There is one final article that I want you to read: Ivars Peterson’s Bordering on Infinity. While this article was published in *Science News* back in 1991, the questions that it poses about the connectedness of the Mandelbrot Set still plague mathematicians today. We’ll chat briefly about this article in class tomorrow.

# Tag Archives: Articles/Readings

# AP Statistics Assignment for week of 12/4

**Update on 12/6: **You should still read the articles listed below, but if you’d like more information about the Stanford Prison Experiment, I recommend you check out Dr. Zimbardo’s own account of the experiment posted here (as well as the additional information, including the participant consent form and Dr. Zimbardo’s application to Stanford’s Human Subjects Review Committee found here).

For the majority of the week, we’ll be watching The Stanford Prison Experiment, a 2015 film starring Billy Crudup, Tye Sheridan, and Ezra Miller that does a pretty accurate job depicting the events of the controversial simulated prison run as a psychological experiment on the Stanford University campus in 1971. On Friday, you’ll be asked to use the movie and the articles below to inform a conversation about experimental ethics. You were assigned a side at the start of the movie, defending one of these two statements:

- As long as all subjects give informed consent,
**there are****no ethical limits**on what researchers can do to human subjects. - Even with informed consent,
**there are ethical limits**on what researchers can do to human subjects.

The discussion on Friday will be highly structured. Please read over the Ethics Discussion Guidelines for details. Also, by Friday, read over the following three articles for some more examples that may be useful for your stance.

- Tuskegee Study
- Randomized Surgical Trials and “Sham” Surgery (Note: This link may not work on mobile devices)
- The Milgram Experiment

# Fractals & Chaos Assignment for 12/1

Read pages 138-145 from Fractals: The Patterns of Chaos – about “Visualizing Chaos”

# Fractals & Chaos Assignment for 11/30

Read the Feigenbaum Plot Article article that you got at the end of class today. In particular, pay attention to the converging ratio of gaps between bifurcation points, and the second page that discussing the ordering of cycles. You may also want to check out this Numberphile video about this same topic.

Also, keep playing with the Feigenbaum Plot applet! Remember that you’ll need to use a Java-permitting internet browser in order to view it.

# Fractals & Chaos Assignment for 11/8

From Fractals: The Patterns of Chaos, please read the following sections by Thursday:

- p 55-60 – Our Weather Today is Chaos
- p 93-97 – Chaos and Symmetry Hybrids
- p 99-106 – Chaos Sculpts Fractal Landscapes

# Fractals & Chaos Assignment for 11/7

From Fractals: The Patterns of Chaos, please read the following sections by Thursday:

- p 55-60 – Our Weather Today is Chaos
- p 93-97 – Chaos and Symmetry Hybrids
- p 99-106 – Chaos Sculpts Fractal Landscapes

# Fractals & Chaos Assignment for 11/6

Finish reading Chaos Hits Wall Street (if you haven’t yet!).

Also, create a diagram showing the relationship between the following variables for a “damped” pendulum (a pendulum that slows down over time)

- Y-position as a function of x-position
- Y-position as a function of time
- X-velocity as a function of time
- X-velocity as a function of x-position

For a more modern take on Chaos Theory in the financial investment industry, check out this 2010 blog post from MoneyMorning.com: What We Can Learn from the Stock Market Genius That Wall Street Loves to Ignore.

Keep in mind, however, that this “technical analysis” approach is not without its detractors. For a counterpoint, see this bluntly-titled post from The Motley Fool, also from 2010: Technical Analysis is Stupid

# Fractals and Chaos Assignment for 11/3

Keep playing with Iterative Canvas and Robert Devaney’s Chaos Game. Make a note of any interesting patterns you find with Iterative Canvas; we’ll do a brief “show and tell” in class on Tuesday.

Importantly, on Tuesday we will also discuss the Chaos Hits Wall Street article you got in class on Thursday. I know that some of you don’t always read every article I ask you to take a look at, but this is a **must read**. I expect **everyone** to contribute meaningfully to the discussion Tuesday.

**UPDATE: The Chaos Hits Wall Street discussion will happen on MONDAY, not Tuesday.**

# Fractals & Chaos Assignment for 11/2

By Tuesday, please read the Discover Magazine article Chaos Hits Wall Street. While this is an old article (1993!) it addresses a lot of the topics we’ll be discussing in the second part of the course. We’ll see some updated takes on the theories presented in the next articles.

# Fractals and Chaos Assignment for 10/13

Please sign up here to bring a small snack item to share with others at our FractaSketch Gallery Art Show on the 19th. See yesterday’s post for a breakdown of what information should be submitted for the show.

For Monday, 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 Assignment for 10/12

Please sign up here to bring a small snack item to share with others at our FractaSketch Gallery Art Show on the 19th!

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

And don’t forget that your designs are due on **Monday, October 16th**. On the 16th, I will be collecting the following:

- The Fractal Art Show flyer, with your name and notes about official vs. additional submissions, folded in half around the rest of the papers below.
- One completed design in
**three**of the following categories.- Spiral
- Tree
- Fern
- Realistic
- Artistic

- On the back of each design, you should write the following:
- Your name
- The category of submission
- A title (for realistic and artistic categories especially)
- A note or arrow indicating which way is up
- Whether the submission is an “Official” submission, to be considered in an above category, or an “Additional Work,” which will be included in a sixth category for works beyond your three official submissions

- The template for one of your official submissions. This is for a game we will play to “pin the template to the fractal,” i.e., match which template goes with which fractal design. To do this on a Windows computer, I recommend using the Snipping Tool, instructions for which can be found here. On an Apple computer, just press the Command (⌘)-Shift-4 to turn the cursor into a crosshair and click/drag a box around just the part of the screen you want to copy.
**Please note**that I want the*template*that you created (with the arrows), not what Stage 1 looks like. So use the grid screen, but turn the grid off before taking your screenshot.

