One of the reoccurring themes at Het Concreet is unpredictability and the practice of creating technological configurations which carry a form of independence. The often deliberately sought-after unpredictability of our instruments forces us to be in dialogue and question our own creative ideas. This article on the Lorenz Attractor is part of Mathijs Leeuwis’ thesis on Co-creational Instability Networks. It describes the development of a chaotic oscillator and its various creative applications.
In a musical dialogue between actants I aim to be surprised, thrown-off, and forced to rethink my position, but I do strive for a dialogue which is more than just randomness being shot back and forth between those that are present. As I search for ways to be changed through the intra-action - “the mutual constitution of entangled agencies,”[1] - with others, I also hope to change the other with my actions, thus coming to a point of communal ownership of whatever emerges. The back and forth movements between actants, the entanglement of material and development made me use chaos as a concept, which has been put into action through the use of the Lorenz Attractor. This article describes why and how this circuitry embodies instability and how this informed the development of this instrument within my set-up.
So in its simplest form, this article is about an instrument: the Lorenz oscillator. It is one of the technological links in my set-up. But since this instrument is the result of my search for ways to add a degree of instability to my instrumentation, it does make sense to provide more background. I was looking for ways to integrate an external autonomous voice into my no-input mixer set-up. Through the work of philosopher of science Ilya Prigogine, I came across so-called “strange attractors”. This concept put me on the path of chaos as a creative building block for my music. Chaos as a means of arriving at new musical situations. What follows here is an overview of the core concepts surrounding chaos and the practical elaborations that emerged from them.
Prigogine uses a pendulum to describe stable and unstable behaviour: if one swings the pendulum in such a manner that its weight is at the bottom, at one point it will stabilise at the “centre of gravity as low as possible,” and “it will return to a minimum swing.”[2] But if the pendulum is set in motion in an upside down manner, it could fall either left or right and the smallest of movements could make it tip over to one side or the other.[3] As Prigogine writes: “The pendulum on its minimum swing is a deterministic object: we know what will happen. In contrast, the problem of the pendulum turned on its head involves a non-deterministic object.”[4] In other words: it becomes hard to predict what will hap- pen exactly when we work with the upside-down pendulum.
To explain certain behaviours the concept of attractors is commonly used in mathematics and physics. Attractors describe a system's tendency to evolve towards a set of states.[5] Prigogine describes a set of different attractors. For instance the stable pendulum which returns to one point, the minimum swing at the centre of gravity; this would be a “punctual attractor”.[6] To describe more complex behaviours, so-called strange attractors are used. These strange attractors correspond to numerous points and “the system moves from one point to another - it is a mixture of stability and instability.”[7] Exactly this mixture of stability and instability, caught in a system, resonated with me. In my search for a more equal dialogue with my instruments, I am aware of my position of power in my role as instrumentalist, composer and initiator. Would it be possible to use a system of strange attractors as a technological/musical parameter? And could my own role within the creative process be forced into a more co-creational attitude when these strange attractors are given power over my work?
In my search for a creative use of chaos, I came across the work of the mathematician Edward Lorenz. In his studies of weather forecasting, he more-or-less accidentally stumbled upon a crucial phenomenon: although he started his experiments with the same set of data, the results kept changing when conducting his experiments. Lorenz unconsciously encountered the workings of chaotic systems, in which minimal anomalies in the starting positions lead to major differences in the long term. Lorenz later described it this way: “Chaos: When the present determines the future, but the approximate pre- sent does not approximately determine the future.”[8] This might seem theoretical, but just look at a double pendulum, it shows chaos: behaviour varies infinitely, with each starting position leading to a different result.[9]
It is important to underline the difference between chaos and randomness. Chaos - although hard to predict - functions in a deterministic manner, it is linked to particular strange attractors, causing all kinds of complex behaviours to emerge, but still it functions deterministically, always taking into account the way the system is put in motion. Whereas randomness can be seen as a state of no definite aim or purpose, not sent or guided in a particular direction.[10]
At the same time as I was reading about these concepts, I worked with artist, inventor and instrument builder Paul van Twist on the question of how to apply these ideas to a musical set-up. In our discussions on the use of chaos, Van Twist suggested to implement the Lorenz equations in an analogue electronic circuit, thus creating an electronic instrument which could be used to integrate the theoretical chaos Lorenz described into my musical set-up. The design Van Twist eventually proposed was based on the circuitry Harvard University physicist Paul Horowitz made as a translation of the Lorenz-equation.[11] One important addition to the design was made: an external input was added to the circuits design. This way it became possible to let the Lorenz circuit be influenced by external parameters, such as other electronic devices or musicians. In essence this is in line with the idea of the feedback loops which are present all through my set-up: all actants present are in some way enabled to influence the other actants, as well as to be influenced by the other actants.
