1. Sounds Like Fractals © MathScience Innovation Center 2007

2. Meet Patti. Listen to this music with her. The music has special patterns. Patti likes patterns.

3. Looking for Patterns Fractal Cent Fractal Dime Fractal Dollar Fractal Ten Dollars 0.01 0.101.00 10.00

4. 1 1 1 1 2 2 2 2 2 2 3 3 3 3 4 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1

5. A sequence is a set of numbers in an order. 1, 3, 5, 7, 9, 11, ___ 13 1, 4, 1, 4, 1, 4, ___ 1 1, 3, 9, 27, 81, 243, ___ 729

6. A fractal sequence A pattern within a pattern within a pattern. The small parts look like the whole. 1 1 2 1 3 2 4 1 5 3 6 2 7 4 8 1 9 1 1 2 1 3 2 4 1 1 1 2 1 fractal

7. A fractal shape A pattern within a pattern within a pattern. The small parts look like the whole.

8. A fractal plant A pattern within a pattern within a pattern. The small parts look like the whole.

9. 1 1 1 1 2 2 2 2 2 2 3 3 3 3 4 1 1 1 3 0 2 2 2 0 1 1 2

10. A sequence is a set of numbers in an order. The sequence of numbers your team has produced is cool… it has a special name- Morse-Thue

11. Time to Make Waves

12. Full cycle Full to and fro movement There and back Complete wave

13. How many full cycles? 3 cycles3 waves

14. Pressure or density Which sound do you think has the higher frequency? time low high

15. Pressure or density Which sound do you think has the higher pitch? time low high

16. Pressure or density Which sound do you think sounds louder? time soft loud

17. Recap: Sound is caused by _________________ of matter vibrations The faster the vibration, the higher the _________________________. frequency or pitch The bigger the vibration the __________ the sound. louder

18. Making Music

19. E Notes: F G A B flat C D E F Higher Pitch Shorter Pipe G

20. Let’s Hear Our Fractal Sequence 0 = C E 1 = C E G 2 = D F A 3 = E G B 4 = G B 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4

21. Let’s listen to our fractal sequence!

22. Twinkle, Twinkle Little Star F melody CCD CC D C harmony AABBA F Twin-kle,Twin-kle lit-tle star

23. melody GF harmony BBAAG GFGFEEC Twinkle, Twinkle Little Star How I won-der what you are

24. melody C C G harmony AABB AA G FG F C Twinkle, Twinkle Little Star Up a-bove the world so high

25. F melody CCD CC D C harmony AA BB A F Twinkle, Twinkle Little Star Like a dia-mond in the sky.

26. melody GF harmony BBAAG GFGFEEC Twinkle, Twinkle Little Star Twin-kle,Twin-kle lit-tle star

27. melody C C G harmony AABB AA G FG F C Twinkle, Twinkle Little Star How I won-der what you are.