Hi all! We are nearing the end of the semester, and only have two more classes to go (on 4/14 and 4/28). On Monday 4/7 I assigned your final project, and you can read details about it here. Look at the bottom of this post for resources that may help with projects.

By next Monday (4/14) you get me an image of a piece of a Julia or Mandelbrot set. You can explore the Mandelbrot and Julia sets at the sights in the list below. You can grab a screen shot and print it out or email it to me. Also by next Monday, I would love to have an idea of what you are going to do for your project — you can give me a note in class or email me about that!

- Need a fairly simple explanation of the Mandelbrot and Julia sets: Look here: http://www.ddewey.net/mandelbrot/.
- The Julia Set creator can draw Julia sets for different values of the constant.
- You can also look at Julia sets pulled from the Mandelbrot set: http://www.ibiblio.org/e-notes/MSet/Anim/ManJuOrb.htm
- There are many other places to explore Mandelbrot and Julia sets:
- http://www.javaview.de/vgp/tutor/fractal/PaFractalImage.html (click in Mandelbrot set and move pointer to select different values for C and see corresponding Julia sets, can also zoom in – press “m” while selecting rectangular regions)
- http://www.ibiblio.org/e-notes/MSet/Anim/ManJuOrbB.htm (creates animations, can zoom into both Mandelbrot and Julia sets)
- http://math.bu.edu/DYSYS/applets/Quadr.html (can create animations, but resolution isn’t that good)
- http://gingerbooth.com/coursewareCBC/mandeljulia.html (can alter coloring schemes, zoom, under “Scenarios” can alter the equation used to iterate)
- You can find others by searching, so feel free to use another tool.

## Project Resources

### Geometric Sculpture Resources

We will be creating some of these forms over the next couple of weeks in class.

- More fractals out of paper:
- Flexagons?
- Check out Vi Hart’s hexaflexagon video: http://www.youtube.com/watch?v=VIVIegSt81k
- Want to make a hexa-hexa flexagon (like the tri-hexa flexagon from class but with a total of 6 faces)? See http://www.youtube.com/watch?v=M4HobuejpJw

- Sliceforms: We may not get to sliceforms in class, so I wanted to collect some links for you here
- John Sharp wrote a book on sliceforms and started some of the current sliceform trend. He has a blog, but isn’t currently putting up anything new.
- Flickr photos of sliceforms: http://fiveprime.org/hivemind/Tags/sliceform

- Modular Origami
- Sonobe (we did this in Tue/Th class but not Mon class)
- PHiZZ
- Folding/using PHiZZ video (then can continue to part 2)
- Making buckyballs video
- Making the torus (doughnut) (88 PHiZZ units): http://www.usd.edu/arts-and-sciences/math/upload/Euler-formula-torus.pdf the blueprint for the torus is on p. 7.

- Other Methods
- http://www.georgehart.com/virtual-polyhedra/classroom.html
- D-forms: http://www.cutoutfoldup.com/1602-d-forms.php
- http://www.instructables.com/id/Geometric-sculpture-from-72-pencils/
- http://blog.craftzine.com/archive/2012/03/diy_3d_geometric_sculpture.html
- http://blog.makezine.com/2009/06/17/how-to-frabjous-cardboard-geometry/
- http://mathcraft.wonderhowto.com/corkboard/design-your-own-playing-card-sculpture-0133148/
- General ideas at: http://mathcraft.wonderhowto.com/

### Fractals

- We watched this TED talk by Ron Eglash on African fractals. You can create your own fractals with this simple tool. Another tool that does a similar job through more iterations is the Fractal Maker.
- We saw Recursive Drawing in class.
- If you use Photoshop, you should know about Pixel Bender, which adds a number of filters, including Escher Droste Effect (useful quick “how to” on this) and Fractal Explorer (see demo video)
- Why stop there? You can do fractals with simple video loops, as discussed in this video. You can also of course create videos and loop them in order to do an “infinite zoom” on a fractal.
- And then there is Scott Draves, well known in computing graphics circles for the creation of the open source flame fractal algorithm behind the Electric Sheep screensaver and the fractal flame editor Apophysis. I found an interesting talk he gave that’s worth checking out if it interests you.
- Another program you can consider for fractal creation is Ultra Fractal.
- Finally, architect Michael Hansmeyer gave a TED talk on some of his algorithmic work and you can see more at his website.
- You can also see the resources on the Mandelbrot set posted above. There are a lot more fractal resources out there — feel free to send me your favorites and I can get them up online.

### 3D Sidewalk Drawing

- Check out Tracy Lee Stum’s website for videos and images. We used her directions for creating a 3D chalk drawing.
- You can also check out Julian Beever‘s site for images and ideas.

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