Next week's assignment is Minimalism, and I was kindly by asked by another member to go a little in-depth into what minimalist photography is.
So here's what I came up with (*deep breath* here we go...).
In a nutshell, it is a photograph that demonstrates its element(s) in the most simple, and well... minimal way possible. Meaning, the least amount of color, texture, values, form, shapes, etc as possible. The subject of the photo is generally objective, so there is little or no question as to what we are looking at, but it is presented to us in a way to exemplify its existence. The background is very plain and not distracting, allowing the subject to stand out. Think "less is more."
When composing a minimal shot, there are a few things to keep in mind.
1. Centralize your subject. That's not to say you should always place the subject in the middle of the frame, but there shouldn't be anything else competing for attention.
2. Watch your background. Make sure it is as clean and straight forward as possible so that your subject shines through and there's no question as to what we
should be looking at.
3. Zoom in, or zoom out. Depending on what you're shooting, you'll either want a tight crop, or a great deal of negative, background space showing.
~Zooming in will remove distracting things from the background and you can focus solely on just your subject. Use of shallow Depth of Field will help here.
~Zooming out will really draw the viewer into the subject. Just make sure your background is pretty even throughout. Wide depth of field generally works well here.
4. Geometry. If you're like me, you hate math, but when venturing out looking for subjects, look for geometric shapes, especially in places you would have never looked before. Such as the T-shape made from a handrail, or single stripe of paint on a wall. This works especially well when zooming in.
5. Chromatics. Look for either very even and neutral coloration, or highly contrasting colors (no more then 2 or 3 usually). B&W is very popular in minimalism because it eliminates competition between colors. Alternatively, having a white wall with a maybe drip of bright blue paint is going to stand out immensely, and you should keep the color. Again, just make sure there's no competition.
As one example, I posted this about a week ago:
Adventures in Minimalism
For me, the reason I feel the shot was successful was because the long exposure allowed the choppy water to become very smooth, allowing the posts to really stand out. Obviously, I chose the zoom out technique because it really forces you to look directly at the subject, because there's nothing else to look at. (And, I couldn't really walk out into the water to get a close-up

).
Imagine taking this yourself with a normal shutter speed. You would see all the waves, and the lines and texture those waves create really start to compete with the posts, which barely extend from the water to begin with.
There is a flickr group based on minimalist photos whose pool is full of examples that demonstrate what I'm trying to say.
http://www.flickr.com/groups/minimal/pool/
For more professional inspiration, Michel Rajkovic is one of my all-time favorite photographers who really encapsulates the modern minimalist style I love.
http://www.michelrajkovic.fr/
Seeing the style visually is what helped me the most when dabbling in Minimalism. So have a a look at those links and examine what makes each image so powerful, despite the lack of powerful subject matter.
Then, get out there and start shooting!

Hopefully this helped some of you, and gave you some ideas to start working with. I highly anticipate seeing all your work for the assignment, and hope I can go out again and participate too.