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