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== Basics ==
<div class="stub"><p>'''The prototype docs have moved to a new website with an improved format.''' This documentation page can now be found here: [https://lua-api.factorio.com/latest/types/NoiseExpression.html https://lua-api.factorio.com/latest/types/NoiseExpression.html]


A fragment of a functional program used to generate coherent noise, probably for purposes related to terrain generation.
</p><p>This wiki page is no longer updated and '''will be removed at some point in the future''', so please update your browser bookmarks or other links that sent you here. If you'd like to contribute to the new docs, you can leave your feedback [https://forums.factorio.com/viewforum.php?f=233 on the forums].</p></div>
 
Noise expressions can be provided as table literals or built using functions in the [https://github.com/wube/factorio-data/blob/master/core/lualib/noise.lua built-in <code>noise</code> library]. The built-in noise library allows writing much more concise code, so its usage will be shown in most examples on this page.<br>
[https://github.com/wube/factorio-data/blob/master/core/lualib/noise.lua#L272 <code>noise.define_noise_function</code>] allows noise expressions to be defined using a shorthand
that's a subset of Lua (see [[#Example definition|example definition]] for an example and its literal equivalent).
 
== Mandatory properties ==
 
=== type ===
 
'''Type''': [[Types/string]]
 
Name of the type of this expression.
Which other properties apply depend on the expression type.
 
== Expression types ==
 
=== variable ===
 
Reference to a pre-defined variable, constant, or a [[Prototype/NamedNoiseExpression|named noise expression]].
 
Predefined variables include "x", "y", and "distance".
 
Properties:
 
* '''variable_name''': a [[Types/string]]
 
=== function-application ===
 
Apply a function to a list or associative array of arguments. Some functions expect arguments to be named and some expect them not to be.
 
Function calls are their own class of expression (as opposed to every function just being its own expression type) because function calls all have similar properties -- arguments are themselves expressions, a function call with all-constant arguments can be constant-folded (due to [[Wikipedia:Referential_transparency|referential transparency]]), etc.
 
Properties:
 
* '''function_name''' (a string; see [[#Functions]], below)
* '''arguments''' (a list or associative array of argument expressions)
 
=== literal-boolean ===
 
Evaluates to the same boolean value (true or false) every time, given by the '''literal_value''' property. May be used as a number value, evaluates to 1 for true and 0 for false.
 
=== literal-number ===
 
Evaluates to the same number every time, given by the '''literal_value''' property. All numbers are treated as [[Types/float]]s internally unless otherwise specified. May be used as a boolean value, evaluates to true for numbers > 0, anything else evaluates to false.
 
Example:
<syntaxhighlight lang="lua">
local ten =
{
  type = "literal-number",
  literal_value = 10
}
 
-- or with the noise lib, see the "Basics" section above
local noise = require("noise")
local twenty_point_five = noise.to_noise_expression(20.5)
</syntaxhighlight>
 
=== literal-string ===
 
Evaluates to the same string every time, given by the '''literal_value''' property.
 
Since the noise generation runtime has no notion of strings or use for them,
this is useful only in constant contexts.
 
=== literal-object ===
 
Evaluates to the same object every time, given by the '''literal_value''' property.
 
e.g.
 
<syntaxhighlight lang="lua">
{
  type = "literal-object",
  literal_value = {
    name = "Bob Hope",
    birth_date = {
      year = 1903,
      month = 5,
      day_of_month = 29
    }
  }
}
</syntaxhighlight>
 
Since the noise generation runtime has no notion of objects or use for them,
this is useful only in constant contexts, such as the argument
of the '''autoplace-probability''' function (where the 'literal object' is an [[Types/AutoplaceSpecification|AutoplaceSpecitication]])
 
=== literal-expression ===
 
Returns the expression represented by its '''literal-value''' property.
 
Useful mostly for passing expressions (to be evaluated later) to the [[#spot-noise|'''spot-noise''']] function.
 
=== array-construction ===
 
'''value_expressions''' property should be a list of expressions,
each of which will be evaluated to come up with the corresponding value
in the resulting array.
 
