Generating Fibonacci Sequences in an Analog Neural Synthesizer

An Expose for a PhD in Art and Science by Wolfgang Spahn

To Develop:
Question: how do neurons communicate, interact,….?
Goal: build an artificial neural network!

Question: how does threshold logic work, can one calculate Fractals?
Goal: build a Fibunacci row out of neurons!

To DO:
Learning Kid for Neural Networks?
Question: How can you support children learning decental networks? Goal: a set of board to play with a network for learning and understanding artificial neural networks!

Question: Can one hear the activity in a neural network?
Goal: Synthesise Sound!

• realize an anaolg version of the Amari Neuron
• artificial analogue neuronal networks
• threshold logic
• interfacing

To develop

• cybernetic
• experiment
• calculate
• mesure

implimentation

• listen
• play

The analog computer was inspired by the articel “Die Chaos-Maschine: Analoge Computer wiederentdecken” Elector Magazine 09-10/2011 by Maarten H. P. Ambaum and R. Giles Harrison (Department of Meteorology, University of Reading, UK).
Further information and wiring examples one can find in the old manuals of analog computer of the online library of the Analogmuseum: http://www.analogmuseum.org/english/library.html.

These oscillator and network behave similar to the one described in Dynamics of Pattern Formation in Lateral-Inhibition Type Neural Fields by Shun-Ichi Amari. The implementation of the analog neuron was described in Implementation of Artificial Neural Oscillators in 2009 by Pavlo V. Tymoshchuk, Yuriy I. Paterega.
Like already mentioned one important origin of the Pop Neuron is the bicore circuit of the BEAM.
A digital implementation on syncing and desyncing processes of two mutually coupled systems one can find on Netze/Networks Neural Oscillators by Lab3 - Laboratory for Experimental Computer Science at the Academy of Media Arts Cologne.
An other example of an electric implementation of an analog neuron for controlling robots one can find in Neurodynamische Module zur Bewegungssteuerung autonomer mobiler Roboter by Manfred Hild.

One can use these neurons to generate pattern and structures for all kind of sequencers and also for synthesize sound for musical instruments similar like the one David Tutor used for his Neural Synthesis Nos. 6-9 in 1993. A description of his work by Forrest Warthman and Mimi Johnson is on the artist web-side: The Neural Network Synthesizer. His neural synthesizer was based on a RC-circuit in combination of the 80170NX Electrically Trainable Analog Neural Network chip by Intel.

1. Build an Analog Computer
Develop an analogue computer based on modern chip and switching technology. For each operation a individual board will be designed.

2. Programming Fractals in the analog computer
Programming a Lorenz Attractor and a Rössler Attractor with thw Analog Computer

3. Develop an Analoge Amari Neurone
Develop a circuit that behaves like the model of a neuron like described by Amari Shun-Ichi Amari.

4. Research on threshold logic
Learning and understanding the principals of Threshold logigic.

5. Setting up an Artificial Analog Netzwerke
Creating some basic pattern in an analog neural network.

6. Fibonacci Sequences in an neural network
Programming a Fibonacci Sequences in an analog neural network.

7. SoundSynthesis with the neuron Oscillator
Creating Sound with an analog neural oscillator. Shaping the waveform, filtering the sound and synchronic the neural oscillators.

8. Controlling the Neural Oscillator with Fibonacci Sequences in the network

• Dublin Seminare
• Residence at Künstlerdorf Schöppinge with Christian Faubel – first prototype of an analog Neuron
• The first version of the analog computer was developed in 2015 for the artwork Strange Attractors.
• The analog computer Confetti was further developed and presented at the residency at Art Science BLR and the Indian Sonic Research Organization at the Srishti Institute of Art, Design and Technology, courtesy of Goethe-Institut Max Mueller Bhavan in 2016.
  
• developing analog electric synthesizer since 2001
• publication: Handmade Electronic Music, Third Edition - Nicolas Collins

* Norbert Wiener * Valentin Breitenberg

The PhD-Project “Computing Fractals in Analog Neural Networks” aims at building analog neural networks as part of an analog computer in order to compute fractals, strange attractors and other chaotic structures. These generated patterns and structures subsequently shall be sonificated and visualised.

The system may be used for both art projects, such as light-sound-installations or light-sound-performances, and education, such as learning tools. Analog neurons and analog computers provide an easy and vivid approach to understand the functionality of electronics, specifically of neural networks. For learners of all levels it is thus a perfect tool to open the black box of KI.

Methodology and steps to undertake

Analogue Computation, Analog Neural Networks and Threshold Logic The technology of analogue computing had been explored and widely spread until the 1970s, when digital computation took over. As analogue computation had been – and still is – at the core of most analogue electronics it proves to be a useful system until today, e.g. it is the base for analogue synthesizers.

I have started to develop the analog computer Confetti as a modular system in order to achieve a flexible system that performs all kind of computations and operations on base of electrical voltage. Confetti Neurons are special modules to implement an analog artificial neural network into the multi-connect system of the Confetti. It is an electronic implementation of an early neural model originally designed by Japanese mathematician Shun'ichi Amari to explain human heart beats. For the PhD-Project I would need to develop modules for further operations that fulfill the projects needs (e.g. Sigmoid functions).

Threshold logic, as described by Raúl Rojas, lies at the core of my PhD-Project. Simply put, threshold logic is a way to calculate with neurons. Research so far has mostly concentrated on it’s effects of small numbers of neurons. To compute threshold logic in complex systems with ten or more neurons a simulation is needed. Analog neurons are a powerful way to realize this, such as the system described above. Thus analog neural networks can solve very complex operations, such as calculating Fractals, which is key to my PhD-Project.

Fractals In 1960 Benoit Mandelbrot coined the term fractals to describe infinitely complex patterns that are self-similar across different scales. Prominent examples of these phenomena are his Mandelbrot Set, the Koch snowflake, and the Fibonacci spiral. In nature, fractals can be found in real snowflakes, coastlines or Romanesco broccoli among others. In the arts, fractals have been used as an important aesthetic composition technique, e.g. Jackson Pollock’s dripping pictures, whose fractal dimension has been described by Richard Taylor.

My project aims at sonificating and visualizing some of the fractals described above. Old technology such as oscilloscopes and XY-Recorder can be used to visualize fractals and other chaotic structures generated by the neural network. As the basic structure of the analog neural network is similar to that of an analog synthesizer these patterns and structures can be made audible as well. In my recent artistic work I have developed special projection techniques and tools that visualize audio signals. For the project, I would apply these to visualize fractals.

Education tool Besides being an artist I’m also a lecturer at the Sound Studies and Sonic Arts at the University of the Arts, Berlin. I also held workshops for the international organisation “r0g - open culture” in the Orangi Pilot Project, which is situated in the squatter areas of Orangi Town, Karachi, Pakistan. Therefore I’m aware how important tools can be that invite adults and children alike to learn in a playful manner the basics of information technology. The system of analog neurons are such an educational tool. I will – like I usually do with my projects – open source the analog neurons to allow everyone to use them for learning and for teaching.