The use of this rather wild circuit has brought me much artistically. Thus what follows now is a detailed description of the musical development and implementation of this circuit including technical and conceptual connections. I have made an effort to give musical examples wherever possible.
The first version of the Lorenz Attractor was build by Paul van Twist and this was the starting point for me to start working with chaos in my set-up. The Lorenz Attractor basically creates oscillations based on the initial equation. If we use this equation to create an oscillator, it creates a distinct form on the oscilloscope, also known as the “owl face”[12]. This visualisation shows the very nature of chaotic processes: it tends to perform more or less in the same manner, but continuously produces small deviations. Van Twist built a version with the option to adjust a lot of the parameters by ad hoc connecting potentiometers on the open circuit. Each time one of these parameters was adjusted the Lorenz Attractor would start a new sequence of “owl face” movements. Depending on where the sequence started the outcome in sound would be determined. The longer I would let the sequence run, the bigger the deviations from its starting position would be. So in comparison to a fixed no-input mixer oscillator this had more of an autonomous voice you could say. In one of the first experiments I did with this circuitry the explicit electronic character is clearly present.[13] Each time a big sonic change occurs, I was adjusting something on the circuit, for instance at 01:05.
The fact that this prototype was built entirely as an open circuit made it possible to make ad hoc changes to the design, for instance changing resistors. It also allowed me to approach the circuit itself as a tactile instrument by making new, temporary connections with my hands. So in this case the open circuit acts as a hard-to-read interface, essentially reducing my position as a composer or instrumentalist. The instrument doesn't really need me to keep producing new sounds. So I can explore, discover the instrument and its physical construction, looking for nooks and crannies where I can find something that appeals to me. But in doing so, both the physical construction of the instrument and the nature of the sounds it produces make it difficult to reproduce certain sounds exactly, if I have found anything at all. This places the instrument very much in the here and now: exact reproduction or reliable repetition of certain elements is almost impossible.
Shortly after the prototype was built and I did my first experiments with it, I started to use the instrument in conjunction with other actants. Initially by implementing the Lorenz Attractor in a fairly simple no-input mixer system. For instance, I was using the Lorenz Attractor as part of a bigger network with a no-input mixer and the Koma Field Kit.[14] The video also shows how I am making ad hoc connections directly on the circuit, for instance at 01:12. It is clear that the deviations and alternations in the musical routes are much bigger in comparison with just the Lorenz Attractor running as a solist, as we could hear in the first demonstration recording ‘Lorenz Demo’ [see note 13].
The next step was to use the Lorenz Attractor with other musicians. Initially I did a lot of improvisations with the instrument together with trombonist Dalton Harris.[15] I connected his signal to the input of the Lorenz Attractor using a contact microphone. This made Harris' trombone a trigger/modulator for the behaviour of the Lorenz Attractor. What I particularly like about this improvisation is that the changes in mutual influence are sometimes hard to pin down: a tiny change in one of the potentiometers can suddenly produce a big result. Other times there is no audible difference when I make chan- ges to the circuitry. Sometimes the Lorenz Attractor and Harris' playing seem to amplify each other, sometimes they seem to circle each other. This searching way of playing the instrument fits well with an attitude to improvisation in which instability is a central theme.
