OpenGeoDa is the open source successor to GeoDa, a software package designed to introduce non-experts to spatial data analysis. was developed under the auspices of the NSF funded Center for Spatially Integrated Social Science (CSISS) [4]. Since its release in 2003, Legacy GeoDa has gained over 40,000 individual users and has become a standard to teach introductory spatial data analysis. (and Open GeoDa) was conceived as enabling researchers to move from geovisualization to exploratory data analysis, the study of spatial autocorrelation and ending up with spatial regression modeling.

Sweeney--Robertson--Tocher (SRT) division, as it was discovered in the late 1950s, represented an important improvement in the speed of division algorithms for computers at the time. A variant of SRT division is still commonly implemented in computers today. Although some bounds on the performance of the original SRT division method were obtained, a great many questions remained unanswered. In this paper, the original version of SRT division is described as a dynamical system. This enables us to bring modern dynamical systems theory, a relatively new development in mathematics, to bear on an older problem. In doing so, we are able to show that SRT division is ergodic, and is even Bernoulli, for all real divisors and dividends. With the Bernoulli property, we are able to use entropy to prove that the natural extensions of SRT division are isomorphic by way of the Kolmogorov--Ornstein theorem. We demonstrate how our methods and results can be applied to a much larger class of division algorithms.

SRT division, as it was discovered in the late 1950s represented an important improvement in the speed of division algorithms for computers at the time. A variant of SRT division is still commonly implemented in computers today. Although some bounds on the performance of the original SRT division method were obtained, a great many questions remained unanswered. The original version of SRT division is described as a dynamical system. This enables us to bring modern dynamical systems theory, a relatively new development in mathematics, to bear on an older problem. In doing so, we are able to show that SRT division is ergodic, and is even Bernoulli, for all real divisors and dividends. With the Bernoulli property, we are able to use entropy to prove that the natural extensions of SRT division are isomorphic by way of the Kolmogorov-Ornstein theorem. We demonstrate how our methods and results can be applied to a much larger class of division algorithms.