# Distance decay

Distance decay is a geographical term which describes the effect of distance on cultural or spatial interactions. The distance decay effect states that the interaction between two locales declines as the distance between them increases. Once the distance is outside of the two locales' activity space, their interactions begin to decrease.

With the advent of faster travel, distance has less effect than it did in the past, except where places previously connected by now-abandoned railways, for example, have fallen off the beaten path. Advances in communications technology, such as telegraphs, telephones, broadcasting, and internet, have further decreased the effects of distance.[1]

Distance decay is graphically represented by a curving line that swoops concavely downward as distance along the x-axis increases. Distance decay can be mathematically represented as an Inverse-square law by the expression

${\displaystyle I=const.\times d^{-2}}$ or ${\displaystyle I\propto 1/d^{2}}$,

where I is interaction and d is distance. It can take other forms such as negative exponential,[2] i.e.

${\displaystyle I\propto e^{-d}}$ .

Distance decay is evident in town/city centres. It can refer to various things which decline with greater distance from the center of the Central Business District (CBD):

• density of pedestrian traffic
• street quality
• quality of shops (depending on definitions of 'quality' and 'center')
• height of buildings
• price of land

Distance decay weighs into the decision to migrate, leading many migrants to move less far.

Related terms include "friction of distance", which describes the force that creates distance decay and Waldo R. Tobler's "First law of geography", an informal statement that "All things are related, but near things are more related than far things." "Loss of Strength Gradient" holds that the amount of a nation's military power that could be brought to bear in any part of the world depends on geographic distance.