In addition to these improvisations that arose completely in the moment and where the Lorenz Attractor was really played like a normal instrument, I also began to look for ways in which the Lorenz Attractor can have a more autonomous function. Without me being involved as a player. First attempt of this approach were recorded with researcher, instrument maker and sound artist Kevin Toksöz Fairbairn.[16] He can be heard playing one of his self-built instruments. All the acoustic sounds - mainly strings stretched over a derivative of a trombone - are Fairbairn's. The deep electronic bass is produced by the Lorenz Attractor. All the Fairbairn sounds were used as modulators/triggers for the circuit. What you can hear is a certain consistency in the behaviour of the circuit in combination with what Fairbairn plays. At the same time, it is not possible to establish a fixed cyclical movement. The circular movement of the Lorenz Attractor forms a focus point for the more detailed and varied playing of Fairbairn, while at the same time also providing some sort of musical dialogue partner which changes through each others actions.
The development of the Lorenz Attractor is still ongoing. At the time of writing we are working on the simplification of the instrument. We are moving away from the open-circuit set-up. This brings forth complete new questions and problems which will be highlighted in the follow-up on this article.
This article is part of the master research thesis by Mathijs Leeuwis, Co-creational Instability Networks, presented at Fontys Academy of the Arts in 2025.
FOOTNOTES
[1] Karen Barad, Meeting the Universe Halfway. Quantum Physics and the Entanglement of Matter and Meaning (Duke University Press, 2007), 33.
[2] Prigogine, The Philosophy of Instability, 396.
[3] Ibidem, 396.
[4] Ibidem, 396.
[5] Eric W. Weisstein, “Attractor.” From Mathworld - A Wolfram Web Resource, accessed November 24, 2024.
[6] Prigogine, The Philosophy of Instability, 398.
[7] Ibidem, 399.
[9] DrAndrewSteele, “This Chaotic Pendulum Is Really Weird,” posted December 23, 2022, Youtube.
[10] Oxford English Dictionary
[11] Paul Horowitz, “Build a Lorenz Attractor,” From Horowitz Group, accessed November 24 2024.
[13] Mathijs Leeuwis “Lorenz Demo,” demonstration recording.
[14] Mathijs Leeuwis “Lorenz + no-input + Koma,” demonstration video.
[15] Mathijs Leeuwis “Lorenz + Harris improvisation,” demonstration video.
[16] Mathijs Leeuwis “Lorenz x Fairbairn,” demonstration recording.
One of the reoccurring themes at Het Concreet is unpredictability and the practice of creating technological configurations which carry a form of independence. The often deliberately sought-after unpredictability of our instruments forces us to be in dialogue and question our own creative ideas. This article on the Lorenz Attractor is part of Mathijs Leeuwis’ thesis on Co-creational Instability Networks. It describes the development of a chaotic oscillator and its various creative applications.
In a musical dialogue between actants I aim to be surprised, thrown-off, and forced to rethink my position, but I do strive for a dialogue which is more than just randomness being shot back and forth between those that are present. As I search for ways to be changed through the intra-action - “the mutual constitution of entangled agencies,”[1] - with others, I also hope to change the other with my actions, thus coming to a point of communal ownership of whatever emerges. The back and forth movements between actants, the entanglement of material and development made me use chaos as a concept, which has been put into action through the use of the Lorenz Attractor. This article describes why and how this circuitry embodies instability and how this informed the development of this instrument within my set-up.
So in its simplest form, this article is about an instrument: the Lorenz oscillator. It is one of the technological links in my set-up. But since this instrument is the result of my search for ways to add a degree of instability to my instrumentation, it does make sense to provide more background. I was looking for ways to integrate an external autonomous voice into my no-input mixer set-up. Through the work of philosopher of science Ilya Prigogine, I came across so-called “strange attractors”. This concept put me on the path of chaos as a creative building block for my music. Chaos as a means of arriving at new musical situations. What follows here is an overview of the core concepts surrounding chaos and the practical elaborations that emerged from them.
Prigogine uses a pendulum to describe stable and unstable behaviour: if one swings the pendulum in such a manner that its weight is at the bottom, at one point it will stabilise at the “centre of gravity as low as possible,” and “it will return to a minimum swing.”[2] But if the pendulum is set in motion in an upside down manner, it could fall either left or right and the smallest of movements could make it tip over to one side or the other.[3] As Prigogine writes: “The pendulum on its minimum swing is a deterministic object: we know what will happen. In contrast, the problem of the pendulum turned on its head involves a non-deterministic object.”[4] In other words: it becomes hard to predict what will hap- pen exactly when we work with the upside-down pendulum.
