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fastmath.random

Various random and noise functions.

Namespace defines various random number generators (RNGs), different types of random functions, sequence generators and noise functions.

RNGs

You can use a selection of various RNGs defined in Apache Commons Math library.

Currently supported RNGs:

  • :jdk - default java.util.Random
  • :mersenne - MersenneTwister
  • :isaac - ISAAC
  • :well512a, :well1024a, :well19937a, :well19937c, :well44497a, :well44497b - several WELL variants

To create your RNG use rng multimethod. Pass RNG name and (optional) seed. Returned RNG is equipped with [[RNGProto]] protocol with methods: irandom, lrandom, frandom drandom, grandom, brandom which return random primitive value with given RNG.

(let [rng (rng :isaac 1337)]
  (irandom rng))

For conveniency default RNG (:jdk) with following functions are created: irand, lrand, frand, drand, grand, brand.

Each prefix denotes returned type:

  • i - int
  • l - long
  • f - float
  • d - double
  • g - gaussian (double)
  • b - boolean

Check individual function for parameters description.

Random Vector Sequences

Couple of functions to generate sequences of numbers or vectors.

To create generator call sequence-generator with generator name and vector size. Following generators are available:

  • :halton - Halton low-discrepancy sequence; range [0,1]
  • :sobol - Sobol low-discrepancy sequence; range [0,1]
  • :r2 - R2 low-discrepancy sequence; range [0,1], more...
  • :sphere - uniformly random distributed on unit sphere
  • :ball - uniformly random distributed from unit ball
  • :gaussian - gaussian distributed (mean=0, stddev=1)
  • :default - uniformly random; range:[0,1]

:halton, :sobol and :r2 can be also randomly jittered according to this article. Call jittered-sequence-generator.

After creation you get lazy sequence

Noise

List of continuous noise functions (1d, 2d and 3d):

  • :value - value noise
  • :gradient - gradient noise (improved Ken Perlin version)
  • :simplex - simplex noise

First two (:value and :gradient) can use 4 different interpolation types: :none, :linear, :hermite (cubic) and :quintic.

All can be combined in following variants:

Noise creation requires detailed configuration which is simple map of following keys:

  • :seed - seed as integer
  • :noise-type - type of noise: :value, :gradient (default), :simplex
  • :interpolation - type of interpolation (for value and gradient): :none, :linear, :hermite (default) or :quintic
  • :octaves - number of octaves for combined noise (like FBM), default: 6
  • :lacunarity - scaling factor for combined noise, default: 2.00
  • :gain - amplitude scaling factor for combined noise, default: 0.5
  • :normalize? - should be normalized to [0,1] range (true, default) or to [-1,1] range (false)

For usage convenience 3 ready to use functions are prepared. Returning value from [0,1] range:

  • noise - Perlin Noise (gradient noise, 6 octaves, quintic interpolation)
  • vnoise - Value Noise (as in Processing, 6 octaves, hermite interpolation)
  • simplex - Simplex Noise (6 octaves)

For random noise generation you can use random-noise-cfg and random-noise-fn. Both can be feed with configuration. Additional configuration:

  • :generator can be set to one of the noise variants, defaults to :fbm
  • :warp-scale - 0.0 - do not warp, >0.0 warp
  • :warp-depth - depth for warp (default 1.0, if warp-scale is positive)

Discrete Noise

discrete-noise is a 1d or 2d hash function for given integers. Returns double from [0,1] range.

Distribution

Various real and integer distributions. See [[DistributionProto]] and [[RNGProto]] for functions.

To create distribution call distribution multimethod with name as a keyword and map as parameters.

Various random and noise functions.

Namespace defines various random number generators (RNGs), different types of random functions, sequence generators and noise functions.

### RNGs

You can use a selection of various RNGs defined in [Apache Commons Math](http://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math3/random/package-summary.html) library.

Currently supported RNGs:

* `:jdk` - default java.util.Random
* `:mersenne` - MersenneTwister
* `:isaac` - ISAAC
* `:well512a`, `:well1024a`, `:well19937a`, `:well19937c`, `:well44497a`, `:well44497b` - several WELL variants

To create your RNG use [[rng]] multimethod. Pass RNG name and (optional) seed. Returned RNG is equipped with [[RNGProto]] protocol with methods: [[irandom]], [[lrandom]], [[frandom]] [[drandom]], [[grandom]], [[brandom]] which return random primitive value with given RNG.

```
(let [rng (rng :isaac 1337)]
  (irandom rng))
```

For conveniency default RNG (`:jdk`) with following functions are created: [[irand]], [[lrand]], [[frand]], [[drand]], [[grand]], [[brand]].

