# D09

Welcome to the Drexel Summer 09 Entry to !

IMPORTANT NOTE: Please put up contact information on Drexel-Swat Partnering page: Drexel-Swat_Partnering

Things to do:

• browse around, leaving comments on the Math Images discussion page and the Swarthmore student's discussion page, looking around for interesting possibilities for interaction on the latter
• look through the Helper Pages in the left navbar and the Hard Math page to see if you can find anything you'd like to work on--if there's anything you've struggled with that isn't there, add it!

Resources:

Check out the Drexel-Swat Partnering page to see who's paired up with whom and keep track of what they're working on...

## Possible Applets/Animations for Drexel Students To Do

• Parametric Equations Page- demonstrate the parametric construction of a circle. Perhaps the user can increase the value of the parameter in the parametric equations of a circle, and see the resulting circle be drawn in real time. The same type of applet would be cool for the butterfly curve, although I already have an animation for this curve (from wikipedia) and making another one would be more difficult than a circle.
• Henon Attractor Page - an applet allowing the users to pick values of a and b to create different Henon Attractor (Mike is now done this applet)
• Blue Fern Page - my ideas for this are pretty vague. Perhaps some sort of an animation or applet showing the different types of matrix transformations and translations involved in making the fern. Maybe showing what each matrix does to an object (rotate it, shrink it...)
• Brunnian Links - an interactive 3D model of the Borromean rings (and possibly high ring levels also) similar to this YouTube. I was thinking about an applet that would allow users to rotate the model with their mouse to see all perspectives of the ring, as well as have an animation showing that after one ring is removed, the ring unravels.
• Torus page- The section n-torus could use an illustration of how an $n$-dimensional object can exist in $n+1$ dimensions. For example a line, which is a 1D object can exist in 2D when it is bent into a circle. Similarly, in 3D, a cube wraps to form a 3-torus. Illustrations could really help explain this section. I've tried searching for images online but could not get one that specifically shows this.

## Tim

Click on my name above for things that I've finished

## Emily G.

### Projects In Progress:

• Line Drawing (manipulating alpha in parametric equation of a line)
• Status- In progress
• Status- Mostly done

### Projects for the Future:

• Status- On hold. Does anyone have any experience with this kind of thing? Mine keep turning out to be more confusing than helpful to the viewer.
• Transformations java applet which allows user to change values in transformational matrices and then see the changes that it makes on the image.
• Status-Not Started
• Rhodonea (Cardioid, Rose Petals, Limacons, etc.)- interactive graphing
• Status- Investigating the possibility of using a webMathematica applet to accomplish this
• Status- Investigating the possibility of using a webMathematica applet to accomplish this

## Steve

Stereographic Projection applet: Stereographic Projection
Hypotrochoid applet: Hypotrochoid
Metaballs applet: Metaballs
Mandelbrot applet: Mandelbrot
Koch Snowflake applet: Koch Snowflake
Catenary applet: Catenary
Julia set applet: Julia set
Hi Steve,
I've seen this applet, and I've like it--it's just very similar to most Julia Set applets out there at only deal with Julia Sets of functions of the form $f(x)=x^2+a+bi$. I'd think it would be *really* cool to have an applet where someone could plug in any old rational function and get a Julia Set, though I know that might be too hard.
As an aside, what computational method did you use (an escape criterion, like my short program on that page, or something else)?
Thanks, and keep up the great work.
~Anna
There's a cool applet showing the relationship between Julia and Mendelbrot sets here. -Tim
Chryzode applet: Chryzode
Conic Section applet: Conic Section
Procedural Images applet: Procedural Images

Test:

## Ayush

I'm a Computer Science sophomore at Drexel University. This Summer term (Summer 09) is my first term working on the Math Images project.

### The Plan:

Working with Josh and Alan to add interactivity in the pages previously created by Alan.
I plan to concentrate on Flash animation while Josh explores the Java.

