4c9704c71d
This isn't a final form, but an interim draft to test both LaTeX and HTML methods of displaying the equation and such.
47 lines
2.2 KiB
Markdown
47 lines
2.2 KiB
Markdown
# Bifurcator
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this is a fantasy sound chip which uses a unique sound generation method: [logistic map](https://en.wikipedia.org/wiki/Logistic_map) iterations.
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## usage
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the core of the Bifurcator is the (iterative) logistic map function:
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<!-- LaTeX -->
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$x_{n+1}=\lambda x_n (1-x_n)$
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<!-- MD/HTML -->
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_x_<sub>_n_+1</sub> = _λx_<sub>_n_</sub>(1 - _x_<sub>_n_</sub>)
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which when iterated across $2\leq\lambda\leq4$ produces this graph:
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_{{ IMAGE HERE – will look sort of like [this](https://en.wikipedia.org/wiki/Logistic_map#/media/File:Logistic_Bifurcation_map_High_Resolution.png) but matching house style }}_
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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 _λ_ in the range 2.0 to 4.0.
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### load value
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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.
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different load values will cause different "attack" sounds before the iterations stabilize (if they do).
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### parameter
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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.
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for most parameter values below 32768 the output converges to a single value (effectively no sound).
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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.
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the default parameter value is 47360.
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## effects
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- `10xx`: **set low byte of channel sample state.**
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- `11xx`: **set high byte of channel sample state.**
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- `12xx`: **set parameter low byte.**
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- `13xx`: **set parameter high byte.**
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## info
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this chip uses the [Bifurcator](../4-instrument/bifurcator.md) instrument editor.
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