What type of data do you have? latest methods of spatial pattern analysis can be use very easily in ARC GIS or QGIS.

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Landuse landcover change analysis and spatial point pattern analysis are some methods of spatial pattern analysis.

I tend to work with polygon spatial units as opposed to point data, but I find that LISA (Anselin, 1995) tools are very beneficial for pattern analysis. If you are using GIS, you can use:

Toolbox>Spatial Statistics Tools> Mapping Clusters > Cluster and Outlier Analysis (Anselin Local Moran I).

As I said, if you are using point data, this may need to be aggregated first. The link to this tool description below should have the information you need.

https://desktop.arcgis.com/en/arcmap/10.3/tools/spatial-statistics-toolbox/h-how-cluster-and-outlier-analysis-anselin-local-m.htm

I find the outputs very beneficial for getting the most out of pattern analysis. This gives you areas of high and low clusters, but also areas that are outliers in comparison to surrounding features and may be worth examining in more detail. The output map is also structured well to convey information clearly to the reader, easy to understand, and gives a good deal of information for just one graphic.

Hope some of that helps, and best of luck with the work.

If you specify the type of point data available to you, we can recommend suitable methods for its analysis in space and time.

Thanks.

The latest methods are many however it depends on the time of the data you have. All in all I would recomend ArcGIS Pro. ArcGIS Pro is the latest professional desktop GIS application a product of Esri. With ArcGIS Pro, you can explore, visualize, and analyze data; create 2D maps and 3D scenes.

QGIS MOLUSCE plugin