Introduction to Fractals
Explore the fascinating world of fractals, self-similar patterns, and their mathematical properties at a Grade 11 level.
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Introduction to Fractals
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Read each question carefully and provide your best answer. Show all your work where applicable.
1. What is a fractal? Describe its key characteristics.
2. Which of the following is NOT a characteristic of most fractals?
Self-similarity
Integer dimension
Infinite perimeter
Generated by iteration
3. The process of repeatedly applying a rule or function to generate a fractal is called .
4. The dimension of a fractal is often a number, unlike the integer dimensions of Euclidean geometry.
5. Consider the first three iterations of the Sierpinski Triangle shown below. If the initial triangle has an area of 1 unit, what is the area of the shaded region after the first iteration and after the second iteration?
Area after 1st iteration:
Area after 2nd iteration:
6. All fractals have an infinite perimeter and a finite area.
True
False
7. The Mandelbrot set is an example of a fractal.
True
False
8. Give an example of a fractal found in nature and explain why it is considered a fractal.