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Thank you for visiting fractal Music. Fractal Sounds - Volume 1 CD is now available. You can listen to previews of the compositions
included in the CD, listed below. These are only 20-second excerpts. Full-length compositions are available in the CD only, totalling 55 minutes of music. It is highly
recommended that you listen to the Hi-Fi version of the excerpts only. The excessive compression of the mp3 file in the 24 kbps version (lo-fi) severely distorts the compositions.
In addition, there are 5 free musical mappings of diverse mathematical methods, rendered with real instruments samples. Enjoy.
Follow this link to learn more about fractal music.
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| Sonification of the '3x+1' problem, also known as the Collatz problem, or hailstone numbers. The controlling function is x = {3x+1 if x = 1 mod 2; x/2 if x = 0 mod 2}, that is, 3x+1 if x is odd; x/2 if x is even. Starting with any number x, the function is iterated until the number 1 is reached, yielding an infinite loop 4,2,1,4,2,1...It is conjectured that all numbers eventually 'fall' to 1, thus entering the 4,2,1 loop. Proving it seems to be extremely difficult. The series of the first 40000 natural numbers were calculated, yielding a four million data set. If any number in the series is greater than 49, its digits are added until the result is no greater than 49. The data set was then normalized in the interval [-1, 1] and read directly at 44.1 KHz. The resulting wave is extremely complex, having a large amount of structure in all frequencies. It resembles the sound one would hear in the heart of a wasp's nest!
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CD: Fractal Sounds - Volume 1
Credits: Gustavo Diaz-Jerez |
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| Electronic mapping of the '3x+1' problem, using the number of steps required for any number x to hit 1 [S(x)]. The following mapping scheme was applied: S(x) was computed for x = [2, 100]. Starting from a fundamental frequency of 300 Hz, the following operation is performed: if S(x) is greater than S(x-1) the frequency is incremented |S(x)-S(x-1)| times in intervals of 2 Hz, with a duration of 45.35 milliseconds per interval. If S(x) is less or equal than S(x-1) the frequency is decremented |S(x)-S(x-1)| times in intervals of 2 Hz, every 45.35 milliseconds. Frequencies are rendered as pure sine tones. The result yields ascending and descending 'glissandi' of varying durations, resembling the wind, which is an aural representation of the apparently chaotic behavior of the process. |
CD: Fractal Sounds - Volume 1
Credits: Gustavo Diaz-Jerez |
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| Another sonification of the 3x+1 problem, but instead of using the iteration values of x, the number of steps required to hit 1 were used. The step values of the first 4 million natural numbers were calculated. If any number in the series is greater than 49, its digits are added until the result is no greater than 49. The data set was then normalized in the interval [-1, 1] and read directly as a 44.1 KHz wave file. The result resembles very much the sound of cracking wood in a fire. |
CD: Fractal Sounds - Volume 1
Credits: Gustavo Diaz-Jerez |
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