Used to construct map positions ({x, y}) and map position lists ({{x0,y0}, {y1,y1}, ...}) for <!-- TODO 1.1.0 [[#offset-points|offset-points]] and --> [[#distance-from-nearest-point|distance-from-nearest-point]].
 
Examples of constructing a map position and map position list:
<syntaxhighlight lang="lua">
local noise = require("noise")
local tne = noise.to_noise_expression
 
local map_pos_1 = -- the map position {x = 100, y = -200} specified directly
{
  type = "array-construction",
  value_expressions = {tne(100), tne(-200)}
}
-- or with make_array from the noise lib required above
local map_pos_2 = noise.make_array({100, 200})
 
local map_pos_list = -- a map position list: {{x = 100, y = -200}, {x = 100, y = 200}}
{
  type = "array-construction",
  value_expressions = {map_pos_1, map_pos_2}
}
-- or with the noise lib
local also_map_post_list = noise.make_point_list({{100, -200}, {100, 200}})
 
</syntaxhighlight>
 
=== procedure-delimiter ===
 
Evaluates and returns the value of its '''expression''' property, which is itself an expression.
 
This hints to the compiler that it should break the subexpression into its own procedure
so that the result can be re-used in multiple places.
For instance if you want to re-use the same multioctave noise for determining probability
of multiple tiles/entities, wrap the multioctave noise expression in a procedure-delimiter.
Alternatively, make the noise its own [[Prototype/NamedNoiseExpression|NamedNoiseExpression]] and reference it by name, using a variable.
 
=== if-else-chain ===
 
Has an '''arguments''' property that is a list of condition-result expression pairs followed by a default result expression, like so:
 
<syntaxhighlight lang="lua">
{
  type = "if-else-chain",
  arguments = {
    condition1, result1,
    condition2, result2,
    ...
    defaultResult
  }
}
</syntaxhighlight >
 
The result of the if-else-chain is the value of the first result expression whose condition expression evaluated to true,
or the value of the default result ('else') expression.
 
== Functions ==
 
=== add ===
 
'''Arguments (positional)''': between 0 and 999 numbers
 
Takes the positional arguments and adds them.
 
=== subtract ===
'''Arguments (positional)''':
* '''minuend''' - number
* '''subtrahend''' - number
 
Takes 2 positional arguments and subtracts the second from the first.
 
=== multiply ===
'''Arguments (positional)''': between 0 and 999 numbers
 
Takes the positional arguments and multiplies them.
 
=== divide ===
'''Arguments (positional)''':
* '''dividend''' - number
* '''divisor''' - number
 
Takes 2 positional arguments and divides the first by the second.
 
=== exponentiate ===
'''Arguments (positional)''':
* '''base''' - number
* '''exponent''' - number
 
Takes 2 positional arguments, and raises the first to the second power.
 
=== absolute-value ===
'''Arguments (positional)''': value to be absoluted
 
Takes a single positional argument and returns its absolute value.  i.e. If the argument is negative, it is inverted.
 
=== clamp ===
'''Arguments (positional)''':
* '''value''' - number to be clamped
* '''floor''' - lower limit
* '''ceiling''' - upper limit
 
First argument is clamped between the second and third.  The second is treated as a lower limit and the third the upper limit.
 
=== compile-time-log ===
'''Arguments''': Between 1 and 999 values of any type
 
Prints all of its arguments to the [[log file]] when the expression is compiled. For that it needs to part of another expression that is compiled. The last argument of the compile-time-log is passed returned as the "result" of the compile-time-log.
 
