sounds like fractals © mathscience innovation center 2007
TRANSCRIPT
Sounds Like Fractals
© MathScience Innovation Center 2007
Meet Patti.
Listen to this music with her.
The music has special patterns.
Patti likes patterns.
Looking for PatternsFractal Cent
Fractal Dime Fractal Dollar
Fractal Ten Dollars
0.01
0.10 1.00
10.00
1
1
1
1
2
2
2
2
2
2
3
3
33
4
0 0 0 1
0 0 1 0
0 1 0 0
0 1 0 10 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 01 1 0 1
1 1 1 0
1 1 1 1
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
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
A fractal shape
• A pattern within a pattern within a pattern.• The small parts look like the whole.
A fractal plant
• A pattern within a pattern within a pattern.• The small parts look like the whole.
1
1
1
1
2
2
2
2
2
2
3
3
33
4
1
1
1
3
0
2
2
2
0
1
1
2
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
Time to Make Waves
Full cycle
• Full to and fro movement• There and back• Complete wave
How many full cycles?
3 cycles 3 waves
Pre
ssu
re
or
densi
ty
Pre
ssu
re
or
densi
ty
Which sound do you think has the higher frequency?
time
time
low
high
Pre
ssu
re
or
densi
ty
Pre
ssu
re
or
densi
ty
Which sound do you think has the higher pitch?
time
time
low
high
Pre
ssu
re
or
densi
ty
Pre
ssu
re
or
densi
ty
Which sound do you think sounds louder?
time
time
soft
loud
Recap:
Sound is caused by _________________ of matter
vibrations
The faster the vibration, the higher the _________________________.frequency or
pitchThe bigger the vibration the __________ the sound. louder
Making Music
Notes:FGABflat
CDEEF
Higher Pitch
Shorter Pipe
G
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
Let’s listen to our fractal sequence!
Twinkle, Twinkle Little Star
Fmelody
CC D
CC
D C
harmony A A BB A
F
Twin-kle,Twin-kle lit-tle star
melody
G F
harmony
B B A A G
G FG F E E C
Twinkle, Twinkle Little Star
How I won-der what you are
melody
CC
Gharmony
AABB
A A
G
FG F C
Twinkle, Twinkle Little Star
Up a-bove the world so high
Fmelody
CC D
CC
D C
harmony A A BB A
F
Twinkle, Twinkle Little Star
Like a dia-mond in the sky.
melody
G F
harmony
B B A A G
G FG F E E C
Twinkle, Twinkle Little Star
Twin-kle,Twin-kle lit-tle star
melody
CC
Gharmony
AABB
A A
G
FG F C
Twinkle, Twinkle Little Star
How I won-der what you are.