Fractal Geometry Exploration

Fractal Geometry Exploration

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

What are Fractals?

Fractals are fascinating geometric shapes that exhibit self-similarity, meaning they look similar at different scales. They are often created through a process of iteration, where a simple rule is applied repeatedly. Many natural phenomena, like coastlines, snowflakes, and tree branches, show fractal characteristics.

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

2. The process of applying a simple rule repeatedly to create a fractal is called:

3. Fractals often exhibit   , meaning they look similar at different scales.

4. The process of repeatedly applying a rule to generate a fractal is called  .

5. Describe in your own words what self-similarity means in the context of fractals. Provide an example of a natural phenomenon that exhibits this property.

6. Consider the first three iterations of a Sierpinski Triangle:

Draw the 4th iteration of the Sierpinski Triangle in the space below. Remember the iterative rule: find the midpoint of each side of the central triangle and connect them to form three smaller triangles. Remove the central triangle, and repeat the process for each of the remaining three triangles.