Steve Lombardi 7/7
I've created a Julia set applet for the page, let me know what you think: Julia set
Chris Taranta 7/6
This is a beautiful, almost haunting image. It's neat that you created it yourself.
If possible (I know it's complicated) tell what a Julia set is in the opening.
More Mathematical Explanation: • The picture uses the term fractals but the opening paragraph does not. • Repelling: You explain it later but it might be helpful to use a mouseover or other explanation here. • How did they get their name? Who’s Julia?
Complex Numbers and the Complex Plane • ⁋2, Sentence 4: Change “switching between” to “switching from”
Iterated Functions: • Sentence 1: Change “we referring” to “we are referring” • Sentence 2: Why change from Q to f?
Periodic and Fixed Points (Should this be called “Fixed and Periodic” Points since you begin with Fixed Points?): • Sentence 5: One more step between the [(1 ± 2i√19 – 19) / 4] + 5 and (1 ± i√19) / 2 would be helpful, as in [(-18 ± 2i√19)/4] + 20/4. • I find the section on periodic points quite challenging to understand. Can you run the z^2+5 example through the discussion of periodic points? • ⁋4, Sentence 2: “For attracting period point,” is not grammatical. • ⁋4, Sentence 5: For the top of a cone analogy, I think of an ice cream cone. There stuff falls to the point at the bottom. I assume you mean a cone with the point at the top. Please clarify.
Julia Set: • S1: I trust you that it is the conceptually easiest way, but it does not seem easy to me. Also, I think you mean “…Julia sets are the closure…” • S2: What do you mean by “root” here? How are roots distinct? It might be helpful to explain why ln(x) and K(x) are not examples of rational functions. Is ln(x) not a rational function because of the ln or because it is not a ratio? • “It may seem like rational functions are undefined for certain values.” I assume you mean where the denominator equals 0.
I stopped at this point because the mathematics got too complicated for me. While I recognize that the math here is very sophisticated, if you intend for any high school student or most college students to grasp this, it needs to have a slower-paced, step-by-step explanation with more examples and more pictures.