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

Method – Wie Arbeite ich damit (siehe Frage) zur Entwicklung - cybernetic - experiment - messen und rechnen zu Anwenung - hören und spielen

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

2. Programming Fractals in the analog computer
3. Develop an Analoge Amari Neurone
4. Research on threshold logic
5. Setting up an Artificial Analog Netzwerke 6. Fibonacci Sequences in an neural network 7. SoundSynthesis with the neuron Oscillator 8. Controlling the Neural Oscillator the network

* Dublin Seminare * Residence at Schöppinge with Christian Faubel – first prototype of an analog Neuron * Art Science Lab, Shristi University Bangalore – prototype analog Computer * developping Synthesizer since 2010 * Publication

* 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.