## illiMath2008 REU of Geometrical Visualization in Virtual Environments

#### June 9, 2008 - August 2, 2008

Preliminary notes on Professor Wang's lecture on developing 4D intuition in virtual reality are available at WangW1.

Figure: This is a triaxial tritorus I made with Mathematica.

I am a math major at Wellesley College.

### Splitting the Mandelbrot Set

This is the Mandelbrot set I made with the code from Stan Blank's Python manual.

My preliminary notes are available at SplitMset.

### Python Manual

I have been reading over Dr. Stan Blank's manual, Python Programming in OpenGL. He originally wrote this tutorial to help teach his computer science high school class. He wants to know how helpful his manual is on an individual level outside the classroom. I am writing a review from the point of view of someone who has not used Python before.

A draft of my write up can be viewed here: StanNotes.

### Fractals

I studied Newton fractals, Julia sets, and the Mandelbrot set using Dr. Blank's manual as well as resources on the internet. I learned how to write programs to draw these fractals in Python. I've been working on understanding the code.

### Nil "Circle"

I worked with Lisa and Geoff to come up with a code in Mathematica to draw a circle in Nilspace by traveling along a vector at a fixed distance and projecting it down onto a plane tangent to the point reached by the vector. Then we turned a fixed angle and repeated the process. This makes a circle on the Euclidean plane but not in Nilspace. We ended up with some interesting graphs though.

Lisa built on this concept and made more Mathematica notebooks.

### Mathematica

Thanks to Chase, I saw my Triaxial Tritorus in the CUBE using caveMathematica.

### Week One: June 9-13

The first week was orientation where we were introduced to the REU lab. Guest professors were invited to give lectures on their research so that we could work with them on our projects. We also made a few trips to the CUBE and CAVE at the Beckman Institute for demonstrations. There were workshops on LaTex, html, unix, and other tools needed for the REU.

### Week Two: June 16-20

This week I worked with Mathematica and LaTex for the first time. The Wolfram Mathematica Documentation Center was very helpful. Using the parameters, I was able to come up with the Triaxial Tritorus pictured above. I also experimented with colors and other 3D surfaces.

Professor Francis gave me a problem to work on with Mathematica building on Lisa's NilCircle notebook.

### Week Three: June 23-27

I talked with Geoff about his quasicrystals so I have a general idea about it. With my lack of cs experience, I wasn't able to help him with his project. Instead I started using and leaning Python with Dr. Stan Blank's Python manual. The first few chapters weren't bad. I started out with writing code to plot points and functions.