Background on the process of diluted gene fragments passing from generation to generation
Here are some good resources to explain gene fragments passed down from a common ancestor to generation to generation.
http://www.isogg.org/wiki/Identical_By_Descent_segment
http://www.isogg.org/wiki/Wiki_Welcome_Page
http://www.isogg.org/wiki/Relative_Finder#Thresholds_for_relationship_matches
http://www.isogg.org/wiki/Autosomal_DNA_tools
There is an interesting user-controlled animation here:
http://learn.genetics.utah.edu/content/begin/tour/