### Saturday Morning Math Group

Spring 2006 Schedule

• Saturday February 4, 2006
•  Location: RLM 4.102 (On the UT campus) Group Leader: Dr. Lorenzo Sadun -----------------------------------------------------> Topic: Self-similar Tilings Title: "Substitution Tilings and the Droste Effect" Poster: Click here for the poster.

What does Dutch cocoa have to do with a tile floor (besides the fact that you can spill one on the other)?

The Droste effect is a pattern that looks the same on many different length scales, with a picture inside a picture inside a picture. We'll see how to construct such patterns and examine their properties.

Check out some fun activities.
Here are some pictures from our meeting!

• Saturday February 25, 2006
•  Location: WEL 1.316 (On the UT campus) Group Leader: Dr. Alistair Windsor --------------------------------------------------> Topic: Fractals Title: "Fun with Fractals" Poster: Click here for the poster.

The word fractal comes from the Latin "fractus" meaning broken but there is no agreed mathematical definition for these objects. However, once you have seen a couple you will always recognize them again.

First we will look at the grand-daddy of all fractal images, the Mandelbrot set, and its associated Julia sets. We will see how these crazy objects are defined and look at some of the really fine structure.
Then we will also look at some fractal patterns in nature and some of the famous fractal patterns such as the Sierpinski triangle and Koch snowflake. Using simple geometric models we can calculate some "dimensions" and show that these fractals are fractional dimensional.

Here are the slides from the talk.

Also, here are some useful links and additional information pertaining to the topic:
This is where you find the Mac program that was used during the first part of the talk.
The best fractal program is the DOS program Fractint.
There are numerous other programs, too.

Next you find a brief bibliography of nice books:

Heinz-Otto Peitgen, Hartmut Jurgens, Dietmar Saupe. Fractals for the Classroom
Part 1: Introduction to Fractals and Chaos. Springer. 1992

Heinz-Otto Peitgen, Hartmut Jurgens, Dietmar Saupe. Fractals for the Classroom
Part 2: Complex Systems and Mandelbrot Set. Springer. 1992

Michael F. Barnsley. Fractals Everywhere. Academic Press. 1988

The books are relatively self contained and require mathematical maturity rather than sophistication. Possible for high school seniors with some struggle.

This is the worksheet.
And here are some pictures from the meeting!

• Saturday April 1, 2006
•  Location: WEL 1.316 (On the UT campus) Group Leader: Zachary Booth Simpson -------------------------------------------------> Topic: Mathematics of 3D Computer Animation Title: "Video Game Mathematics" Poster: Click here for the poster.

Mathematics plays a vital part in computer graphics involving representations of 3-dimensional space, especially in video games and computer-animated movies.

Some of the questions we can ask in this context are:
How do we model a 3-D body?
How do we show a 3-D model on a 2-dimensional screen?
How do we deal with (different ways of) moving the "camera" or point of view?

Finally, many bodies are not "rigid". Humans and animals have joints, machines have moving parts, etc. So, for instance, we might ask:
How can we deal with the individual movements of the upper arm, forearm, hand and fingers of a character and how are these related to each other?

These problems can be tackled by using a branch of mathematics called linear algebra. This area of math helps us deal with perspective and projection (onto a 2-D screen), with motion and transformation (rotation, translation, scaling, skewing).

We will see how game developers use linear algebra to solve these problems so they can create their video games.

Here are the slides from the talk.
Find here the worksheet a
nd some pictures from the meeting!

• Saturday April 29, 2006
•  Location: RLM 4.102 (On the UT campus) Group Leader: Dr. Lauren Ancel Meyers ---------------------------------------------> Topic:  Mathematics and Biology Title:  "New Mathematical Methods for Forecasting the Spread of Infectious Diseases"         Poster: Click here for the poster.

For the "Hot Science - Cool Talks" outreach lecture series, Dr. Meyers gave a talk similar to todays. Here is the corresponding power point presentation.
Find here the worksheet a
nd some pictures from the meeting!