documentation for version 1.0 beta2 (released : 28-June-1996)
• What is the bifurcation function?
The bifurcation function is a well-known chaotic function, which simulates population growth of a living thing. The function is :
N = r * Np (1-Np)
where N is the new level of population (of the new generation), r is reproductive constant, and Np is the previous level of population (of the last generation).
N should range from 0 to 1, r should range from 0 to 4.
As r is various, the result of the function shows sudden transitions to different behaviors:
For 0 < r ≤ 1: the population goes to extinction.
For 1 < r ≤ 3: the population settles down to a single value.
For 3 < r ≤ 3.57: the population follows a periodic series of values.
For 3.57 < r < 4: the population begins to show chaotic behavior.
• Graphic area
The main window of this program has a graphic area, on which the values can be drawn. Use 'Control' menu to run, stop and reset it. You can examine the result of the function graphically after specifying parameter values.
• What is the bifurcation oscillator?
This program uses chaotic values from the bifurcation function to produce sound.
While the bifurcation function is a basic numerical system, the transformer that converts those values into a real sound is very important. So the transforming method is the key of the quality of sound.
In this version, it provides three types of transforming:
- transformer 1 : Frequency modulating.
- transformer 2 : Amplitude modulating.
- transformer 3 : Frequency and amplitude modulating simultaneously.
• Frequency modulating transforming
You specify three parameters. Those are minimum frequency, maximum frequency, and modulating trigger frequency.
As I said above, the value from the bifurcation function ranges from 0 to 1. When the value is 0, the frequency of wave will be the minimum frequency you specify, and when the value is 1, it will be the maximum frequency you specify.
The modulating trigger frequency determines how frequently it modulates the wave.
• Amplitude modulating transforming
You specify four parameters. Those are frequency of wave, minimum amplitude, maximum amplitude, and modulating trigger frequency.
When the value is 0, the amplitude of wave will be the minimum amplitude you specify, and when the value is 1, it will be the maximum amplitude you specify. You should specify them in percentage. That is, 0% means no sound, 100% means full volume.
The modulating trigger frequency determines how frequently it modulates the wave.
• FM & AM transforming
This method generates a wave first by frequency modulating transforming, and then by amplitude modulating transforming.
• Transition options
Between two values, or between two frequencies, or between two amplitudes, you can specify a transition method. That is, the first value can be increased linearly to the next value, or the frequency can be increased sinusoidally to the next frequency. Otherwise they will be changed suddenly.
In this version, it provides three types of transition:
- no transition
- linear transition : increase(or decrease) slowly.
- sinusoidal transition : increase(or decrease) slowly, faster and faster, slower and slower.
• Sound files
This program saves sound in an AIFF file. So you can use it in any other sound program.
Sound files made by this program remember all parameter values used to make the sound. So you can refer it in the future. Use 'Open' menu in the 'File' menu to open one, or just double click the sound file you want to open.
Sound files made by another program can be played by this program (use 'Open' menu).
• More about this program
- This program is completely free. But if you find this program is useful, please register! (See below for register info)
- Please always include this documentation when you copy the program or give it to somebody.
- This program is written in C++ with CodeWarrior.
• Register, bug report, suggestions, or anything !
Don't panic. There's no registration fee. Just send me an email for registration. If you register, I will keep sending the upgrade versions to you, and also sending some useful informations about sound, music, and so on.
Send an email to this address : jaeho@xs4all.nl
with this contents :
register BifurcationOscillator
name - (your name please)
organization - (your company, school, or anything)
bug report - (if any)
suggestions - (if any)
other comments - (if any)
You can send me your bug report or suggestions anytime. Your supporting makes me happy and this program more useful and powerful !
