These simulators explore the core mathematical models of Ecology. Several received top ratings from JARS and MERLOT. Some look dated now, and some were abandoned around 2001. But at the time, this was ground-breaking work.

One of our first semesters teaching with CourseWare, back in the late '90's, was a cross-listed undergrad-graduate course. The undergrads were taught modeling with CourseWare. The grad students went deeper, programming the models themselves. It was soon clear to the grad students that the undergrads had it easier. And worse, the undergrads learned the material much better - they blew the grad students away on tests. After that, the students all used the CourseWare.

Differential Equation Plotter

The DiffEQPlotter explores graphical solutions to differential equation systems. Nine equation system families are provided - some simple algebraic systems, some ecology models, and some limit cycles. Each can be tuned by setting constants. Paired time plot and phase plot show the behavior of the system (trajectory) from any selected starting point. The phase plot also shows the "nullclines" (where the derivative of each equation is zero), and a vector field showing the tendency of the system across a grid over the plane.

Though not "fractals" software, it was developed for the same mathematics professor, Michael Frame of Yale University.

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Diversity Metrics

Diversity Metrics explores species diversity measures. There are 625 possible worlds to explore (four preset). The user samples the species landscape by positioning sample plots or transects one by one, or by using an autosample button. Diversity metrics include the species-area curve, the Shannon-Weaver index, the Simpson index, and beta diversity. Used in teaching Conservation Biology at Yale.

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Predator/Prey

Predator/Prey explores predator/prey coupled population equations. Starting from simple linear codependence, successive scenarios add saturation to the predator, then logistic growth to the prey, then predator interference. At Yale, we assign the functional response variant of this.

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