Fractals & Chaos Recap for 10/16

We’ve finalized our fractal designs and everyone has submitted their works. We will have our Fractal Art Gala on Thursday, October 18. Please be sure to bring in some snacks to share!

For Wednesday, you should read Pollack’s Fractals, an article from Discover Magazine about the math underlying Jackson Pollack’s famous paintings.  For some interesting follow-up reading, check out this article from the New York Times about the use of fractal analysis to examine the authenticity of supposed Pollack paintings and this article from the Science Daily blog suggesting that such an analysis is not scientifically valid.

Fractals & Chaos Recap for 10/15

Please sign up for snacks for next week’s Fractal Art Show

Your fractal art designs are due! By today, you should have turned in one submission in three of the following categories

  • Fern
  • Tree
  • Spiral
  • Realistic
  • Artistic

All works should have your name, the category, a notation on which way is up, a title (for the realistic and artistic categories) and a note about whether it is an “official” work, i.e., one of the three expected from all students, or an “additional” work that you would like to be considered in an “Additional Works” category.

In addition, for one of your official submissions, I also need one template. You’ll need to take a screenshot of the template, including its arrows, and print that as a separate page. Use the “snipping tool” in Windows, and try to make it small. My goal is to fit all templates on a single piece of paper.

Do not print the images directly. Instead, I recommend importing your images into a single Google Docs file, one image per page, and printing that document. This allows you to resize your images more appropriately and generally makes the resolution of the images less grainy.

Fractals & Chaos Recap for 10/11

For Monday, read this article from Nature about the connection between fractals and the famous Rorschach inkblot test.

Please sign up for snacks for next week’s Fractal Art Show

A reminder that the due date for our Fractal artwork will be Monday, October 15th.

On Monday, you will turn in one submission in three of the following categories

  • Fern
  • Tree
  • Spiral
  • Realistic
  • Artistic

All works should have your name, the category, a notation on which way is up, a title (for the realistic and artistic categories) and a note about whether it is an “official” work, i.e., one of the three expected from all students, or an “additional” work that you would like to be considered in an “Additional Works” category.

In addition, for one of your official submissions, I also will be collecting one template. You’ll need to take a screenshot of the template, including its arrows, and print that as a separate page.

I recommend importing your images into a single Google Docs file, one image per page, and printing that document. This seems to work well.

Fractals & Chaos Recap/Assignment for 10/9

Please sign up for snacks for next week’s Fractal Art Show

We have decided that the due date for our Fractal artwork will be Monday, October 15th.

On Tuesday, you will turn in one submission in three of the following categories

  • Fern
  • Tree
  • Spiral
  • Realistic
  • Artistic

All works should have your name, the category, a notation on which way is up, a title (for the realistic and artistic categories) and a note about whether it is an “official” work, i.e., one of the three, or an “additional” work that you would like to be considered in an “Additional Works” category.

In addition, for one of your official submissions, I also will be collecting one template. You’ll need to take a screenshot of the template, including its arrows, and print that as a separate page.

Today also starts a series of more recent articles on how Fractals are being used in today’s research. To start this off, check out this article from The Atlantic about why fractals can be so visually soothing

Fractals & Chaos Recap/Assignment for 9/28

We finished our discussion of the first dimension calculation practice sheet with an observation that the S^d = N definition for dimension has some weaknesses, primarily:

  • What do you do with fractals with non-iterating stems (e.g., 2 and 13)?
  • What if the fractal is not exactly self-similar (like 5)?
  • What if it is self-similar, but at differing scales (like 15)?

We will continue to work on our definition of dimension to accommodate these issues. You have also been issued a challenge: use what you’ve learned from the S^d=N definition to design a fractal with a dimension of exactly 1.5. Think about this as you read Gould’s essay Size and Shape.

We spent the rest of the period working on our FractaSketch designs.

Fractals & Chaos 9/20 Recap/Assignment

We wrapped up yesterday’s lesson with an explanation of the formula for the Hausdorff Dimension of a fractal and a few examples of finding the dimension for the Sierpinski Triangle, Koch Curve, and a newly designed fractal called the Sierpinski Carpet (essentially the same design as the Sierpinski Triangle, but with a square as the starting shape). We spent the rest of the time in class working with FractaSketch.

Fractals & Chaos Assignment for 9/19

We had a day working with FractaSketch today, which included an announcement of the 2018 Fractal Art Show.

The exact date of the art show will be determined later, but I will expect one entry from each student in three of falling into the following categories:

  • Fern
  • Tree (or shrubs, bushes, weeds, etc.)
  • Spiral
  • Realistic (other natural phenomena)
  • Artistic (patterns, designs, etc.)

Again, each student will be submitting three entries, each falling in a separate category.

Please feel free to work on your designs outside of class. We’re still trying to get the PC mobile lab open, so until then we will continue to work with the MacBook lab.

For tomorrow: continue to think about what the term “dimension” really means, per yesterday’s conversation.