Logistic Map

Type: Module

Category: Source

Updated: Aug 02, 2019

Manufacturer: Benard

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This module uses an implementation of the logistic map equation Xn+1 = λXn(1 - Xn) to produce CV values. The rate knob controls how often new values are produced, or alternatively you can use an external clock by connecting it to the input on the right and engaging the external clock toggle. Lambda determines the behavior of the system, with a range between 3 and 4 to achieve the desired chaotic behavior. There is also a glide control that interpolates between the CV values produced. Both of these parameters are CV controllable, which makes it possible to create very interesting chaotic patterns of CV for controlling oscillators, filters, or any parameter you want in your patches.

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

At slow rates the module can be used to produce melodies in chaotic patterns, whereas at fast rates it can produce many different kinds of noise. Through the use of CV control, it can create a variety of patterns and some very interesting behavior.

Keep in mind that even though the implementation of the logistic equation is accurate, this module doesn't pretend to specifically reproduce the behavior of the dynamical systems associated with the logistic map, 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. The aesthetic value of the output 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 logistic map check out the link below:



-Lambda - This knob controls the value of labda in the logisitc equation. It goes between 3 and 4. 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.

-Lambda CV In - This input allows you to modulate the value of Lambda with a CV signal, which will be added to the value of the Lambda knob, and capped between 3 and 4.

-Lambda CV Knob - This is an attenuverter that affects the Lambda CV input signal.

-Rate - This knob controls how quickly new values will be produced. Its range is set by the switch to its right.

-Range Switch - This switch allows you to set the range of the rate between slow, medium and fast.

-External Clock In - This input allows you to use and external clock signal to drive the module at different rates, and to sync it to other clocks.

-External Clock Toggle - This button selects the external clock. When engaged, the rate knob and range switch will be dimmed to make clear that they have no effect.

-Glide - This knob allows you to interpolate between the values produced by the equation.

-Glide CV In - This input allows you to modulate the glide value with a CV signal, which will be added to the value set by the glide knob and capped at 2000 ms.

-Glide CV Knob - This is knob attenuates the Glide CV input signal.

-Inject - Use this button to inject a random value into the equation to restart it and push it out of a stable zone. This is particularly effective at slow rates, as you can hear how the patterns are pulled by the attractors to the stable points.

-Inject input - This input allows you to use CV signals to trigger the injection of random values every time the signal goes to positive.