### Work Progress:

Week 1:
Surfed around the MathImages website. Familiarized myself with the many different pages and projects.
Spoke with Alan and Josh and made a tentative plan of what is to be achieved in the duration of the research project.
Installed and set up Adobe Flash CS4. Started reading tutorials and watching videos to learn using Flash.
Learned basic wiki tags and wiki usage and embedding flash .swf files into wiki
Created a simple flash animation to show matrix multiplication of two 2x2 matrices. May be incorporated in the Matrix helper page.
Matrix Calculator:
Currently working on a Matrix calculator.
After making the barebones framework in week 3, I have been adding features in it this week. It now has the option to add and recall from memory, a Clear option, the calculator returns an error if the user does not select any operator, it does not accept non-numeric values etc.
You can see the beta ver. here : [1]
Some features I am currently working on:
• Allowing user to select dimensions of Matrix
• Calculation of Invert, Adjoint and Determinant of Matrix
• Show tutorials for all operations

## Josh

I just completed my freshman year at Drexel, going for a BS in Computer Science

### Projects:

Working with Ayush and Alan to add interactivity in the pages previously created by Alan.
Working mainly with Java

### Progress After Week 1

Because I am really working on this project part-time I did not make any major strides this week but I did get a few things accomplished

I learned the basics of writing Java Applets
I'm about 1/3 of the way done a program that segments a rectangle into thirds and then illustrates the Golden Spiral

## Mhershey1

test:

What I have so far: http://www.pages.drexel.edu/~smh86/index.html

• Blue Wash, applet changing k (in Inclined Recursive Method) & animation drawing the basic no k method (in Basic Recursive Method)
• Blue Fern, Henon Attractor, redo the animations with small points
• Hyperbolic Tilings, applet where users input Schläfli symbol to create a tiling
• This would take too long for me to do. Maybe someone else can do this one, or we could just use the already made applet?
• Newton's Basin, redo the animation (maybe users input the equations)
• Logarithms, interactive quiz with exponential and logarithmic equations
• Harter-Heighway Dragon, animating the curve at each iteration stage

## Matt

If you see the green box below, you have Java installed. To view the Change of Coordinate Systems Applet, your version number should at least be 1.6.0_14. If it still does not work, please let me know!

### Projects:

• Status: Finished
• Description: An applet which allows for a visual representation of user defined points in 3-space
• Link: Change of Coordinate Systems Applet
• Notes: Finished applet, if you find any bugs, please let me know! email: mjh96@drexel.edu
• Status: Not Started
• Description:An applet or animation that displays the gradient at different points on a surface
• Status: Finished
• Description: An applet allowing for an interactive representation of 2D vector algebra, mainly consisting of: addition and subtraction. Scalar multiplication was not included as it would be a detriment to the applet's simple point and click interface. However, if anyone feels this feature should be added, I can certainly do so.
• Link: 2D Vector Applet
• Notes: If you find any bugs, please let me know! email: mjh96@drexel.edu. Also, I am aware of the annoying tendency of vectors clipping with the bounds of the graph when the addition procedure is carried out.
• Status: Finished
• Description: An applet allowing the user to simulate rolling a six-sided dice, and graphically keep track of the outcome distribution.
• Link: Dice Probability Applet
• Notes: Let me know if you have any suggestions. email: mjh96@drexel.edu
• Status: In Progress
• Description: An applet allowing the user to enter the components of 2 vectors and display a graphical representation of a vector cross product
• Status: Finalizing
• Description: An applet that generates a random arithmetic sequence and allows the user to fill in missing spots. A geometric version is likely to follow.
Note: If a project is listed as "Not Started," feel free to pick it up if you wish

### Week 1 Progress

After getting comfortable with writing Java applets, I began to read the Java 3D tutorial provided by Sun. After getting down some of the basics, I began to work on the Change of Coordinates applet. So far I have created a 3D graph that has the ability to graphically display a point in 3-space as specified by the user. This point may then be displayed with a rectangular/cartesian, cylindrical, or spherical representation. As of now, the points are input via the console, yet in the finished version, the user will be able to click any location in 3-space to select a point. The user will also be able to navigate the space with a mouse or keyboard.