Think of a drop of water impacting a larger body of water. The impact site has the most intense energy. One then can see the energy disperse and get weaker as the energy moves away from the impact site. This thought of a water impact can be transferred into the realm of geographic thought. Viruses, political protests, fires, ideas, etc all can be effected by distance decay on both a macro and micro scale.
Not all space is equal so distance decay is not equal. Roads, mountains, water ways, and many more natural and man made obstacles slow and speed up distance decay. Other things can compete for space against the decaying phenomena and become stuck or even reversed.
Catholicgauze has even noticed some things act stronger in the ends rather than distance decay from some center point. Nationalism in particular becomes stronger when threatened by some foreign/counter force. Look at diaspora groups (Irish-Americans have greater militant republican tendencies than do most Irish) or near aboard groups (ethnic Russians fought and defeated Moldova in a war as the Soviet Union was falling apart).