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

Template:Cd

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).
  • Template:NbtTemplate:Nbt: Template:Json ref/density function — The input to be cached.

Template:Cd

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.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, interpolated).
  • Template:NbtTemplate:Nbt: Template:Json ref/density function — The input to be interpolated.
  • Template:Nbt: Size in blocks of the interpolation grid cells on the X and Z axes. The number must not be negative.
  • Template:Nbt: 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.

Template:Cd

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.
  • Template:Nbt: Optional; A domain warp to apply on X. If not specified, no warping will be applied (equivalent to 0).
  • Template:Nbt: Optional; A domain warp to apply on Y. If not specified, no warping will be applied (equivalent to 0).
  • Template:Nbt: Optional; A domain warp to apply on Z. If not specified, no warping will be applied (equivalent to 0).

Template:Cd

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).

Template:Cd

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:Nbt: Template:Json ref — The noise to sample.

Template:Cd

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:Nbt: Template:Json ref — The noise to sample.

Template:Cd

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:Nbt: Template:Json ref — The noise to sample.

Mathematical density functions

These density functions are used to perform mathematical operations.

Template:Cd

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:Nbt: Template:Json ref/density function — The input of the calculation.

Template:Cd

Adds two density functions together.

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

Template:Cd

Rounds the input value to positive infinity.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, ceil).
  • Template:NbtTemplate:NbtTemplate:Nbt: Density Function to round.
  • Template:NbtTemplate:NbtTemplate:Nbt: 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.

Template:Cd

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:NbtTemplate:Nbt: One density function — 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).

Template:Cd

A constant value.

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

Template:Cd

Cubes the input (x^3).

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

Template:Cd

Performs division between two arguments.

• 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.

Template:Cd

Rounds the input value to negative infinity.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, floor).
  • Template:NbtTemplate:NbtTemplate:Nbt: Density Function to round.
  • Template:NbtTemplate:NbtTemplate:Nbt: 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.

Template:Cd

Computes the natural logarithm of the given input.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, log).
  • Template:NbtTemplate:NbtTemplate:Nbt: Density Function for which to compute the natural logarithm.

Template:Cd

Multiplies two inputs.

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

Template:Cd

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:Nbt: Template:Json ref/density function — The first input of the calculation.
  • Template:NbtTemplate:Nbt: Template:Json ref/density function — The second input of the calculation.

Template:Cd

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:Nbt: Template:Json ref/density function — The first input of the calculation.
  • Template:NbtTemplate:Nbt: Template:Json ref/density function — The second input of the calculation.

Template:Cd

Negates the input.

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

Template:Cd

Raises the given base value to an exponent.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, pow).
  • Template:NbtTemplate:NbtTemplate:Nbt: the base value (Density Function).
  • Template:NbtTemplate:NbtTemplate:Nbt: the exponent (Density Function).

Template:Cd

Inverts the input (1/x).

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

Template:Cd

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

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

Template:Cd

Performs subtraction between two arguments.

• 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.

Template:Cd

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.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, sign).
  • Template:NbtTemplate:NbtTemplate:Nbt: Density Function for which to compute the sign.

Template:Cd

Computes the square root of the given input.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, sqrt).
  • Template:NbtTemplate:NbtTemplate:Nbt: Density Function for which to compute the square root.

Template:Cd

Squares the input. (x^2)

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

Template:Cd

Rounds the input value to 0.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, truncate).
  • Template:NbtTemplate:NbtTemplate:Nbt: Density Function to round.
  • Template:NbtTemplate:NbtTemplate:Nbt: 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.

Template:Cd

File:Gradient tiling.png

Demonstration of the different tiling options for the Template:Cd density function, using both an input range of -100 to 100 and an output range of -1 to 1.

Clamps the given coordinate and maps the gradient to a range.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, gradient).
  • Template:Nbt: Template:Cd, Template:Cd. or Template:Cd: The axis over which to define the gradient .
  • Template:Nbt: 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.
  • Template:Nbt: The coordinate at which the gradient starts.
  • Template:Nbt: The coordinate at which the gradient ends. It must not equal Template:Cd.
  • Template:Nbt: The value at which the gradient starts.
  • Template:Nbt: The value at which the gradient ends.

Template:Cd

Performs (unclamped) linear interpolation between two arguments based on an alpha. The returned value is: first*(1-alpha) + second*alpha

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

Template:Cd

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:Nbt: Template:Json ref/density function — The input of the calculation.

Template:Cd

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.

Conditional density functions

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

Template:Cd

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:Nbt: Template:Json ref/density function — The input of the calculation.

Template:Cd

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:NbtTemplate:NbtTemplate:Nbt: Density Function to be compared with any given Template:Cd.
  • Template:Nbt: (List of Floats) 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.

Template:Cd

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:Nbt: Template:Json ref/density function — The input of the calculation.

Template:Cd

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.

Other density functions

Template:Cd

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).

Template:Cd

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).

Template:Cd

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:Nbt: Template:Json ref/density function — The desired density of new chunks.

Template:Cd

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).

Template:Cd

File:Distance to point options.png

Demonstration of the different metric options for the Template:Cd density function, using the distance from the point (0, 0).

Computes the distance to a fixed point using the specified distance function.

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, distance_to_point).
  • Template:Nbt: Template:Cd; the point to compute distance to
  • Template:Nbt:
    • Template:Nbt: (i.e. Template:Cd)
    • Template:Nbt: (i.e. Template:Cd)
    • Template:Nbt: (i.e. Template:Cd)
    • Template:Nbt: (i.e. Template:Cd)

Template:Cd

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_outer_islands).

Template:Cd

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.

Template:Cd

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, ore_vein).
  • Template:Nbt: The ore block to place.
  • Template:Nbt: The raw ore block to place.
  • Template:Nbt: The filler block to place.
  • Template:Nbt: The probability for a raw ore block to be placed instead of an ore block. Value between 0 and 1 (inclusive).
  • Template:Nbt: The probability for the ore vein to replace a block. If the value is 0 or lower, no block will be replaced.
  • Template:Nbt: The probability for an ore block or a raw ore block to be placed, as opposed to Template:Cd. 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.
  • Template:Nbt: Overrides Template:Cd; if the value is positive, Template:Cd will always be placed.

Template:Cd

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).

• Template:Nbt: Root object.
  • Template:Nbt: The ID of the density function type (in this case, slice).
  • Template:Nbt: Template:Cd, Template:Cd, or Template:Cd; the axis to remove.
  • Template:Nbt: The fixed coordinate to be passed to the input function.
  • Template:NbtTemplate:NbtTemplate:Nbt: The input function.

Removed density functions

Template:Cd

Removed in Minecraft:26.3-snap10

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:Nbt: Template:Json ref/density function — The input to be cached.

Template:Cd

Removed in Minecraft:26.3-snap10

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:Nbt: Template:Json ref/density function — The input to be cached.

Template:Cd

Removed in Minecraft:26.3-snap10

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:Nbt: Template:Json ref/density function — The input to be cached.

Template:Cd

Removed in Minecraft:26.3-snap10

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.

Template:Cd

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).

Template:Cd

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

Template:Cd

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.

Template:Cd

Removed in Minecraft:26.3-snap6

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).

External links

• Density Function Generator on misode.github.io