Lorenz Attractor

Type: Module

Category: Source

Updated: Aug 02, 2019

Manufacturer: Benard

Contact Manufacturer

$20.00

This module uses an implementation of the Lorenz system of ordinary differential equations to produce chaotic CV values.

The parameters of the system are controlled by the setting of the sigma (σ), rho (ρ), and beta (β) knobs, and the delta T knob (dT) controls the rate at which values will grow per time increment. Each of these parameters can be CV controlled using the inputs and attenuverters to the right of the knobs.

The system produces 3 outuput values, X, Y and Z. Each of these values has its own output and output level control. There are also scale and offset knobs that affect each of these values. These are useful for bringing the outputs into the desired ranges for specific purposes. The scale and offset knobs are also CV controllable, which adds a lot of power to this module. There is also a Mix Output at the bottom right, which outputs the combined X, Y and Z values.

The inject button and CV input introduce random numbers into the system to kick it out of a stable zone when it gets stuck, or simply to restart the system. This is particularly useful at low values of dT, but it will hardly be noticeable at higher dT values, since the system will quickly be pulled back into a stable zone. However, interesting effects can be achieved by sending quick triggers to the inject input, especially when dT is at around its mid-range or is being CV controlled.

The Cap toggle and trigger input restrict the values produced by the system to prevent them from growing too big and going out of the usable range, which can happen especially when the value of dT is high. Notice however, that when this is engaged the system is not really behaving as a Lorenz system anymore. But it still results in interesting and useful musical behavior that adds possibilities to the system, and can help to keep its output within musically useful ranges. That is why it has been implemented in the module, favoring musical usefulness over purity of implementation. If the system gets stuck while using high dT values, try engaging Cap, and press inject to reset the system.

Keep in mind that even though the implementation of the Lorenz System aims to be accurate, this module doesn't pretend to specifically reproduce the behavior of this dynamical system, nor does it assume that such behavior should be of musical interest per se. It is rather meant simply as a creative tool and a starting point for producing interesting behavior. This applies even more to this module than to the Logistic Map module, due to its increased control options that can result in the output deviating greatly from the strict mathematical implementation of the unperturbed system, as mentioned above. But the goal is simply to produce interesting and usable behavior, rather than to strictly recreate a mathematical system. The aesthetic value of the output of the module will depend solely on how the user applies it in a musical or sound design context.

Included in the Benard Mega Bundle Vol. 2.

For more information about the Lorenz System check out the Wikipedia link below: https://en.wikipedia.org/wiki/Lorenz_system

Documentation

-Sigma σ - This knob controls the value of sigma in the Lorenz system. It goes between 6 and 35 in this implementation. The most interesting behavior will happen around the middle of the range. Values towards the extremes will tend to settle more quickly into stable repetitive regions.

-Rho ρ - This knob controls the value of rho in the Lorenz system. It goes between 20 and 50 in this implementation. The most interesting behavior will happen around the middle of the range. Values towards the extremes will tend to settle more quickly into stable repetitive regions.

-Beta β - This knob controls the value of beta in the Lorenz system. It goes between 2 and 6 in this implementation. The most interesting behavior will happen around the middle of the range. Values towards the extremes will tend to settle more quickly into stable repetitive regions.

-Delta T (dT) - This knob controls the rate at which values will grow as time advances (i.e. per time increment).

All of the parameters above can be CV controlled with the CV inputs and attenuverters to the right of the knobs, which will add the CV input to the value of the respective knob.

The system outputs 3 values, X, Y and Z, and each has its own scale and offset knob, with CV control, as well as a final level knob for further adjustments.

The Mix Out combines the outputs of all 3 paramters, and also has its own level control.

-Inject - Use this button to inject a random value into the system to restart it and push it out of a stable zone. This is particularly effective at low dT values, as you can hear how the values are gradually pulled by the attractors to the stable zones. You can also trigger this with a signal using the input to the right of the button.

-Cap - When this toggle is activated, the values of the system are rescaled to keep them from growing to large, thus restricting them to a usable range. This can be useful especially for high dT values, where the system changes more rapidly. You can also engage this toggle with a trigger signal using the input to the right of the button.

N.B. Notice that the default values for the scale parameters for X, Y and Z is zero. Therefore, you won't get any output until you adjust these knobs!