# Fractals and Chaos Lesson Recap for 10/17

We had our official Fractal Art Show Gallery Opening today!

For tomorrow, please read Mandelbrot’s revolutionary paper that sparked the recognition of fractals and fractal geometry How Long is the Coast of Britain? You might also want to read this version, where Mandelbrot himself explains how he originally wrote this paper as a “Trojan Horse” to introduce his vision of fractal dimension into the scientific community conversation.

# Fractals & Chaos Recap for 10/16

One more chance to sign up for snacks for tomorrow’s Fractal Art Show!

In class today, we finished up the dimension classwork sheet and practiced how the segments of each fractal design that you measure to calculate its dimension can be used to recreate the fractal in FractaSketch (aka “stealing the template”). Neat!

We also have an important reading assignment: By Friday, October 18, please read Mandelbrot’s revolutionary paper that sparked the recognition of fractals and fractal geometry How Long is the Coast of Britain? You might also want to read this version, where Mandelbrot himself explains how he originally wrote this paper as a “Trojan Horse” to introduce his vision of fractal dimension into the scientific community conversation.

# Fractals & Chaos Recap for 10/15

In class today, we worked on our fourth and final dimension classwork sheet (while a handful of stragglers turned in their Fractal Art Show designs) and looked at how the analysis we do to find the dimension of the shapes can be used to recreate them in FractaSketch. Neat!

We also have an important reading assignment: By Friday, October 18, please read Mandelbrot’s revolutionary paper that sparked the recognition of fractals and fractal geometry How Long is the Coast of Britain? You might also want to read this version, where Mandelbrot himself explains how he originally wrote this paper as a “Trojan Horse” to introduce his vision of fractal dimension into the scientific community conversation.

# Fractals & Chaos Recap for 10/11

Your FractaSketch designs were due today! You should be turning in one entry in three of the following categories:

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

On the back of each of your submissions, you should write 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 leave the image “actual size” (don’t blow it up). My goal is to fit all templates on a single piece of paper for a matching game as a part of the art contest.

Do not print the .png 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 convenient and generally makes the resolution of the images less grainy.

# Fractals & Chaos Recap for 10/10

Your FractaSketch designs are due tomorrow, Friday, October 11. Remember, I expect from each of you one entry in three of the following categories:

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

On the back of each of your submissions, you should write 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 leave the image “actual size” (don’t blow it up). My goal is to fit all templates on a single piece of paper for a matching game as a part of the art contest.

Do not print the .png 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 convenient and generally makes the resolution of the images less grainy.

# Fractals & Chaos Recap for 10/8

We spent the day working on FractaSketch again. Your submissions for the Fractal Art Show are due this Friday, October 11. Remember, I expect from each of you one entry in three of 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. You are welcome to submit more designs if you would like, but they will be placed in a separate “Additional Works” category.

In addition, I will want you to submit the template for one of those official submissions for a template/design matching challenge.

Please feel free to work on your designs outside of class and transfer them to the laptops we’ve been using in class.

# Fractals & Chaos Recap for 10/4

We spent the day working on FractaSketch. Your submissions for the Fractal Art Show are due next Friday, October 11. Remember, I expect from each of you one entry in three of 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. You are welcome to submit more designs if you would like, but they will be placed in a separate “Additional Works” category.

In addition, I will want you to submit the template for one of those official submissions for a template/design matching challenge.

Please feel free to work on your designs outside of class and transfer them to the laptops we’ve been using in class.

For Monday, please read this recent piece from The Atlantic (Why Fractals Are So Soothing)

# Fractals & Chaos Recap for 9/26

We discussed Ivars Peterson’s Ants in Labyrinths at the start of class, noting some interesting passages and talking about questions we had. In particular, I made a note to remember the part towards the beginning, where Peterson suggests an interesting problem with measuring a particular coastline:

Finer and finer scales reveal more and more detail and lead to longer and longer coastline lengths. On a world globe, the eastern coast of the United States looks like a fairly smooth line that stretches somewhere between 2000 and 3000 miles. The same coast on an atlas page showing only the United States […] seems more like 4000 or 5000 miles. […] A person walking along the coastline, staying within a step of the water’s edge, would have to scramble more than 15,000 miles to complete the trip.

This is an important idea. Remember it! We’ll be revisiting it later in the course.

The rest of our time in class was spent working on our fractal designs in FractaSketch. Don’t forget the expectations for the soon-to-be-announced Fractal Art Show! I expect from each of you one entry in three of 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. You are welcome to submit more designs if you would like, but they will be placed in a separate “Additional Works” category.

Please feel free to work on your designs outside of class and transfer them to the laptops we’ve been using in class.

Homework: Read On Being the Right Size, an essay written by biologist JBS Haldane in 1926. We will discuss this reading tomorrow. As you read, ask yourself this classic question from the Internet: “Which would you rather fight: one horse-sized duck or 100 duck-sized horses?”

# Fractals & Chaos Lesson Recap for 9/25

We spent today practicing finding the Hausdorff Dimension for a variety of fractal and template designs, running into some interesting potential problems as well as a few surprising results.

By tomorrow (Thursday), please read the passage Ants in Labyrinths, from Ivars Peterson’s The Mathematical Tourist. As usual, make a note of questions you have and passages you think are significant.

And don’t forget the expectations for the soon-to-be-announced Fractal Art Show! I expect from each of you one entry in three of 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. You are welcome to submit more designs if you would like, but they will be placed in a separate “Additional Works” category.

Please feel free to work on your designs outside of class and transfer them to the laptops we’ve been using in class.