Spatial point configurations are collections of points (or events) in space. Examples include the location of trees in a forest, the location of gold deposits, the location of stars, the location of earthquakes, crime locations, animal sightings, etc. Often the objective is to quantify trends in the density of points, presence of clustering or regularity and to give models that can generate similar point patterns. Spatial point pattern and point process analysis is used in ecology, epidemiology, geoscience, astronomy, econometrics and crime research, etc. The Wolfram Language provides a complete toolkit for working with spatial point patterns and point processes, from exploratory analysis with visualization and descriptive statistics to modeling and simulation.

Spatial Point Data

SpatialPointData — create and represent spatial point data with observation region

SpatialBinnedPointData — represent aggregated point data with any region partition

ResourceData — spatial point datasets from a variety of sources

RandomPointConfiguration — simulated data from spatial point processes

SpatialPointSelect  ▪  SpatialObservationRegionQ  ▪  RipleyRassonRegion

Models of Spatial Point Data »

RandomPointConfiguration — simulate a point process

EstimatedPointProcess — estimate a point process from spatial point configurations

PoissonPointProcess  ▪  MaternPointProcess  ▪  GibbsPointProcess  ▪  ...

PointValuePlot — plot point configurations with value annotations

Spatial Point Visualization

GeoListPlot  ▪  ListPlot  ▪  ListPointPlot3D

Spatial Point & Annotation Visualization

GeoBubbleChart  ▪  BubbleChart  ▪  BubbleChart3D

Spatial Point Intensity Visualization

GeoHistogram  ▪  GeoSmoothHistogram  ▪  DensityHistogram  ▪  SmoothDensityHistogram  ▪  Histogram3D  ▪  SmoothHistogram3D

Location Measures

Mean — centroid of points

SpatialMedian — location in region with minimum distance to all points

CentralFeature — point in collection with minimum distance to all points

Density Measures

MeanPointDensity — average number of points per area, volume, etc.

PointDensity — varying point density function

HistogramPointDensity  ▪  SmoothPointDensity  ▪  PointDensityFunction

Counting Measures

PointCountDistribution — the distribution of point counts for any region

Homogeneity Measures

RipleyK — expected number of points within distance r of each point

BesagL — normalized version of Ripley's K function

EmptySpaceF — probability of finding another point within distance r of any location

NearestNeighborG — probability of finding another point within distance r of a point

PairCorrelationG — probability density of having two points a distance apart

SpatialJ — the function

SpatialBoundaryCorrection  ▪  SpatialObservationRegionQ  ▪  RipleyRassonRegion  ▪  PointStatisticFunction

Hypothesis Tests

SpatialRandomnessTest — test whether data is uniformly distributed

PointProcessFitTest — test whether data follows a point process

Spatial Graphs & Meshes

SpatialGraphDistribution  ▪  FindSpanningTree

NearestNeighborGraph  ▪  DelaunayMesh  ▪  VoronoiMesh

Locations of 1854 London cholera outbreak - ExampleData["Sample Data: London Cholera"]

Craters in Uganda volcanic field - ExampleData["Sample Data: Bunyaruguru Crater Field"]

Locations of trees with trunk diameters - ExampleData["Sample Data: Longleaf Pines"]

Nesting sites for a group of gorillas - ExampleData["Gorilla Nesting Sites"]

Locations of geological features in Ozarks - ExampleData["Sample Data: Ozarks Karst"]