater, no blocks will be the filler block.
- [Int] filler_gap: Overrides richness; if the value is positive, filler_block will always be placed.

`slice`

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]}

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, slice).
- [String] axis: x, y, or z; the axis to remove.
- [Int] coordinate: The fixed coordinate to be passed to the input function.
- [String][Double][NBT Compound / JSON Object] input: The input function.

Removed density functions

This section describes content that has been removed from Minecraft.

This feature was present in earlier versions of Minecraft, but has since been removed.

`slide`

Removed in 22w12a

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, slide).
- [String][Double][NBT Compound / JSON Object] argument: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition)

The legacy "spline"

Removed in 22w11a

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, spline).
- [Float][NBT Compound / JSON Object] spline: The spline. Can be either a number or an object.
  - [String][Double][NBT Compound / JSON Object] coordinate: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition) — Input determining the location on the spline.
  - [NBT List / JSON Array] points: (Cannot be empty) List of points of the cubic spline.
    - [Float] location: The location of this point.
    - [Float][NBT Compound / JSON Object] value: The value of this point. Can be either a number or a spline object.
    - [Float] derivative: The slope at this point.
- [Double] min_value: The min value of the output. Value between −1000000.0 and 1000000.0 (both inclusive).
- [Double] max_value: The max value of the output. Value between −1000000.0 and 1000000.0 (both inclusive).

`terrain_shaper_spline`

Removed in 22w11a

Calculate the spline from the noise settings.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, terrain_shaper_spline).
- [String] spline: Can be offset, factor, orjaggedness.
- [Double] min_value: The min value of the output. Value between −1000000.0 and 1000000.0 (both inclusive).
- [Double] max_value: The max value of the output. Value between −1000000.0 and 1000000.0 (both inclusive).
- [String][Double][NBT Compound / JSON Object] continentalness: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition)
- [String][Double][NBT Compound / JSON Object] erosion: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition)
- [String][Double][NBT Compound / JSON Object] weirdness: One density function (an [String] ID, or a new [Double][NBT Compound / JSON Object] density function definition)

`weird_scaled_sampler`

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.

[NBT Compound / JSON Object]: Root object.
- [String] type: The ID of the density function type (in this case, weird_scaled_sampler).
- [String] rarity_value_mapper: 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.)
- [String] noise: One noise (an [String] ID) — The noise to sample.
- [String][Double][NBT Compound / JSON Object] input: 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.

History

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`.
1.18.2	pre2	Added density function `spline`.
1.19	22w11a	Removed density function `terrain_shaper_spline`.
	22w11a	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.
	22w12a	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`.
	snap5	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.
	snap10	Added the `ore_vein` density function.
		`cache_once` has been renamed to `cache`.
		Added the `shift_x`, `shift_y`, and `shift_z` fields to the `noise` density function.
		Added the `cell_size_xz` and `cell_size_y` fields to the `interpolated` density function.
		Removed the following density functions: `cache_2d` `cache_all_in_cell` `flat_cache` `shifted_noise`

Issues

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

References

External links

Density Function Generator on misode.github.io

Density function

JSON format

Marker functions

cache_2d

cache_all_in_cell

cache_once

flat_cache

interpolated

Noise sampling functions

noise

old_blended_noise

shift

shift_a

shift_b

shifted_noise

Mathematical density functions

abs

add

ceil

clamp

constant

cube

div

floor

invert

log

mul

min

max

negate

pow

round

sub

sign

sqrt

square

truncate

Mapped density functions

gradient

lerp

squeeze

spline

y_clamped_gradient

Conditional density functions

half_negative

interval_select

quarter_negative

range_choice

Other density functions

beardifier

blend_alpha

blend_density

blend_offset

distance_to_point

end_islands

find_top_surface

ore_vein

slice

Removed density functions

slide

The legacy "spline"

terrain_shaper_spline

weird_scaled_sampler

History

Issues

References

External links

Navigation

Navigation menu

`cache_2d`

`cache_all_in_cell`

`cache_once`

`flat_cache`

`interpolated`

`noise`

`old_blended_noise`

`shift`

`shift_a`

`shift_b`

`shifted_noise`

`abs`

`add`

`ceil`

`clamp`

`constant`

`cube`

`div`

`floor`

`invert`

`log`

`mul`

`min`

`max`

`negate`

`pow`

`round`

`sub`

`sign`

`sqrt`

`square`

`truncate`

`gradient`

`lerp`

`squeeze`

`spline`

`y_clamped_gradient`

`half_negative`

`interval_select`

`quarter_negative`

`range_choice`

`beardifier`

`blend_alpha`

`blend_density`

`blend_offset`

`distance_to_point`

`end_islands`

`find_top_surface`

`ore_vein`

`slice`

`slide`

`terrain_shaper_spline`

`weird_scaled_sampler`