A fractal is a geometric figure that is self-similar, meaning it is exactly or approximately similar to its parts. Fractals are created using repeating patterns and include shapes like the Koch snowflake, Sierpinski triangle, Dragon Curve, and Mandelbrot set. Examples of fractals shown were the Koch snowflake, Sierpinski triangle and gasket, Cantor set, Dragon Curve, and Mandelbrot set.

1. Fractals

2. What is a fractal? A fractal is a geometric figure that can be broken down into parts; each part is a reduced-sized copy of the whole. A Fractal Uses the idea of “Self-Similarity” to make its design

3. Self Similarity In mathematics, an object is self-similar if it is exactly (or approximately) similar to itself In other words, the whole object has the same shape as one or more of its parts.

4. Self Similarity

5. Examples of Fractals… The Koch Snowflake - Helge von Koch

6. Examples of Fractals… The Koch Snowflake/Curve

7. Examples of Fractals… The Sierpinski Gasket aka The Sierpinski Triangle - Wacław Sierpiński

8. Examples of Fractals… The Sierpinski Carpet

9. Examples of Fractals… The Cantor Set - Georg Cantor

10. Examples of Fractals… The Dragon Curve Aka the Heighway Dragon (John Heighway )

11. Examples of Fractals… The Dragon Curve Aka the Heighway Dragon (John Heighway )

12. Examples of Fractals… The Mandelbrot Set

13. Examples of Fractals… Mandelbrot Zoom Videos Zoom Video #1 (Slow) Zoom Video #2 (Fast)

14. Fractal Art

15. Fractal Art

16. Fractal Art

17. Fractal Art

18. Fractal Art

19. Fractal Video Clip

20. Now, you are going to create one of the fractals that we saw in the slides…