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

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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

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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

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

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.**

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.

On the piece of graph paper I gave you in class (or on your own if you weren’t), draw a path based on a coin flip. Orient your paper in Landscape mode (so it is wider than it is tall), mark a dot halfway down the short edge, and draw a path:

- Go up one square (and to the right) on a heads
- Go down one square (and to the right) on a tails

Bring this path in tomorrow.

For some more interesting Tales From the Fourth Dimension, check out the following:

- The Adventures of Fred, Bob, and Emily – a detailed look at how the lives of a 2D (Fred), 3D (Bob), and 4D (Emily) creature interact with each other. See especially the “World” section, where the author, Garrett Jones, imagines how wheels, water, and war would work in these universes.
- And He Built a Crooked House – a short story by “Big Three” science fiction writer Robert A. Heinlein about an eccentric architect who designs a house in the shape of an unfolded hypercube. An earthquake hits, and the house folds back up on itself to concerning results (see also this student film version of the story)
- Some Notes on the Fourth Dimension – some animations and movies showing the geometry of the fourth dimension, including some of those featured in the Flatland dvd bonus features.

For some more interesting Tales From the Fourth Dimension, check out the following:

- The Adventures of Fred, Bob, and Emily – a detailed look at how the lives of a 2D (Fred), 3D (Bob), and 4D (Emily) creature interact with each other. See especially the “World” section, where the author, Garrett Jones, imagines how wheels, water, and war would work in these universes.
- And He Built a Crooked House – a short story by “Big Three” science fiction writer Robert A. Heinlein about an eccentric architect who designs a house in the shape of an unfolded hypercube. An earthquake hits, and the house folds back up on itself to concerning results (see also this student film version of the story)
- Some Notes on the Fourth Dimension – some animations and movies showing the geometry of the fourth dimension, including some of those featured in the Flatland dvd bonus features.

The last topic of the first section of the course is to further expand our notion of dimension, but in a different direction: Can there be dimensions in excess of 3?

As we are 3-dimensional creatures, it is challenging for us to conceptualize what a 4-dimension world would be like. It is best understood by analogy: by considering how a 2-dimensional creature would experience the 3-dimensional world. Fortunately, much of this heavy lifting has already been done for us!

In 1884, Edwin Abbott Abbott published Flatland: A Romance of Many Dimensions. It is told from the perspective of A. Square, a denizen of the titular 2-dimensional world, and starts off explaining aspects of their universe in great detail. The second part describes his first encounter with the 3-dimensional Spaceland, and the changes to his world-view as a result.

Abbott wrote the book partly as an exercise in geometry, but also partly as a satire on the regimented Victorian-era social hierarchy. As a result, there are some rather uncomfortable characterizations of women as lower-class citizens, among other shocking commentary.

You can read the full book here (I have paper copies if you’d prefer that), but for Monday please at least read this excerpt.

There’s no actual homework tonight, but you will need to use this Google Sheet to report your work from in class.

In class today, we discussed the final method for calculating dimension: the so-called Box Counting method. Your homework is to finish counting boxes for Great Britain (remember that you’re only counting boxes for the **coastline** of the large island, so don’t count any other islands, and don’t count the *interior* of the large island).

Report your results to today’s activity here.

**For tomorrow**, read pages 83-92, about “Fractal Math Imitations” in Fractals: The Patterns of Chaos.

No actual homework over the weekend, but please report your Richardson Plot results here.

Hello and welcome to my website! As I mentioned during the open house, I use this site to communicate with students, parents, and whomever else might be interested outside of class. On this site, you can find assignments, announcements, links to instructional videos and online review, copies of handouts I distribute in class, and the occasional mathematical musing.

Please take some time to check out this website. If you’re looking for course information, you can find it under “IHS Student Quicklinks” in the column to the right. If you’re wondering about how to obtain some extra help for your student, I recommend checking the “Class Information and Getting Help” link at the top. For more general information about what you can find on this site, check out the welcome post from the beginning of the year. Thanks for stopping by!

For Friday, please read pages 61-73 – “Between Things: Fractal Dimensions” from Fractals: The Patterns of Chaos. As usual, make a note of things you find interesting to share in a class discussion.

Our Fractal Art Show is tomorrow, so be sure to bring in whatever snack or treat you signed up for by then.

For Friday, please read pages 61-73 – “Between Things: Fractal Dimensions” from Fractals: The Patterns of Chaos. As usual, make a note of things you find interesting to share in a class discussion.

Our Fractal Art Show will be on Thursday, so be sure to bring in whatever snack or treat you signed up for by then.

In class today, you got a copy of Fractals: The Patterns of Chaos. For the first assignment from this book, please read pages 61-73 – “Between Things: Fractal Dimensions.” As usual, make a note of things you find interesting to share in a class discussion tomorrow.

Your fractals are due today! A reminder of what I want from each person:

- 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.

If you have not yet already, please sign up here to bring a small snack item to share with others at our FractaSketch Gallery Art Show on the 19th.

And for Tuesday, 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.

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.

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.