# Fractals & Chaos Assignment for 10/11

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

And don’t forget that your designs are due on **Monday, October 16th**. On the 16th, I want you to **print and submit **the following:

- The Fractal Art Show flyer, with your name and notes about official vs. additional submissions, folded in half around the rest of the papers below.
- One completed design in three of the following categories.
- Spiral
- Tree
- Fern
- Realistic
- Artistic

- On the back of each design, you should write the following:
- Your name
- The category of submission
- A title (for realistic and artistic categories especially)
- A note or arrow indicating which way is up
- Whether the submission is an “Official” submission, to be considered in an above category, or an “Additional Work,” which will be included in a sixth category for works beyond your three official submissions

- The template for one of your official submissions. This is for a game we will play to “pin the template to the fractal,” i.e., match which template goes with which fractal design. To do this on a Windows computer, I recommend using the Snipping Tool, instructions for which can be found here. On an Apple computer, just press the Command (⌘)-Shift-4 to turn the cursor into a crosshair and click/drag a box around just the part of the screen you want to copy.
**Please note**that I want the*template*that you created, not what Stage 1 looks like. So use the grid screen, but turn the grid off before taking your screenshot.

# Fractals & Chaos Assignment for 10/10

By tomorrow, read Why Fractals are So Soothing, a January, 2017 article written by Florence Williams for *The Atlantic* about some work done by physicist Richard Taylor (and his magnificent hair).

And don’t forget that your designs are due on **Monday, October 16th**. On the 16th, I want you to **print and submit **the following:

- The Fractal Art Show flyer, with your name and notes about official vs. additional submissions, folded in half around the rest of the papers below.
- One completed design in three of the following categories.
- Spiral
- Tree
- Fern
- Realistic
- Artistic

- On the back of each design, you should write the following:
- Your name
- The category of submission
- A title (for realistic and artistic categories especially)
- A note or arrow indicating which way is up
- Whether the submission is an “Official” submission, to be considered in an above category, or an “Additional Work,” which will be included in a sixth category for works beyond your three official submissions

- The template for one of your official submissions. This is for a game we will play to “pin the template to the fractal,” i.e., match which template goes with which fractal design. To do this on a Windows computer, I recommend using the Snipping Tool, instructions for which can be found here. On an Apple computer, just press the Command (⌘)-Shift-4 to turn the cursor into a crosshair and click/drag a box around just the part of the screen you want to copy

# Fractals & Chaos Assignment for 10/6

I want to turn now to some more modern publications on the research and applications of fractal geometry. First, we’ll start Why Fractals are So Soothing, a January, 2017 article written by Florence Williams for *The Atlantic* about some work done by physicist Richard Taylor (and his magnificent hair)

# Fractals & Chaos Assignment for 10/4

If you’re interested in reading a bit more about the central topics of the past two articles, check out this NPR article as a follow-up. Also note the New York Times article linked there. Both articles have really interesting information on Galileo’s Square Cube Law and something called Kleiber’s Law, which governs the relationship between an animal’s size and metabolic rate.

I want you to read a bit more about the man mentioned in so many of these articles: Benoit Mandelbrot, the father of fractal geometry. Mandelbrot died in 2010, and the New York Times’ article about his death has a good summary of his life and contributions. Please read this by Friday.

# Fractals & Chaos Assignment for 10/3

By Wednesday, read Size and Shape, paleontologist and evolutionary biologist Stephen Jay Gould‘s follow up to Haldane’s essay. If Gould’s name sounds familiar, it’s because he co-developed the idea of (and coined the term for) punctuated equilibrium, a theory of evolution.

# Fractals & Chaos Assignment for 10/2

By Wednesday, read Size and Shape, paleontologist and evolutionary biologist Stephen Jay Gould‘s follow up to Haldane’s essay. If Gould’s name sounds familiar, it’s because he co-developed the idea of (and coined the term for) punctuated equilibrium, a theory of evolution.

And continue to work on your FractaSketch designs, of course.

# Fractals & Chaos Assignment for 9/29

By Monday, read On Being the Right Size, an essay written by biologist JBS Haldane in 1926 and consider its relevance for that age-old Internet question “Which would you rather fight: One duck-sized horse or one hundred horse-sized ducks?”

Also, finish finding the dimensions of the fractals on this sheet (Dimension Classwork 1). Note that some of the images are of completed fractals while others are only templates. Also note that the S^d = N definition of dimension may not be sufficient for some of these fractals. Try to identify which and in what way that definition comes up lacking.

# Fractals & Chaos Assignment for 9/28

By Monday, read On Being the Right Size, an essay written by biologist JBS Haldane in 1926. Also, finish finding the dimensions of the fractals on this sheet (Dimension Classwork 1). Note that some of the images are of completed fractals while others are only templates. Also note that the S^d = N definition of dimension may not be sufficient for some of these fractals. Try to identify which and in what way that definition comes up lacking.

# Fractals & Chaos Assignment for 9/27

As noted yesterday, by class tomorrow, please read over the chapter 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.