11.1.10
- Today we had an introduction to fractals. Fractals are infinitely detailed and they are self-similar (made of small copies of themselves). Here are the links to the videos we watched:
The Mandelbrot Set is a complex fractal. We’re starting with a simple one – Cantor Dust. The procedure for creating Cantor Dust is to remove the middle third of each existing segment. Then repeat. Let’s call the length of the original ONE UNIT.
Your HW for November 8th:
- Make a table (neat & ready to be handed in) of the cantor dust through the first eight stages.
The headings of your table should be:
Stage / Number of segments / Length of each segment / Total length
For stage 1, for example, the number of segments is 1, the length of each is 1 and the total is 1.
For stage 2, the number of segments is 2, the length of each is 1/3 and the total is 2/3.
Make a note (mentally) of any patterns you see and be ready to talk about them.
- Imagine what would happen if the iterations continued to infinity. What would the fractal look like? How big might it be? Write a few sentences about your ideas.