Each prefix denotes returned type:

* i - int
* l - long
* f - float
* d - double
* g - gaussian (double)
* b - boolean

Check individual function for parameters description.

### Random Vector Sequences

Couple of functions to generate sequences of numbers or vectors.

To create generator call [[sequence-generator]] with generator name and vector size.
Following generators are available:

* `:halton` - Halton low-discrepancy sequence; range [0,1]
* `:sobol` - Sobol low-discrepancy sequence; range [0,1]
* `:r2` - R2 low-discrepancy sequence; range [0,1], [more...](http://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/)
* `:sphere` - uniformly random distributed on unit sphere
* `:ball` - uniformly random distributed from unit ball
* `:gaussian` - gaussian distributed (mean=0, stddev=1)
* `:default` - uniformly random; range:[0,1]

`:halton`, `:sobol` and `:r2` can be also randomly jittered according to this [article](http://extremelearning.com.au/a-simple-method-to-construct-isotropic-quasirandom-blue-noise-point-sequences/). Call [[jittered-sequence-generator]].

After creation you get lazy sequence

### Noise

List of continuous noise functions (1d, 2d and 3d):

* `:value` - value noise
* `:gradient` - gradient noise (improved Ken Perlin version)
* `:simplex` - simplex noise

First two (`:value` and `:gradient`) can use 4 different interpolation types: `:none`, `:linear`, `:hermite` (cubic) and `:quintic`.

All can be combined in following variants:

* Noise - pure noise value, create with [[single-noise]]
* FBM - fractal brownian motion, create with [[fbm-noise]]
* Billow - billow noise, [[billow-noise]]
* RidgedMulti - ridged multi, [[ridgedmulti-noise]]

Noise creation requires detailed configuration which is simple map of following keys:

* `:seed` - seed as integer
* `:noise-type` - type of noise: `:value`, `:gradient` (default), `:simplex`
* `:interpolation` - type of interpolation (for value and gradient): `:none`, `:linear`, `:hermite` (default) or `:quintic`
* `:octaves` - number of octaves for combined noise (like FBM), default: 6
* `:lacunarity` - scaling factor for combined noise, default: 2.00
* `:gain` - amplitude scaling factor for combined noise, default: 0.5
* `:normalize?` - should be normalized to `[0,1]` range (true, default) or to `[-1,1]` range (false)

For usage convenience 3 ready to use functions are prepared. Returning value from `[0,1]` range:

* [[noise]] - Perlin Noise (gradient noise, 6 octaves, quintic interpolation)
* [[vnoise]] - Value Noise (as in Processing, 6 octaves, hermite interpolation)
* [[simplex]] - Simplex Noise (6 octaves)

For random noise generation you can use [[random-noise-cfg]] and [[random-noise-fn]]. Both can be feed with configuration. Additional configuration:

* `:generator` can be set to one of the noise variants, defaults to `:fbm`
* `:warp-scale` - 0.0 - do not warp, >0.0 warp
* `:warp-depth` - depth for warp (default 1.0, if warp-scale is positive)

#### Discrete Noise

[[discrete-noise]] is a 1d or 2d hash function for given integers. Returns double from `[0,1]` range.

### Distribution

Various real and integer distributions. See [[DistributionProto]] and [[RNGProto]] for functions.

To create distribution call [[distribution]] multimethod with name as a keyword and map as parameters.
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->seqclj

(->seq)
(->seq rng)
(->seq rng n)
(->seq rng n sampling-method)

Returns lazy sequence of random samples (can be limited to optional n values).

Additionally one of the sampling methods can be provided, ie: :uniform, :systematic and :stratified.

Returns lazy sequence of random samples (can be limited to optional `n` values).

