MaternPointProcess
✖
MaternPointProcess
represents a Matérn cluster point process with density μ, cluster mean λ and radius rm in .
Details

- MaternPointProcess models clustered point configurations with cluster centers uniformly distributed over space and cluster points isotropically distributed with a uniform radial distribution.
-
- Typical uses include things like plants or trees as centers with seedlings as the points of the cluster.
- The cluster centers are placed according to PoissonPointProcess with density μ.
- The point count of a cluster is distributed according to PoissonDistribution with mean λ.
- The cluster points are uniformly distributed in a ball of radius rm around the cluster center.
-
- MaternPointProcess allows μ, λ and rm to be any positive real numbers and d to be any positive integer.
- The following settings can be used for PointProcessEstimator for estimating MaternPointProcess:
-
"FindClusters" use FindClusters function "MethodOfMoments" use a homogeneity measure to estimate the parameters - MaternPointProcess can be used with such functions as RipleyK, PointCountDistribution and RandomPointConfiguration.
Examples
open allclose allBasic Examples (3)Summary of the most common use cases
Sample from a Matérn point process over a unit disk:

https://wolfram.com/xid/0k7xsqtlgylde-4mqsf


https://wolfram.com/xid/0k7xsqtlgylde-d381by

Sample from a Matérn point process over a unit ball:

https://wolfram.com/xid/0k7xsqtlgylde-dgk7lg


https://wolfram.com/xid/0k7xsqtlgylde-svdcv0

Sample from a Matérn point process over a geo region:

https://wolfram.com/xid/0k7xsqtlgylde-uf2aio

https://wolfram.com/xid/0k7xsqtlgylde-uc5jvc


https://wolfram.com/xid/0k7xsqtlgylde-ng3ovh

Scope (3)Survey of the scope of standard use cases
Sample from a valid region whose dimension is equal to its embedding dimension:

https://wolfram.com/xid/0k7xsqtlgylde-qxrhco

https://wolfram.com/xid/0k7xsqtlgylde-pacet0

Sample from a Matérn point process in the region and visualize the points:

https://wolfram.com/xid/0k7xsqtlgylde-ydq337


https://wolfram.com/xid/0k7xsqtlgylde-h8cla8

Simulate a point configuration from a Matérn point process:

https://wolfram.com/xid/0k7xsqtlgylde-8c7zax

https://wolfram.com/xid/0k7xsqtlgylde-9g5xhe

Use the "FindClusters" method to estimate a point process model:

https://wolfram.com/xid/0k7xsqtlgylde-3o7emz

Compare the Ripley measure between the original process and the estimated model:

https://wolfram.com/xid/0k7xsqtlgylde-m5qyr2

Pair correlation function of a Matérn point process:

https://wolfram.com/xid/0k7xsqtlgylde-0puauw

Visualize the function with given parameter values:

https://wolfram.com/xid/0k7xsqtlgylde-daj61m

Properties & Relations (5)Properties of the function, and connections to other functions
PointCountDistribution is known:

https://wolfram.com/xid/0k7xsqtlgylde-pfh07m

https://wolfram.com/xid/0k7xsqtlgylde-69w4w


https://wolfram.com/xid/0k7xsqtlgylde-6765kl


https://wolfram.com/xid/0k7xsqtlgylde-iw9fj7


https://wolfram.com/xid/0k7xsqtlgylde-k0gjl
The probability density histogram:

https://wolfram.com/xid/0k7xsqtlgylde-nd9jc

Ripley's and Besag's
for Matérn point process in 2D:

https://wolfram.com/xid/0k7xsqtlgylde-zht24f

https://wolfram.com/xid/0k7xsqtlgylde-rsadsn


https://wolfram.com/xid/0k7xsqtlgylde-tcihup


https://wolfram.com/xid/0k7xsqtlgylde-5pj0tq

Ripley's of Matérn point process is larger than for a Poisson point process:

https://wolfram.com/xid/0k7xsqtlgylde-zglflc

https://wolfram.com/xid/0k7xsqtlgylde-forzeq

Compare to the Poisson point process:

https://wolfram.com/xid/0k7xsqtlgylde-cp3zmu

https://wolfram.com/xid/0k7xsqtlgylde-9isgv3

Besag's of Matérn point process is larger than for a Poisson point process:

https://wolfram.com/xid/0k7xsqtlgylde-ch3e7z

https://wolfram.com/xid/0k7xsqtlgylde-egoxn6

Compare to the Poisson point process:

https://wolfram.com/xid/0k7xsqtlgylde-cgq77l

https://wolfram.com/xid/0k7xsqtlgylde-sqgcvm

Pair correlation of Matérn point process is larger than 1:

https://wolfram.com/xid/0k7xsqtlgylde-2w2wb7

Compare to homogeneous Poisson point process:

https://wolfram.com/xid/0k7xsqtlgylde-ydohzs

Possible Issues (1)Common pitfalls and unexpected behavior
The estimation algorithm splitting the point data into clusters may find a different cluster radius than in a model used to create a given point collection:

https://wolfram.com/xid/0k7xsqtlgylde-w9v2sr

https://wolfram.com/xid/0k7xsqtlgylde-xjutht

Therefore, specifying a smaller cluster radius than is inferred from the data will result in the failure of finding a point process model:

https://wolfram.com/xid/0k7xsqtlgylde-esn2pa


Wolfram Research (2020), MaternPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/MaternPointProcess.html.
Text
Wolfram Research (2020), MaternPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/MaternPointProcess.html.
Wolfram Research (2020), MaternPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/MaternPointProcess.html.
CMS
Wolfram Language. 2020. "MaternPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MaternPointProcess.html.
Wolfram Language. 2020. "MaternPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MaternPointProcess.html.
APA
Wolfram Language. (2020). MaternPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaternPointProcess.html
Wolfram Language. (2020). MaternPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaternPointProcess.html
BibTeX
@misc{reference.wolfram_2025_maternpointprocess, author="Wolfram Research", title="{MaternPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/MaternPointProcess.html}", note=[Accessed: 19-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_maternpointprocess, organization={Wolfram Research}, title={MaternPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/MaternPointProcess.html}, note=[Accessed: 19-June-2025
]}