Download Sounds Like Fractals

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 Patterns
Fractal Cent 0.01
Fractal Dime
0.10
Fractal Ten Dollars 10.00
Fractal Dollar
1.00
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A sequence is a
set of numbers in an order.
1
1, 4, 1, 4, 1, 4, ___
1, 3, 5, 7, 9, 11, ___
13
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
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.
0
1
1
2
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2
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3
1
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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 nameMorse-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
Pressure
or density
Pressure
or density
low
time
Which sound do you think
has the higher frequency?
high
time
Pressure
or density
Pressure
or density
low
time
Which sound do you think
has the higher pitch?
high
time
Pressure
or density
Pressure
or density
soft
time
Which sound do you think
sounds louder?
time
loud
Recap:
vibrations
Sound is caused by _________________
of matter
The faster the vibration, the higher
frequency or pitch
the _________________________.
The bigger the vibration the
louder
__________
the sound.
Making Music
Higher Pitch
Shorter Pipe
Notes:
F
G
A
Bflat
C
D
E
F
G
Let’s Hear Our
Fractal Sequence
•
•
•
•
•
0=C E
1=C E G
2=DF A
3=EG 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
melody F
harmony
C
C
C D
D
C
C A
A B
B
A
F
Twin-kle,Twin-kle lit-tle star
Twinkle, Twinkle Little Star
melody
B
B
A
A
G
G
F
harmony
G
G
F
F
E
E
C
How I won-der what you are
Twinkle, Twinkle Little Star
melody
C
C
B
B
A
A
G
harmony
A
A
G
G
F
F
C
Up
a-bove the world so high
Twinkle, Twinkle Little Star
melody F
F
harmony
C A A
C
C
C D
B
D
C
B
A
Like a dia-mond in the sky.
Twinkle, Twinkle Little Star
melody
B
B
A
A
G
G
F
harmony
G
G
F
F
E
E
C
Twin-kle,Twin-kle lit-tle
star
Twinkle, Twinkle Little Star
melody
C
C
B
B
A
A
G
harmony
A
A
G
G
F
F
C
How I
won-der what you are.