Example of usage inside a [[Prototype/NamedNoiseExpression|NamedNoiseExpression]]:
<syntaxhighlight lang="lua">
local noise = require("noise")
local tne = noise.to_noise_expression
 
local test = noise.compile_time_log(tne(2000), noise.var("y"), tne(100) - noise.var("distance"))
 
-- see the named noise expression docs linked above the code for how this works
data:extend{{
  type = "noise-expression",
  name = "compile-log-test",
  intended_property = "elevation",
  expression = test
}}
 
-- When "compile-log-test" is selected as the map type and a map preview or map is generated, this logs:
--  Info data-updates.lua:24: 2000.000000 reference to variable 'y' subtract
-- Furthermore, the elevation noise expression is set to 'tne(100) - noise.var("distance")', producing a circular island with a 100 tile radius
</syntaxhighlight>
 
=== distance-from-nearest-point ===
'''Arguments (named)''':
* '''x''' - number
* '''y''' - number
* '''points''' - list of map positions
* '''maximum_distance''' (constant, default: max double) - number
 
Computes the [[Wikipedia:Euclidean_distance|euclidean distance]] of the position {x, y} to all position listed in '''points''' and returns the shortest distance. The returned distance can be '''maximum_distance''' at most.
 
See [[#array-construction|array-construction]] for how to specify a map position list.
 
Example:
<syntaxhighlight lang="lua">
-- Shortest distance at the current {x, y} from the two given points, but at most 1000
 
local noise = require("noise")
local tne = noise.to_noise_expression
local positions = noise.make_point_list({{-100, -40}, {-50, -200}})
 
local shortest_distance =
{
  type = "function-application",
  function_name = "distance-from-nearest-point",
  arguments = {x = noise.var("x"), y = noise.var("y"), points = positions, maximum_distance = tne(1000)}
}
-- or with the noise lib
local also_shortest_distance = noise.function_application("distance-from-nearest-point", {x = noise.var("x"), y = noise.var("y"), points = positions, maximum_distance = 1000})
</syntaxhighlight>
 
=== ridge ===
'''Arguments (positional)''':
* '''value''' - number to be ridged
* '''floor''' - lower limit
* '''ceiling''' - upper limit
 
Similar to clamp but the input value is folded back across the upper and lower limits
until it lies between them.
 
Example:
<syntaxhighlight lang="lua">
local noise = require("noise")
 
local ridge_1 = noise.ridge(6, 1, 5) -- this returns 4
 
local ridge_2 = noise.ridge(-1, 1, 5) -- this returns 3
</syntaxhighlight>
 
=== terrace ===
'''Arguments (positional)''':
* '''value''' - number
* '''offset''' (constant) - number
* '''width''' (constant) - number
* '''strength''' - number
 
=== modulo ===
'''Arguments (positional)''':
* '''dividend''' - number
* '''divisor''' - number
 
Takes 2 positional arguments and divides the first by the second and returns the remainder. This is implemented using [https://en.cppreference.com/w/cpp/numeric/math/fmod fmod(double, double)].
 
=== floor ===
'''Arguments (positional)''':
* '''value''' - number
 
Takes one 1 numeric value and returns its floor.
 
=== ceil ===
'''Arguments (positional)''':
* '''value''' - number
 
Takes one 1 numeric value and returns its ceiling.
 
=== bitwise-and ===
'''Arguments (positional)''': between 0 and 999 numbers
 
Casts the positional arguments to signed 32-bit integers and performs bitwise AND on them.
 
=== bitwise-or ===
'''Arguments (positional)''': between 0 and 999 numbers
 
Casts the positional arguments to signed 32-bit integers and performs bitwise OR on them.
 
=== bitwise-xor ===
'''Arguments (positional)''': between 0 and 999 numbers
 
Casts the positional arguments to signed 32-bit integers and performs bitwise exclusive or on them.
 
=== bitwise-not ===
'''Arguments (positional)''':
* '''value''' - number to be negated
 
Casts the positional argument to a signed 32-bit integer and bitwise negates it.
 
=== sin ===
'''Arguments (positional)''':
* '''value''' - number
 
Takes one 1 value and returns its sine.
 
=== cos ===
'''Arguments (positional)''':
* '''value''' - number
 
Takes one 1 value and returns its cosine.
 
=== atan2 ===
'''Arguments (positional)''':
* '''y''' - number
* '''x''' - number
 
Returns the arc tangent of y/x using the signs of arguments to determine the correct quadrant.
 
=== less-than ===
'''Arguments (positional)''':
* '''lhs''' - number
* '''rhs''' - number
 
Returns the result of lhs < rhs as literal number that is 0 for false and 1 for true.
 
