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RandomPointConfiguration—Wolfram Documentation

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RandomPointConfiguration[pproc,reg]

generates a pseudorandom spatial point configuration from the spatial point process pproc in the observation region reg.

RandomPointConfiguration[pproc,reg, n]

generates an ensemble of n spatial point configurations.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Method  
WorkingPrecision  
Applications  
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RandomPointConfiguration

RandomPointConfiguration[pproc,reg]

generates a pseudorandom spatial point configuration from the spatial point process pproc in the observation region reg.

RandomPointConfiguration[pproc,reg, n]

generates an ensemble of n spatial point configurations.

Details and Options

  • RandomPointConfiguration takes a point process pproc and generates a point configuration as a SpatialPointData object.
  • RandomPointConfiguration gives a different realization of pseudorandom point configurations whenever you run the Wolfram Language. You can start with a particular seed using SeedRandom.
  • The same process can generate an ensemble consisting of different realizations.
  • The observation region reg needs to be a parameter-free region, as well as SpatialObservationRegionQ.
  • The following options can be given:
  • Method Automaticwhat method to use
    WorkingPrecision MachinePrecisionprecision used in internal computations
  • With the setting WorkingPrecisionp, random numbers of precision p will be generated.
  • Special settings for Method are documented under the individual point process reference pages.
  • Typical Method settings include:
  • "MCMC"Markov chain Monte Carlo birth and death
    "Thinning"random thinning
    "Exact"coupling from the past

Examples

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Basic Examples  (3)

Sample from a Poisson point process:

Wolfram Language code: pts = RandomPointConfiguration[PoissonPointProcess[10, 2], Disk[]]
Wolfram Language code: Show[RegionPlot[pts["ObservationRegion"]], ListPlot[pts]]

Sample 5 realizations from a binomial point process:

Wolfram Language code: reg = Ellipsoid[{1, 0, 0}, {1, 2, 3}]; pts = RandomPointConfiguration[BinomialPointProcess[10, reg], reg, 5]
Wolfram Language code: pts["ConfigurationCount"]
Wolfram Language code: pts["PointCountList"]

Sample from a cluster point process defined on the surface of the Earth:

Wolfram Language code: reg = Entity["Country", "Switzerland"]["Polygon"]
Wolfram Language code: proc = MaternPointProcess[Quantity[.005, "Kilometers" ^ -2], 30, Quantity[30, "Kilometers"], 2];
Wolfram Language code: pts = RandomPointConfiguration[proc, reg]
Wolfram Language code: PointValuePlot[pts]

Scope  (5)

RandomPointConfiguration returns a SpatialPointData object:

Wolfram Language code: sample = RandomPointConfiguration[PoissonPointProcess[3, 3], Ball[]]

Obtain a list of locations of the points:

Wolfram Language code: sample["Points"]

Simulate a Strauss point process in a rectangle:

Wolfram Language code: proc = StraussPointProcess[20, 0.2, 0.2, 2]; data = RandomPointConfiguration[proc, Rectangle[{0, 0}, {4, 6}]]

Retrieve points that lie within a unit disk centered at {2,3}:

Wolfram Language code: data1 = SpatialPointData[data, Disk[{2, 3}]]

Visualize points on the plane:

Wolfram Language code: ListPlot[data]

Estimate the parameters for a point process using a simulated point configuration:

Wolfram Language code: data = RandomPointConfiguration[HardcorePointProcess[10, 0.1, 2], Disk[]];
Wolfram Language code: EstimatedPointProcess[data, HardcorePointProcess[mu, r, 2]]

Simulate from a Cauchy point process:

Wolfram Language code: proc = CauchyPointProcess[100, 50, 0.005, 2]; data = RandomPointConfiguration[proc, Triangle[]];
Wolfram Language code: ListPlot[data]

Estimate Ripley's function from the sampled point configuration and compare it with the theoretical function:

