A selection of the mathematical models that I’ve created with a bit more detail.


An Individual-Based Model to understand how shorebird populations are affected by changes in their coastal habitats

In classic population modeling, each individual of a population represents the same unit, an identical entity with the same abilities and chance for survival. Populations, however, are made up of unique individuals whose different abilities and traits ultimately affect the success of both current and future generations. Individual-based modeling is a technique that uses this idea to understand how collective population features emerge from the different behaviors and traits of individuals that make up the population.

I use individual-based modeling in my Thesis Research to simulate the foraging and survival dynamics of the Long-billed Curlew population at Humboldt Bay. Shorebird populations, like the Long-billed Curlew, are complex systems that depend on many aspects, ranging from changing environmental factors to the differences between individual curlews. Such a system considers phenomena such as constantly changing tides, decreasing resources in fall and winter, and the interactions between birds that arise from territorial behavior and local hierarchies in dominance.


“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth”

-Mandelbrot, B. B. in The Fractal Geometry of Nature

Fractal Geometry Generator

A program to explore the fractal geometries that resemble the complex shapes we see in nature

Fractal geometry is an amazing juncture of Mathematics, Computer Science, Natural Science, and Art. To me, it is a field that always inspires wonder and curiosity towards nature and its beautiful complexity. As a fun side-project while learning C# and WPF, I decided to test my fundamental skills and gain more experience with the vast field of possibilities that object-oriented programming encompasses.

Test out the beta and explore classic fractals that started the every-growing family of fractals.

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I’m always looking for exciting ways to flex my mathematical muscles* for the greater good.
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