Fractal Generating Software

A learning tool for advanced mathematics students to model Iterated Function Systems (ISFs)

Motivation

In my third year of undergrad, I enrolled in Dynamical Systems, an advanced mathematics course that ultimately focuses on the study of fractals. Upon learning the concepts of iterated function systems (IFSs), my friend Gina and I, both of us being visual learners, searched online for a program that would model these ISFs to generate their resulting fractals but found no programs that were truly effective. Thus, we decided to create a VPython program for our final project to accomplish this fractal generation, as a tool for students enrolled in this class to visualize the phenomena learned.

Team & Timeline

Doria Spiegel, Gina Haugen

October - December 2015

How the Program Works:

One first visualizes the intended resulting object and comes up with a set of functions that, if applied to this object, would transform it to the next largest parts of the object (the limbs of a tree, or its trunk for example). If these functions are iterated on these smaller parts, they, too would transform to the next largest parts and so on. For each of these functions, there are coefficients that minimize the object’s dimensions, constants that change its location, and an angle that rotates it. These values, for each function, are entered into the program. The user chooses a number of iterations by which to apply the functions which determines the amount of detail in the final product. Finally, the user runs the module and voila! The user sees the fractal, the iterations of each function distinguished by color.

Images taken of some fractals generated using this software after at least 2500 iterations as well as their function inputs

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