Introduction to Fractals

Introduction to Fractals

Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.

Fractals are complex geometric shapes that have self-similarity, meaning they appear the same at different scales. They are often generated by repeating a simple process in an ongoing feedback loop.

1. Which of the following is a key characteristic of fractals?

2. The process of generating a fractal by repeating a simple rule is called:

3. Fractals often exhibit a property called  -similarity, where parts of the fractal resemble the whole.

4. The Mandelbrot set is a famous example of a  .

5. Describe in your own words what makes a shape a fractal. Provide an example of a fractal found in nature.

6. All fractals have an integer dimension.

7. The Koch snowflake is an example of a fractal.

8. Consider the following iterative process for constructing a fractal:

Step 0: Start with a straight line segment.

Step 1: Divide the middle third of the line segment into three equal parts. Replace the middle segment with two segments of the same length, forming an equilateral triangle pointing outwards.

Step 2: Repeat Step 1 for each new line segment.

a) Draw the first two iterations (Step 0, Step 1, and Step 2) of this fractal construction.

b) What is the name of this fractal?