Additionally one of the sampling methods can be provided, ie: `:uniform`, `:systematic` and `:stratified`.
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ball-randomclj

(ball-random dims)
(ball-random rng dims)

Return random vector from a ball

Return random vector from a ball
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billow-noiseclj

(billow-noise)
(billow-noise cfg__6114__auto__)

Create billow noise function with optional configuration.

Create billow noise function with optional configuration.
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brandclj

Random boolean with default RNG.

Returns true or false with equal probability. You can set p probability for true

Random boolean with default RNG.

Returns true or false with equal probability. You can set `p` probability for `true`
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brandomclj

(brandom rng)
(brandom rng p)

Random boolean with provided RNG

Random boolean with provided RNG
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cdfclj

(cdf d v)
(cdf d v1 v2)

Cumulative probability.

Cumulative probability.
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continuous?clj

(continuous? d)

Does distribution support continuous domain?

Does distribution support continuous domain?
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covarianceclj

(covariance d)

Distribution covariance matrix (for multivariate distributions)

Distribution covariance matrix (for multivariate distributions)
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default-normalclj

Default normal distribution (u=0.0, sigma=1.0).

Default normal distribution (u=0.0, sigma=1.0).
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default-rngclj

Default RNG - JDK

Default RNG - JDK
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dimensionsclj

(dimensions d)

Distribution dimensionality

Distribution dimensionality
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discrete-noiseclj

(discrete-noise X)
(discrete-noise X Y)

Discrete noise. Parameters:

  • X (long)
  • Y (long, optional)

Returns double value from [0,1] range

Discrete noise. Parameters:

* X (long)
* Y (long, optional)

Returns double value from [0,1] range
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distributioncljmultimethod

Create distribution object.

  • First parameter is distribution as a :key.
  • Second parameter is a map with configuration.

All distributions accept rng under :rng key (default: default-rng) and some of them accept inverse-cumm-accuracy (default set to 1e-9).

Create distribution object.

* First parameter is distribution as a `:key`.
* Second parameter is a map with configuration.

All distributions accept `rng` under `:rng` key (default: [[default-rng]]) and some of them accept `inverse-cumm-accuracy` (default set to `1e-9`).
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distribution-idclj

(distribution-id d)

Distribution identifier as keyword.

Distribution identifier as keyword.
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distribution-parametersclj

(distribution-parameters d)
(distribution-parameters d all?)

Distribution highest supported value.

When all? is true, technical parameters are included, ie: :rng and :inverser-cumm-accuracy.

Distribution highest supported value.

When `all?` is true, technical parameters are included, ie: `:rng` and `:inverser-cumm-accuracy`.
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distributions-listclj

List of distributions.

List of distributions.
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drandclj

(drand)
(drand mx)
(drand mn mx)

Random double number with default RNG.

As default returns random double from [0,1) range. When mx is passed, range is set to [0, mx). When mn is passed, range is set to [mn, mx).

Random double number with default RNG.

As default returns random double from `[0,1)` range.
When `mx` is passed, range is set to `[0, mx)`. When `mn` is passed, range is set to `[mn, mx)`.
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drandomclj

(drandom rng)
(drandom rng mx)
(drandom rng mn mx)

Random double number with provided RNG

Random double number with provided RNG
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fbm-noiseclj

(fbm-noise)
(fbm-noise cfg__6114__auto__)

Create fbm noise function with optional configuration.

Create fbm noise function with optional configuration.
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flipclj

(flip)
(flip p)

Returns 1 with given probability, 0 otherwise

Returns 1 with given probability, 0 otherwise
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flipbclj

(flipb)
(flipb p)

Returns true with given probability, false otherwise

Returns true with given probability, false otherwise
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frandclj

(frand)
(frand mx)
(frand mn mx)

Random double number with default RNG.

As default returns random float from [0,1) range. When mx is passed, range is set to [0, mx). When mn is passed, range is set to [mn, mx).

Random double number with default RNG.

  As default returns random float from `[0,1)` range.
When `mx` is passed, range is set to `[0, mx)`. When `mn` is passed, range is set to `[mn, mx)`.
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frandomclj

(frandom rng)
(frandom rng mx)
(frandom rng mn mx)

Random double number with provided RNG

Random double number with provided RNG
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grandclj

(grand)
(grand stddev)
(grand mean stddev)

Random gaussian double number with default RNG.

