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I have 50m X 200m polygon which has several small polygons inside. I would like to define how scattered small polygons inside a big polygon. I was wondering if there is a tool which can calculate some index based on the distribution of polygons across a big polygon. For example, if polygons are gathered it would give index 0 and if they are scattered well index would be 1. Is there any tool that I can use? ArcGIS or QGIS would be good.

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ArcGIS's Spatial Analyst toolset has

I don't see any tool in QGIS that definitely does the same thing. Here are a few things that look like they might do something relevant.

  • The SAGA Spatial point pattern analysis tool provides "a simple indication of the spatial distribution of points." This tool has a tutorial here. The centroids tool will convert your polygons to points so you can run the spatial point pattern analysis tool.

  • QGIS also has various cluster analysis tools. Most of them just divide points up into clusters without providing any measure of "clustered-ness" (ie spatial homo/heterogeneity).

  • The Visualist plugin has the tag spatial autocorrelation map.

  • Per user30184's comment, you could try to implement the spatial homogeneity measures (Ripley's K and L functions) explained in this Wikipedia article. Ripley's K function is explained in more detail in this article. Here are a few tips/suggestions:

    • As above, convert the small polygons to points.
    • Use the distance matrix tool to calculate the distance between each pair of points (this will provide the dij values).

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