Wolfram Language code: kfun = RipleyK[data];
Wolfram Language code: Plot[{kfun[r], RipleyK[proc, r]}, {r, 0, 0.25}, PlotLegends -> {"Estimated", "Theoretical"}]

Simulate an ensemble of 5 realizations over the same region:

Wolfram Language code: data = RandomPointConfiguration[InhomogeneousPoissonPointProcess[Function[{x, y}, 2Exp[Sin[x - y]]], 2], Rectangle[{0, 0}, {10, 10}], 4];

Number of points in each realization:

Wolfram Language code: data["PointCountList"]

Visualize the distribution of points in different realizations:

Wolfram Language code: ListPlot[data]

Options  (3)

Method  (2)

Sample from an InhomogeneousPoissonPointProcess using the different methods:

Wolfram Language code: reg = Ellipsoid[{1, 0}, {2, 1.5}];
Wolfram Language code: proc = InhomogeneousPoissonPointProcess[Function[{x, y}, 2 * Exp[x + y]], 2];

Use the method "Thinning":

Wolfram Language code: pts1 = RandomPointConfiguration[proc, reg, Method -> "Thinning"]

Use the Markov chain Monte Carlo method "MCMC":

Wolfram Language code: pts2 = RandomPointConfiguration[proc, reg, Method -> "MCMC"]

Visualize samples over the region:

Wolfram Language code: {Show[RegionPlot[reg], ListPlot[pts1]], Show[RegionPlot[reg], ListPlot[pts2]]}

Sample from a Gibbs point process using the Markov chain Monte Carlo method "MCMC" with the number of iterations equal to 30000:

Wolfram Language code: β = 10;h = Function[pts, β ^ Length[pts]]; region = Disk[];n = 20;
Wolfram Language code: sample = RandomPointConfiguration[GibbsPointProcess[h, 2], region, n, Method -> {"MCMC", "LengthOfRun" -> 30000}]
Wolfram Language code: Show[RegionPlot[sample["ObservationRegion"]], ListPlot[sample]]

WorkingPrecision  (1)

Generate a sample point configuration with default machine precision:

Wolfram Language code: RandomPointConfiguration[PoissonPointProcess[3, 2], Disk[]]["Points"]

Use WorkingPrecision to generate a sample point configuration with higher precision:

Wolfram Language code: RandomPointConfiguration[PoissonPointProcess[3, 2], Disk[], WorkingPrecision -> 20]["Points"]

Applications  (2)

Estimate the density of a PoissonPointProcess from a sample:

Wolfram Language code: β = 10;region = Disk[]; samples = RandomPointConfiguration[PoissonPointProcess[β, 2], region]

The intensity estimate:

Wolfram Language code: N[μ /. FindPointProcessParameters[samples, PoissonPointProcess[μ, 2]]]

Compare the expected point counts and the average of number of points for an inhomogeneous Poisson point process:

Wolfram Language code: reg = Ellipsoid[{1, 0}, {1, 3}]; pts = RandomPointConfiguration[InhomogeneousPoissonPointProcess[Function[{x, y}, Exp[x + y]], 2], reg, 500, Method -> "Thinning"]
Wolfram Language code: {Integrate[Exp[x + y], {x, y}∈reg], Mean[pts["PointCountList"]]}//N
Wolfram Research (2020), RandomPointConfiguration, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomPointConfiguration.html.

Text

Wolfram Research (2020), RandomPointConfiguration, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomPointConfiguration.html.

CMS

Wolfram Language. 2020. "RandomPointConfiguration." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RandomPointConfiguration.html.

APA

Wolfram Language. (2020). RandomPointConfiguration. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomPointConfiguration.html

BibTeX

@misc{reference.wolfram_2026_randompointconfiguration, author="Wolfram Research", title="{RandomPointConfiguration}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/RandomPointConfiguration.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_randompointconfiguration, organization={Wolfram Research}, title={RandomPointConfiguration}, year={2020}, url={https://reference.wolfram.com/language/ref/RandomPointConfiguration.html}, note=[Accessed: 14-November-2026]}