=== less-or-equal ===
'''Arguments (positional)''':
* '''lhs''' - number
* '''rhs''' - number
 
Returns the result of lhs <= rhs as literal number that is 0 for false and 1 for true.
 
=== equals ===
'''Arguments (positional)''':
* '''lhs''' - number
* '''rhs''' - number
 
Returns the result of lhs == rhs as literal number that is 0 for false and 1 for true.
 
=== factorio-basis-noise ===
 
'''Arguments (named)''':
 
* '''x'''
* '''y'''
* '''seed0''' - integer between 0 and 4294967295 (inclusive) used to populate the backing random noise
* '''seed1''' - integer between 0 and 255 (inclusive) used to provide extra randomness when sampling
* '''input_scale''' (default: 1) - x and y will be multiplied by this before sampling
* '''output_scale''' (default: 1) - output will be multiplied by this before being returned
 
Scaling input and output can be accomplished other ways, but are done so commonly
as to be built into this function for performance reasons.
 
=== factorio-quick-multioctave-noise ===
 
'''Arguments (named)''':
 
* '''x''' - number
* '''y''' - number
* '''seed0''' - number
* '''seed1''' - number
* '''input_scale''' - number
* '''output_scale''' - number
* '''octaves''' - number
* '''octave_input_scale_multiplier''' - number
* '''octave_output_scale_multiplier''' - number
* '''octave_seed0_shift''' - number
 
=== random-penalty ===
 
'''Arguments (named)''':
 
* '''x''' - number
* '''y''' - number
* '''source''' - number
* '''seed''' (constant) - number
* '''amplitude''' (constant) - number
 
=== log2 ===
 
'''Argument (positional)''': value (number)
 
=== noise-layer-name-to-id ===
 
'''Argument (positional)''': value (string)
 
=== autoplace-probability ===
 
'''Argument (positional)''': value (object)
 
=== autoplace-richness ===
 
'''Argument (positional)''': value (object)
 
<!-- Until 1.1.0 this will report "NoiseExpressions::fromPropertyTree not yet implemented for function 'offset-points'"
=== offset-points ===
 
'''Arguments (positional)''':
* '''offset''' - map position - Vector of how the positions should be shifted
* '''positions''' - list of map positions - The positions that should be shifted
 
See [[#array-construction|array-construction]] for how to specify map positions.
 
Example:
<syntaxhighlight lang="lua">
-- Shifts "positions" by {100, 90}
 
local noise = require("noise")
local positions = noise.make_point_list({{-10, -40}, {-50, -20}})
local offset = noise.make_array({100, 90})
local offset_positions =
{
  type = "function-application",
  function_name = "offset-points",
  arguments = {offset, positions}
}
-- or with the noise lib
local also_offset_positions = noise.function_application("offset-points", {offset, positions})
</syntaxhighlight>
 
-->=== factorio-multioctave-noise ===
 
'''Arguments (named)''':
 
* '''x'''
* '''y'''
* '''seed0''' - integer between 0 and 4294967295 (inclusive) used to populate the backing random noise
* '''seed1''' - integer between 0 and 255 (inclusive) used to provide extra randomness when sampling
* '''octaves''' - how many layers of noise at different scales to sum
* '''persistence''' (constant number) - how strong is each layer compared to the next larger one
* '''input_scale''' (default: 1) - x and y will be multiplied by this before sampling
* '''output_scale''' (default: 1) - output will be multiplied by this before being returned
 
=== spot-noise ===
 
Generates random conical spots.  The map is divided into square regions, and within each region, candidate points are chosen at random and target density, spot quantity, and radius are calculated for each point (or one of every '''skip_span''' candidate points) by configured expressions.  Each spot contributes a quantity to a regional target total (which is the average of sampled target densities times the area of the region) until the total has been reached or a maximum spot count is hit.  The output value of the function is the maximum height of any spot at a given point.
 
The parameters that provide expressions to be evaluated for each point (all named '''something_expression''') need to actually return expression objects. 
 
