simplex~

Pure Data (Pd) external for signal rate simplex noise sampling with 1d, 2d, 3d and 4d multichannel input

The current version's noise implementation is based on https://github.com/stegu/perlin-noise/blob/master/src/sdnoise1234.c by Stefan Gustavson.

Build and Installation Instructions

To compile and install, follow these steps. Note that Makefile.pdlibbuilder is included as submodule, requiring the --recursive parameter.

git clone --recursive https://github.com/ben-wes/pd-simplex.git
cd pd-simplex
make install

Usage

Inlets and Outlets

• 1st inlet: expects a multichannel signal with up to 4 dimensions for the noise sampling position (the noise algorithm, and hence its performance, is determined by the number of channels)
• 2nd inlet: can be used to control the persistence value with a signal or float inputs
• outlet: outputs the sampled noise value at signal rate

Creation Arguments

Optional flags

• -n flag activates normalization of the octaves' sum to keep values in the [-1..1] range
• -s <int> flag initializes the noise's permutation table with a given seed
• -d flag activates derivatives multichannel output on additional 2nd outlet
• -dim <int> flag switches to single-channel mode with given dimension count

Optional numerical arguments (must be written after the flags)

• first arg sets the number of octaves (defaults to 1, max. is 1024)
• second arg sets initial persistence (defaults to 0.5)

Messages

• [seed <int>( generates different (deterministic) permutation tables for the simplex function
• [normalize 0/1( (de)activates normalization (off by default)
• [octaves <int>( dynamically changes the number of octaves
• [persistence <float>( sets persistence (while no signal is connected)
• [coeffs <float> <float> ... <float>( let's you customize the octave scaling (default is 1, 2, 4, ...)

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Additional Information

Octaves

In case of more than 1 octave, additional noise octaves get sampled, i.e., downscaled instances of the noise space (higher noise frequencies) are added. This downscaling is achieved by multiplying the sampling coordinate with 2^(octave-1) - for example:

• input (1, -3) samples from 2*(1, -3) = (2, -6) for 2nd octave
• input (1, -3) samples from 4*(1, -3) = (4, -12) for 3rd octave

Persistence

The persistence value determines the influence of successive octaves on the final output. It is a multiplier applied to each octave’s amplitude. Lower persistence values cause the amplitudes to decrease rapidly with each octave, leading to a smoother noise pattern. Conversely, higher persistence values maintain stronger amplitudes in higher octaves, resulting in more detailed and rougher (high frequency) patterns - for example:

• persistence of 0.5 yields octaves' amplitudes 1, 0.5, 0.25, 0.125, 0.0625, ...
• persistence of 0.9 yields octaves' amplitudes 1, 0.9, 0.81, 0.729, 0.6561, ...

Normalization

If normalization is activated (via creation argument or message), the sum of all octaves' amplitudes is normalized to 1.

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History

The initial code of this external was an experiment generated with ChatGPT4. The fascinating part of this was, that with a few feedback loops (feeding errors back to it), it managed to create a working Pd external. After some more research around simplex noise, the noise algorithm of the external turned out to be a pretty exact copy of this SimplexNoise.cpp though (including variable names and comments).