44 lines
2 KiB
Markdown
44 lines
2 KiB
Markdown
# Bifurcator
|
|
|
|
this is a fantasy sound chip which uses a unique sound generation method: [logistic map](https://en.wikipedia.org/wiki/Logistic_map) iterations.
|
|
|
|
## usage
|
|
|
|
the core of the Bifurcator is the (iterative) logistic map function:
|
|
|
|
_x_<sub>_n_+1</sub> = _rx_<sub>_n_</sub>(1 - _x_<sub>_n_</sub>)
|
|
|
|
which when iterated across 2 ≤ _r_ ≤ 4 produces this graph:
|
|
|
|
|
|
|
|
|
|
in Bifurcator the current output (and initial "load value") ranges from 0 to 65535, which maps directly to _x_ in the range 0.0 to 1.0. the parameter ranges from 0 to 65535, which maps directly to _r_ in the range 2.0 to approximately 4.0.
|
|
|
|
### load value
|
|
|
|
the first value of _x_ is set with the **load value**. it must be set to a non-zero value, otherwise the next iteration would also be zero... and the next one too... and so on, generating silence. default is 1.
|
|
|
|
different load values will cause different "attack" sounds before the iterations stabilize (if they do).
|
|
|
|
### parameter
|
|
|
|
by varying the parameter, the values of _x_ may change drastically, producing a variety of sounds. the higher the parameter, the more "chaos" is present, effectively yielding noise.
|
|
|
|
for most parameter values below 32768 the output converges to a single value (effectively no sound).
|
|
|
|
above 32768 the output starts to oscillate. from 32768 to 47496, it bifurcates to oscillate between between 2 values, generating a square wave. from 47497 to 51433, it bifurcates again and becomes a period of 4 values. beyond that, the system rapidly becomes chaotic (noise). there's an "island of stability" starting at around parameter value 59914 where the output oscillates between 3 values, then bifurcates from there.
|
|
|
|
the default parameter value is 47360.
|
|
|
|
## effects
|
|
|
|
- `10xx`: **set low byte of load state.**
|
|
- `11xx`: **set high byte of load state.**
|
|
- `12xx`: **set low byte of parameter.**
|
|
- `13xx`: **set high byte of parameter.**
|
|
|
|
## info
|
|
|
|
this chip uses the [Bifurcator](../4-instrument/bifurcator.md) instrument editor.
|