To explain certain behaviours the concept of attractors is commonly used in mathematics and physics. Attractors describe a system's tendency to evolve towards a set of states.[5] Prigogine describes a set of different attractors. For instance the stable pendulum which returns to one point, the minimum swing at the centre of gravity; this would be a “punctual attractor”.[6] To describe more complex behaviours, so-called strange attractors are used. These strange attractors correspond to numerous points and “the system moves from one point to another - it is a mixture of stability and instability.”[7] Exactly this mixture of stability and instability, caught in a system, resonated with me. In my search for a more equal dialogue with my instruments, I am aware of my position of power in my role as instrumentalist, composer and initiator. Would it be possible to use a system of strange attractors as a technological/musical parameter? And could my own role within the creative process be forced into a more co-creational attitude when these strange attractors are given power over my work?
In my search for a creative use of chaos, I came across the work of the mathematician Edward Lorenz. In his studies of weather forecasting, he more-or-less accidentally stumbled upon a crucial phenomenon: although he started his experiments with the same set of data, the results kept changing when conducting his experiments. Lorenz unconsciously encountered the workings of chaotic systems, in which minimal anomalies in the starting positions lead to major differences in the long term. Lorenz later described it this way: “Chaos: When the present determines the future, but the approximate pre- sent does not approximately determine the future.”[8] This might seem theoretical, but just look at a double pendulum, it shows chaos: behaviour varies infinitely, with each starting position leading to a different result.[9]
It is important to underline the difference between chaos and randomness. Chaos - although hard to predict - functions in a deterministic manner, it is linked to particular strange attractors, causing all kinds of complex behaviours to emerge, but still it functions deterministically, always taking into account the way the system is put in motion. Whereas randomness can be seen as a state of no definite aim or purpose, not sent or guided in a particular direction.[10]
At the same time as I was reading about these concepts, I worked with artist, inventor and instrument builder Paul van Twist on the question of how to apply these ideas to a musical set-up. In our discussions on the use of chaos, Van Twist suggested to implement the Lorenz equations in an analogue electronic circuit, thus creating an electronic instrument which could be used to integrate the theoretical chaos Lorenz described into my musical set-up. The design Van Twist eventually proposed was based on the circuitry Harvard University physicist Paul Horowitz made as a translation of the Lorenz-equation.[11] One important addition to the design was made: an external input was added to the circuits design. This way it became possible to let the Lorenz circuit be influenced by external parameters, such as other electronic devices or musicians. In essence this is in line with the idea of the feedback loops which are present all through my set-up: all actants present are in some way enabled to influence the other actants, as well as to be influenced by the other actants.
The use of this rather wild circuit has brought me much artistically. Thus what follows now is a detailed description of the musical development and implementation of this circuit including technical and conceptual connections. I have made an effort to give musical examples wherever possible.
The first version of the Lorenz Attractor was build by Paul van Twist and this was the starting point for me to start working with chaos in my set-up. The Lorenz Attractor basically creates oscillations based on the initial equation. If we use this equation to create an oscillator, it creates a distinct form on the oscilloscope, also known as the “owl face”[12]. This visualisation shows the very nature of chaotic processes: it tends to perform more or less in the same manner, but continuously produces small deviations. Van Twist built a version with the option to adjust a lot of the parameters by ad hoc connecting potentiometers on the open circuit. Each time one of these parameters was adjusted the Lorenz Attractor would start a new sequence of “owl face” movements. Depending on where the sequence started the outcome in sound would be determined. The longer I would let the sequence run, the bigger the deviations from its starting position would be. So in comparison to a fixed no-input mixer oscillator this had more of an autonomous voice you could say. In one of the first experiments I did with this circuitry the explicit electronic character is clearly present.[13] Each time a big sonic change occurs, I was adjusting something on the circuit, for instance at 01:05.
