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Jae Ho Chang 
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Logistic Synth
chaotic oscillators project #2
programmed by Jae Ho Chang
documentation for version 0.2 (released : 11November1996)
* This program is freeware. It can be freely distributed as long as it is not modified and there’s no charge for it, but it may not be included in any commercial package without the written consent of the author.
* Please register if you are interested in this program. There’s no registration fee. Just email to me that you are using this program. And I hope you join me in developing chaotic sound synthesis (please visit the web site addressed above).
• What is Logistic Synth?
Logistic Synth is a chaotic sound generator which uses one of well known chaotic maps called ‘Logistic Map’. This version features only realtime synthesis with only one method.
• What is the logistic map?
The logistic map simulates population growth of a living thing. The function is :
N = r * Np (1Np)
where N is the population level of the new generation, r is reproductive constant, and Np is the population level of the previous generation.
N should range from 0 to 1, r should range from 0 to 4.
As r is various, the result of the map shows sudden transitions to different behaviors:
For 0 < r ≤ 1: the population level goes to extinction.
For 1 < r ≤ 3: the population level settles down to a single value.
For 3 < r ≤ 3.57: the population level follows a periodic series of values.
For 3.57 < r < 4: the population level begins to show chaotic behavior.
We usually concentrate on the last range of r.
• Common parameters in windows
Xi
The initial N value of the function. Changing this value does not affect to the sound very much.
R
The r vlaue of the function. 0 to 3 will not produce any sound. 3 to 3.57 will produce just a periodic sound, and 3.57 to 4 will produce chaotic sound.
• How does it generate sound?
In this version, there’s only one method.
1. Direct Method
Each value from the function is used just as a sample value. Of course, the function values are adjusted to fit to the range of sample values.
 Parameters
Carrier frequency: This determines the number of samples which are generated by one value from the function.
Transition: This determines the shape of a sample group (in other words, the shape of transition from the first sample of a group to the first sample of the next group). No transition produces sqaurewavelike sound, linear transition produces trianglewavelike sound, and sinusoidal transition produces sinewavelike sound.