Archive for March 2011
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The Theis Equation and Flow
Mathematics is remarkably effective in describing the physical world in part due to isomorphisms, relationships between concepts that reveal a similar underlying structure. In 1935 Charles Vernon Theis was working on groundwater flow, a subject with little mathematical treatment at the time. He thought that perhaps a well tapping a confined aquifer could be described [...]
Convergence in the Lorenz Attractor
Most visualizations of the Lorenz attractor are of a long history of a single point after convergence to the attractor has occurred. I was interested in what the surrounding space looked like, so I randomly selected 20,000 starting points from a three dimensional Gaussian distribution with a standard deviation of 100. Each point was iterated, [...]
