- Dynamics Homework due today.
- Homework, section 6.3, due next time.
- Upcoming "show-n-tell": Next week -- 4/29. Stop putting it off!
- You can start doing the "final homework" -- the attitude survey -- on-line, at Blackboard.
- It's a graph that possesses "self-similarity".
- It often possesses a simple and recursive (or iterative) definition.
- 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 #5, p. 450 (homework...).
- Mindscape #14, p. 452.
- Why is the Golden Spiral an example of a fractal?
| 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?
- 'Father of Fractals' takes on the stock market:
The fractal stock market segues right into our unit on financial math....
- Homework: pp. 678-681, #1, 3, 4, 9, 10, 12; Type up #20. Due
Wednesday, 4/29
- How
do the credit card companies make so much money?
- (Answer: the dynamics of compounding interest).
- Good news: the dynamics of compounding interest are the
same as the dynamics of population growth that we saw before!
- Simple rule, applied over and over
- One twist: how often does the bank compound?
- Interest and loan amounts grow exponentially, which one can show with a graph. The surprise is that they may start slowly, but then they take off!
- Pretty straight forward: #6, p. 678
- Here's a twist: #11, p. 679
- How do
mortgages work?
- Other loans can be calculated the same way: for example, CitiFinancial's loan shark fishing attempt on me.
- Here's another straight-forward mortgage problem: #16, p. 680
- A "real-world" example: do you use those balance-transfer
checks? I got
this offer awhile back.
- What are the hidden costs (buried in the fine print)?
- What would $1000 cost me for a year, if I take it out May 1, and pay nothing back? (By the way, the balance transfer APR is 18.99%).