As default returns random double from N(0,1). When std is passed, N(0,std) is used. When mean is passed, distribution is set to N(mean, std).

Random gaussian double number with default RNG.

As default returns random double from `N(0,1)`.
When `std` is passed, `N(0,std)` is used. When `mean` is passed, distribution is set to `N(mean, std)`.
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grandomclj

(grandom rng)
(grandom rng stddev)
(grandom rng mean stddev)

Random gaussian double number with provided RNG

Random gaussian double number with provided RNG
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icdfclj

(icdf d v)

Inverse cumulative probability

Inverse cumulative probability
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irandclj

(irand)
(irand mx)
(irand mn mx)

Random integer number with default RNG.

As default returns random integer from full integer range. When mx is passed, range is set to [0, mx). When mn is passed, range is set to [mn, mx).

Random integer number with default RNG.

  As default returns random integer from full integer range. 
When `mx` is passed, range is set to `[0, mx)`. When `mn` is passed, range is set to `[mn, mx)`.
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irandomclj

(irandom rng)
(irandom rng mx)
(irandom rng mn mx)

Random integer number with provided RNG

Random integer number with provided RNG
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jittered-sequence-generatorclj

(jittered-sequence-generator seq-generator dimensions)
(jittered-sequence-generator seq-generator dimensions jitter)

Create jittered sequence generator.

Suitable for :r2, :sobol and :halton sequences.

jitter parameter range is from 0 (no jitter) to 1 (full jitter). Default: 0.25.

See also sequence-generator.

Create jittered sequence generator.

Suitable for `:r2`, `:sobol` and `:halton` sequences.

`jitter` parameter range is from `0` (no jitter) to `1` (full jitter). Default: 0.25.

See also [[sequence-generator]].
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likelihoodclj

(likelihood d vs)

Likelihood of samples

Likelihood of samples
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log-likelihoodclj

(log-likelihood d vs)

Log likelihood of samples

Log likelihood of samples
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lower-boundclj

(lower-bound d)

Distribution lowest supported value

Distribution lowest supported value
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lpdfclj

(lpdf d v)

Log density

Log density
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lrandclj

(lrand)
(lrand mx)
(lrand mn mx)

Random long number with default RNG.

As default returns random long from full integer range. When mx is passed, range is set to [0, mx). When mn is passed, range is set to [mn, mx).

Random long number with default RNG.

  As default returns random long from full integer range. 
When `mx` is passed, range is set to `[0, mx)`. When `mn` is passed, range is set to `[mn, mx)`.
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lrandomclj

(lrandom rng)
(lrandom rng mx)
(lrandom rng mn mx)

Random long number with provided RNG

Random long number with provided RNG
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meanclj

(mean d)

Distribution mean

Distribution mean
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meansclj

(means d)

Distribution means (for multivariate distributions)

Distribution means (for multivariate distributions)
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noiseclj

(noise x)
(noise x y)
(noise x y z)

Improved Perlin Noise.

6 octaves, quintic interpolation.

Improved Perlin Noise.

6 octaves, quintic interpolation.
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noise-generatorsclj

List of possible noise generators as a map of names and functions.

List of possible noise generators as a map of names and functions.
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noise-interpolationsclj

List of possible noise interpolations as a map of names and values.

List of possible noise interpolations as a map of names and values.
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noise-typesclj

List of possible noise types as a map of names and values.

List of possible noise types as a map of names and values.
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observecljmacro

(observe d vs)

Log likelihood of samples. Alias for log-likelihood.

Log likelihood of samples. Alias for [[log-likelihood]].
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observe1clj

(observe1 d v)

Log of probability/density of the value. Alias for lpdf.

Log of probability/density of the value. Alias for [[lpdf]].
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pdfclj

(pdf d v)

Density

Density
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probabilityclj

(probability d v)

Probability (PMF)

Probability (PMF)
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random-noise-cfgclj

(random-noise-cfg)
(random-noise-cfg pre-config)

Create random noise configuration.

Optional map with fixed values.

Create random noise configuration.

Optional map with fixed values.
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random-noise-fnclj

(random-noise-fn)
(random-noise-fn cfg)

Create random noise function from all possible options.

Optionally provide own configuration cfg. In this case one of 4 different blending methods will be selected.

Create random noise function from all possible options.

