(Math with Mrs. Vickmark)
I used this project at the end of an exploratory unit on Fractals in my Applied Math course.
The document is designed so that students can lead themselves through the project without too much teacher guidance along the way. Essentially, students create their own fractals online using a free fractal generator and then modify it however they wish in order to create their own fractal by hand. The project guides the students through the mathematics at each iteration of their fractal, and it requires them to document everything for reference and grading purposes.
The grading rubric is included in the document.
I believe we spent about a week and a half working on the project because my students needed many drafts in order to get their fractals correct. However, the time frame could easily be adjusted to suit your classroom needs.