The quantity of the spot is assumed to be the same as its volume.  Since the volume of a cone is '''pi * radius^2 * height / 3''',
the height ('peak value') of any given spot is calculated as '''3 * quantity / (pi * radius^2)'''
 
'''Arguments (named)''':
 
* '''x''' (number)
* '''y''' (number)
* '''seed0''' (constant integer) - random seed, part 1 - usually the map seed is used
* '''seed1''' (constant integer) - random seed, part 2 - usually chosen to identify the noise layer
* '''region_size''' (constant integer, default: 512) - width/height of each region
* '''skip_offset''' (constant integer, default: 0) - offset of the first candidate point to use
* '''skip_span''' (constant integer, default: 1) - number of candidate points to skip over after each one used as a spot, including the used one
* '''candidate_point_count''' (constant integer, default:256) - how many candidate points to generate
* '''candidate_spot_count''' (constant integer, default depends on skip_span) - an alternative to candidate_point_count - number of spots to generate: '''candidate_spot_count = X''' is equivalent to '''candidate_point_count / skip_span = X'''
* '''suggested_minimum_candidate_point_spacing''' (constant number, default depends on region size and candidate_point_count) - minimum spacing to *try* to achieve while randomly picking points; spot noise may end up placing spots closer than this in crowded regions
* '''hard_region_target_quantity''' (constant boolean, default: true) - whether to place a hard limit on the total quantity in each region by reducing the size of any spot (which will be the last spot chosen) that would put it over the limit.
* '''density_expression''' (number-returningexpression) - an expression that will be evaluated for each candidate spot to calculate density at that point
* '''spot_quantity_expression''' (number-returningexpression) - an expression that will be evaluated for each candidate spot to calculate the spot's quantity
* '''spot_radius_expression''' (number-returning expression) - an expression that will be evaluated for each candidate spot to calculate the spot's radius (this, together with quantity, will determine the spots peak value)
* '''spot_favorability_expression''' (number-returning expression) - an expression that will be evaluated for each candidate spot to calculate the spot's favorability; spots with higher favorability will be considered first when building the final list of spots for a region
 
The infinite series of candidate points (of which '''candidate_point_count''' are actually considered) generated by '''spot-noise''' expressions with the same '''seed0''', '''seed1''', '''region_size''', and '''suggested_minimum_candidate_point_spacing''' will be identical.  This allows multiple spot-noise expressions (e.g. for different ore patches) to avoid overlap by using different points from the same list, determined by '''skip_span''' and '''skip_offset'''.
 
== Example definition ==
 
To override the 'temperature' named noise expression with one that linearly increases to the southeast:
 
<syntaxhighlight lang="lua">
local noise = require("noise");
 
data:extend{
  {
    type = "noise-expression",
    name = "new-temperature-function",
    intended_property = "temperature", -- Makes this available in the 'temperature generator' drop-down
    expression = noise.define_noise_function( function(x,y,tile,map)
      return (x + y) / 1000
    end)
  }
}
</syntaxhighlight>
 
Which is equivalent to:
 
<syntaxhighlight lang="lua">
data:extend{
  {
    type = "noise-expression",
    name = "new-temperature-function",
    intended_property = "temperature",
    expression = {
      type = "function-application",
      function_name = "divide",
      arguments = {
        {
          type = "function-application",
          function_name = "add",
          arguments = {
            {
              type = "variable",
              variable_name = "x"
            },
            {
              type = "variable",
              variable_name = "y"
            }
          }
        },
        {
          type = "literal-number",
          literal_value = 1000
        }
      }
    }
  }
}
</syntaxhighlight>
 
== See also ==
 
* [https://togos.github.io/togos-example-noise-programs/ A tutorial on authoring noise functions]

Latest revision as of 14:32, 25 October 2024

The prototype docs have moved to a new website with an improved format. This documentation page can now be found here: https://lua-api.factorio.com/latest/types/NoiseExpression.html

This wiki page is no longer updated and will be removed at some point in the future, so please update your browser bookmarks or other links that sent you here. If you'd like to contribute to the new docs, you can leave your feedback on the forums.

Retrieved from "https://wiki.factorio.com/index.php?title=Types/NoiseExpression&oldid=202822"