- Dynamics homework returned
- There were some really good examples of "tiny differences,
huge differences" (the butterfly effect):
- For want of a condom a baby is born;
- The day you weren't there, the group with which you had been buying lottery tickets as a group hits a 27 million dollar ticket (nothing for you!);
- A CD purchase leads to a music career;
- Letting a car go by, right into an accident;
- Seeing an on-line add for a university, and going there.
- Someone mentioned small architectural changes....
- Stock results (here Procter and Gamble Co (PG))
- There were some really good examples of "tiny differences,
huge differences" (the butterfly effect):
- Homework for the graphs unit is due today.
- Today we start the "Fractals and Trees" unit. I hope that you've
read section 6.3. Homework for this unit:
Mindscapes, section 6.3, pp. 450-, #4, 5, 13, 20, 21, 24, 25, 32; Due Monday, 11/24
- I found a really neat website -- manyeyes -- that allows us to visualize data easily, and in very interesting ways.
- Here are KY lung cancer deaths compared to other states -- we're #1!
- On a more positive note, how about Green Eggs and Ham?
- It's a graph that possesses "self-similarity".
- It often possesses a simple and recursive (or iterative) definition.
- We're going to be looking at more graphs in this unit, but they're
graphs of a very different nature.
- Let's start by having a glimpse at the beautiful gallery of
section 6.1, for these are the subjects of our unit.
- Deterministic
fractals: delve into an infinite, dynamic world, created by
a simple mathematical process:
- a simple rule
- repeated over and over and over.... but
- simple rules, intense content!
- Can you explain how these fractal images illustrate chaos?
- The pictures remind me of the "acres of dominoes" from Robert Graves's Warning to Children.... Here's the poem in manyeyes.
- Building deterministic fractals with sticks
- Fractal ferns (p. 443), and even names!
- Let's see the process, but a little slower.
- Now let's introduce a little bit of randomness:
- Fractal Islands, and coastlines.
- Sierpinski triangle (p. 436):
- First deterministically: fractals by subtraction
- After we're finished removing all that stuff, how much area is left in the triangle?
- The Chaos game - generating fractals using random movement! (p. 447)
- Once again, simple rules lead to complex objects. This time, however, we don't proceed methodically, but rather haphazardly - and yet we still produce the complex images!
- Here's
a better version of that, that has more general options.
From randomness comes order; from simple rules comes complicated objects! Then all hell broke loose....
- The collage making process -- see page 437.
- Mindscape #14, p. 452.
| Here's our mascot for this unit: Bessie the fractal cow: |
|
| We might have easily taken the Japanese artist Hokusai. |
So what is a fractal? A couple of things we'll generally see?
