QGIS (http://www.qgis.org/zh_CN/site/) is the most commonly used free open source software for analysis and visualization of spatial data. It is user friendly, well-documented, equipped with hundreds of tools, and enables implementation of user's algorithms.
SAGA GIS (https://sourceforge.net/projects/saga-gis/) and GRASS GIS (https://grass.osgeo.org/) are also worth to consider. They can be installed as standalone, but they are additionally integrated in QGIS.
I think it is always worth playing around with R. It is a bit of a steep learning curve but if you can find someone to help you get started it is not that hard.
QGIS (http://www.qgis.org/zh_CN/site/) is the most commonly used free open source software for analysis and visualization of spatial data. It is user friendly, well-documented, equipped with hundreds of tools, and enables implementation of user's algorithms.
SAGA GIS (https://sourceforge.net/projects/saga-gis/) and GRASS GIS (https://grass.osgeo.org/) are also worth to consider. They can be installed as standalone, but they are additionally integrated in QGIS.
I concur with Selim that the best software is ArcGIS to do the kind of analysis required though it is a Professional software - with relatively affordable versions. The free software usually have limited operations and affects the map output accuracy and quality - neccesary for informed decion making . See ESRI @; www.esri.com
I highly recomend you use R for spatial analysis. Here i attach you two references that may help: - https://www.researchgate.net/publication/258151270_An_Introduction_to_Mapping_and_Spatial_Modelling_in_R
- In my opinion "raster" library is very useful, almost you can do the same as with others not free sofwares as ArcMap: https://cran.r-project.org/web/packages/raster/raster.pdf
And also, as others mentioned above, QGIS is a good tool. Here you can find a tutorial that can help for your first contact with it: http://www.qgistutorials.com/es/
Good luck!
Book An Introduction to Mapping and Spatial Modelling in R
If you use Python, you can try Pysal for spatial analysis (https://github.com/pysal/pysal). For regression based methods, you can use GeoDa and GWR software.
In addition to all the above softwars, I gust recommend "ILWIS for windows" which is one of the most useful and Applicable; in the spatial data analysis. it is a package that can be used by Free "R" statistical program in developing steps.
Hello, I am kinda new to remote sensing, what satellite images are best for the analysis of land use patterns in the urban areas and why? - ResearchGate. Available from: https://www.researchgate.net/post/Hello_I_am_kinda_new_to_remote_sensing_what_satellite_images_are_best_for_the_analysis_of_land_use_patterns_in_the_urban_areas_and_why?tpr_view=OUMTBDy454MNdnVvmoLr5W1v1Le2ALcIobig_3#5892d7fd48954ccc661a860b [accessed Feb 2, 2017].
Article Peri-Urban to Urban Landscape Patterns Elucidation through S...
Article Land Surface Temperature Responses to Land Use Land Cover Dynamics
Article Spatio-temporal dynamics along the terrain gradient of diver...
Article Geospatial analysis of forest fragmentation in Uttara Kannad...
TdhGIS (http://www.tdhgis.com) is totally free spatial analysis software. Users can be accomplishing useful work within minutes on virtually any hardware running MS Windows or Linux. TdhGIS focuses on spatial analysis functionality and data exchange with 3rd party software.
Since TdhGIS shares much code with TdhCAD, it provides much CAD like functionality for graphical manipulation of geometric data, exchanges geometric data with TdhCAD and allow a CAD overlay for annotations and symbols.
TdhGIS is a great tool for users who need basic spatial analysis functionality without all the baggage of commercial GIS software.
Spatial Efficiency metric (SPAEF) is proven to be robust when comparing two raster maps. Python and Matlab codes are available at: http://space.geus.dk/tools_products/index.html
For doing spatial pattern analysis, you can use FRAGSTATS software (open source) which is designed to compute a wide variety of landscape metrics for categorical map patterns. It is available at: https://www.umass.edu/landeco/research/fragstats/fragstats.html
McGarigal, K., SA Cushman, and E Ene. 2012. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical and Continuous Maps. Computer software program produced by the authors at the University of Massachusetts, Amherst. Available at the following web site: http://www.umass.edu/landeco/research/fragstats/fragstats.html
QGIS and GRASS if you come from the GIS world and you want to produce nice looking maps.
SAGA GIS if you come from the soils/terrain analysis world, and you want to perform analysis that integrates rasters and DEM metrics.
R if you come from the statistics world and you are interested in real stat analysis.
Julia if you come from a computer science background and speed is important for you.
It all dependes on your expertise. R is probably the most flexibility but with the steepest learning curve for a non-statistician, together with Julia.