The fact that this prototype was built entirely as an open circuit made it possible to make ad hoc changes to the design, for instance changing resistors. It also allowed me to approach the circuit itself as a tactile instrument by making new, temporary connections with my hands. So in this case the open circuit acts as a hard-to-read interface, essentially reducing my position as a composer or instrumentalist. The instrument doesn't really need me to keep producing new sounds. So I can explore, discover the instrument and its physical construction, looking for nooks and crannies where I can find something that appeals to me. But in doing so, both the physical construction of the instrument and the nature of the sounds it produces make it difficult to reproduce certain sounds exactly, if I have found anything at all. This places the instrument very much in the here and now: exact reproduction or reliable repetition of certain elements is almost impossible.
Shortly after the prototype was built and I did my first experiments with it, I started to use the instrument in conjunction with other actants. Initially by implementing the Lorenz Attractor in a fairly simple no-input mixer system. For instance, I was using the Lorenz Attractor as part of a bigger network with a no-input mixer and the Koma Field Kit.[14] The video also shows how I am making ad hoc connections directly on the circuit, for instance at 01:12. It is clear that the deviations and alternations in the musical routes are much bigger in comparison with just the Lorenz Attractor running as a solist, as we could hear in the first demonstration recording ‘Lorenz Demo’ [see note 13].
The next step was to use the Lorenz Attractor with other musicians. Initially I did a lot of improvisations with the instrument together with trombonist Dalton Harris.[15] I connected his signal to the input of the Lorenz Attractor using a contact microphone. This made Harris' trombone a trigger/modulator for the behaviour of the Lorenz Attractor. What I particularly like about this improvisation is that the changes in mutual influence are sometimes hard to pin down: a tiny change in one of the potentiometers can suddenly produce a big result. Other times there is no audible difference when I make chan- ges to the circuitry. Sometimes the Lorenz Attractor and Harris' playing seem to amplify each other, sometimes they seem to circle each other. This searching way of playing the instrument fits well with an attitude to improvisation in which instability is a central theme.
In addition to these improvisations that arose completely in the moment and where the Lorenz Attractor was really played like a normal instrument, I also began to look for ways in which the Lorenz Attractor can have a more autonomous function. Without me being involved as a player. First attempt of this approach were recorded with researcher, instrument maker and sound artist Kevin Toksöz Fairbairn.[16] He can be heard playing one of his self-built instruments. All the acoustic sounds - mainly strings stretched over a derivative of a trombone - are Fairbairn's. The deep electronic bass is produced by the Lorenz Attractor. All the Fairbairn sounds were used as modulators/triggers for the circuit. What you can hear is a certain consistency in the behaviour of the circuit in combination with what Fairbairn plays. At the same time, it is not possible to establish a fixed cyclical movement. The circular movement of the Lorenz Attractor forms a focus point for the more detailed and varied playing of Fairbairn, while at the same time also providing some sort of musical dialogue partner which changes through each others actions.
The development of the Lorenz Attractor is still ongoing. At the time of writing we are working on the simplification of the instrument. We are moving away from the open-circuit set-up. This brings forth complete new questions and problems which will be highlighted in the follow-up on this article.
This article is part of the master research thesis by Mathijs Leeuwis, Co-creational Instability Networks, presented at Fontys Academy of the Arts in 2025.
FOOTNOTES
[1] Karen Barad, Meeting the Universe Halfway. Quantum Physics and the Entanglement of Matter and Meaning (Duke University Press, 2007), 33.
[2] Prigogine, The Philosophy of Instability, 396.
[3] Ibidem, 396.
[4] Ibidem, 396.
[5] Eric W. Weisstein, “Attractor.” From Mathworld - A Wolfram Web Resource, accessed November 24, 2024.
[6] Prigogine, The Philosophy of Instability, 398.
[7] Ibidem, 399.
[9] DrAndrewSteele, “This Chaotic Pendulum Is Really Weird,” posted December 23, 2022, Youtube.
[10] Oxford English Dictionary
[11] Paul Horowitz, “Build a Lorenz Attractor,” From Horowitz Group, accessed November 24 2024.
[13] Mathijs Leeuwis “Lorenz Demo,” demonstration recording.
[14] Mathijs Leeuwis “Lorenz + no-input + Koma,” demonstration video.
[15] Mathijs Leeuwis “Lorenz + Harris improvisation,” demonstration video.
[16] Mathijs Leeuwis “Lorenz x Fairbairn,” demonstration recording.
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