distances - Does Tobler's First Law of Geography Apply to Star Composition?

There have of course been extensive observations of clusters of stars. To all intents and purposes, to the limits of experimental accuracy, it looks like stars that are born in the same open cluster or star-forming region are all born with the same composition. e.g. http://adsabs.harvard.edu/abs/2014A%26A...567A..55S , http://adsabs.harvard.edu/abs/2002AJ....124.2799W , http://adsabs.harvard.edu/abs/2007AJ....133.1161D

There are of course various photospheric abundance anomalies in some stars, but these are normally ascribed to mixing processes or nucleosynthesis within the stars, not their birth composition.

The situation in globular clusters is not so clear cut. Multiple populations distinguished by their chemical compositions have been found. Possibly as a result of ancient mergers. So this does not perhaps represent a violation of Tobler's law since these stars would actually have been born in different environments.

Once stars leave their birth environment then they very quickly become mixed around the Galaxy. A star with a peculiar velocity of only 1km/s will travel a parsec in a million years. Stars born in the same place are probably widely distributed around the galaxy in a billion years or so. Most of the mixing is in azimuth or vertically, rather than Galactocentric radius.

Nevertheless there is a radial dependence (Galactocentric radius) of chemical composition (e.g. http://adsabs.harvard.edu/abs/2010A%26A...511A..56P ). Thus stars with similar Galactocentric radii have similar gross chemical compositions (with some scatter). But then this does violate Tobler's law because it means there is a similarity between objects that are on opposite sides of the Galaxy but with similar distance from the Galactic centre.