Optionally provide own configuration `cfg`. In this case one of 4 different blending methods will be selected.
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randvalcljmacro

(randval)
(randval prob)
(randval v1 v2)
(randval prob v1 v2)

Retrun value with given probability (default 0.5)

Retrun value with given probability (default 0.5)
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ridgedmulti-noiseclj

(ridgedmulti-noise)
(ridgedmulti-noise cfg__6114__auto__)

Create ridgedmulti noise function with optional configuration.

Create ridgedmulti noise function with optional configuration.
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rngcljmultimethod

Create RNG for given name (as keyword) and optional seed. Return object enhanced with [[RNGProto]]. See: rngs-list for names.

Create RNG for given name (as keyword) and optional seed. Return object enhanced with [[RNGProto]]. See: [[rngs-list]] for names.
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rngs-listclj

List of all possible RNGs.

List of all possible RNGs.
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sampleclj

(sample d)

Random sample

Random sample
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sequence-generatorcljmultimethod

Create Sequence generator. See sequence-generators-list for names.

Values:

  • :r2, :halton, :sobol, :default - range [0-1] for each dimension
  • :gaussian - from N(0,1) distribution
  • :sphere - from surface of unit sphere (ie. euclidean distance from origin equals 1.0)
  • :ball - from an unit ball

Possible dimensions:

  • :r2 - 1-15
  • :halton - 1-40
  • :sobol - 1-1000
  • the rest - 1+

See also jittered-sequence-generator.

Create Sequence generator. See [[sequence-generators-list]] for names.

Values:

* `:r2`, `:halton`, `:sobol`, `:default` - range `[0-1] for each dimension`
* `:gaussian` - from `N(0,1)` distribution
* `:sphere` -  from surface of unit sphere (ie. euclidean distance from origin equals 1.0)
* `:ball` - from an unit ball

Possible dimensions:

* `:r2` - 1-15
* `:halton` - 1-40
* `:sobol` - 1-1000
* the rest - 1+

See also [[jittered-sequence-generator]].
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sequence-generators-listclj

List of random sequence generator. See sequence-generator.

List of random sequence generator. See [[sequence-generator]].
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set-seed!clj

(set-seed!)
(set-seed! v)
(set-seed! rng v)

Sets seed.

If rng is :smile calls smile.math.MathEx/setSeed().

Without rng sets both :smile and default-rng

Sets seed.

If `rng` is `:smile` calls `smile.math.MathEx/setSeed()`.

Without `rng` sets both `:smile` and `default-rng`
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simplexclj

(simplex x)
(simplex x y)
(simplex x y z)

Simplex noise. 6 octaves.

Simplex noise. 6 octaves.
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single-noiseclj

(single-noise)
(single-noise cfg__6114__auto__)

Create single noise function with optional configuration.

Create single noise function with optional configuration.
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source-objectclj

(source-object d)

Returns Java or proxy object from backend library (if available)

Returns Java or proxy object from backend library (if available)
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synced-rngclj

(synced-rng m)
(synced-rng m seed)

Create synchronized RNG for given name and optional seed. Wraps rng method.

Create synchronized RNG for given name and optional seed. Wraps [[rng]] method.
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upper-boundclj

(upper-bound d)

Distribution highest supported value

Distribution highest supported value
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varianceclj

(variance d)

Distribution variance

Distribution variance
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vnoiseclj

(vnoise x)
(vnoise x y)
(vnoise x y z)

Value Noise.

6 octaves, Hermite interpolation (cubic, h01).

Value Noise.

6 octaves, Hermite interpolation (cubic, h01).
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warp-noise-fnclj

(warp-noise-fn)
(warp-noise-fn noise)
(warp-noise-fn noise scale)
(warp-noise-fn noise scale depth)

Create warp noise (see Inigo Quilez article).

Parameters:

  • noise function, default: vnoise
  • scale factor, default: 4.0
  • depth (1 or 2), default 1

Normalization of warp noise depends on normalization of noise function.

Create warp noise (see [Inigo Quilez article](http://www.iquilezles.org/www/articles/warp/warp.htm)).

Parameters:

* noise function, default: vnoise
* scale factor, default: 4.0
* depth (1 or 2), default 1

Normalization of warp noise depends on normalization of noise function.
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