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One mathematical approach got introduced to world in 1970 by the British mathematician John Horton Conway, the Game of Life.
One mathematical approach got introduced to world in 1970 by the British mathematician John Horton Conway, the Game of Life.
The so called Game of Life (or GoL in short) is a 'cellular automaton', a type of simulation that works on a regular grid of cells and in discrete time-steps. For every time-step a set of rules is enforced for every cell, determining it's state. In most cellular automaton there are only two states 'living' and 'dead'. Depending on the rules and other constrains of the simulation, complex patterns might occur and this project will try to take these patterns and represent them as notes in a 'cellular automaton synthesizer'.
The so called Game of Life (or GoL in short) is a 'cellular automaton', a type of simulation that works on a regular grid of cells and in discrete time-steps. For every time-step a set of rules is enforced for every cell, determining it's state. In most cellular automaton there are only two states 'living' and 'dead'. Depending on the rules and other constrains of the simulation, complex patterns might occur and this project will try to take these patterns and represent them as notes in a 'cellular automaton synthesizer'.


[[File:dim.png|800px]]
[[File:dim.png|800px]]
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For this project I will use a one-dimensional or so called elementary cellular automaton, represented as a line of 32 cells. In every time-step of the simulation the state of the cell (living or dead) is considered and than the state of the two neighboring cells, edge-cells will be wrapped around. Living cells will be represented as black and dead cells as white pixel. Rules are encoded by all of the possible combinations of the dead cell itself and its neighboring (2^3 = 8). To represent the rules, they are encoded in one-bit-array of length eight like the following graphic illustrates.
For this project I will use a one-dimensional or so called elementary cellular automaton, represented as a line of 32 cells. In every time-step of the simulation the state of the cell (living or dead) is considered and than the state of the two neighboring cells, edge-cells will be wrapped around. Living cells will be represented as black and dead cells as white pixel. Rules are encoded by all of the possible combinations of the dead cell itself and its neighboring (2^3 = 8). To represent the rules, they are encoded in one-bit-array of length eight like the following graphic illustrates.


[[File:rules.png|500px]
 
 
[[File:rules.png|800px]]


One rule-set and its representation  
One rule-set and its representation  


With theses 8-bits there are 256 possible combinations of rules that can be used for the simulation, these rules often form reoccurring patterns that will be important later.  
With theses 8-bits there are 256 possible combinations of rules that can be used for the simulation, these rules often form reoccurring patterns that will be important later.  


[[File:all_rules.png|500px]]
 
 
[[File:all_rules.png|800px]]


Some elementary cellular automaton rules and their pattern  
Some elementary cellular automaton rules and their pattern  


To interpret the simulation as music in every time-step the current line of the simulation is read and the different cells interpreted as notes in a musical scale. To minimize dissonance a anhemitonic pentatonic scale is used.
To interpret the simulation as music in every time-step the current line of the simulation is read and the different cells interpreted as notes in a musical scale. To minimize dissonance a anhemitonic pentatonic scale is used.
Because there are only five notes per octave and no semitones in a pentatonic scale, they produce a simple harmonies that work well with random, pseudo-random and chaotic but structured input.
Because there are only five notes per octave and no semitones in a pentatonic scale, they produce a simple harmonies that work well with random, pseudo-random and chaotic but structured input.


[[File:scales.png|500px]]
 
 
[[File:scales.png|800px]]


Different penatonic scales and the matching notes
Different penatonic scales and the matching notes


===Approach:===
===Approach:===
The synthesizer works like the following, the cellular automaton is simulated using the selected rule-set. The current state or line of the automaton is than read from left to right and the matching notes of the selected pentatonic scale played (low notes left, high notes right). To give the user more control over the sound, the notes are split up into eight channels of differing pitch.   
The synthesizer works like the following, the cellular automaton is simulated using the selected rule-set. The current state or line of the automaton is than read from left to right and the matching notes of the selected pentatonic scale played (low notes left, high notes right). To give the user more control over the sound, the notes are split up into eight channels of differing pitch.   


[[File:approach.png|500px]]
 
 
[[File:approach.png|800px]]


One simulation step visualized  
One simulation step visualized  


The synthesizer is web-based using HTML, CSS and JavaScript. To play notes the library Tone.js (js/tone.js)and their default synthesizer is used (js/synth.js). The simulation is visualized using the Canvas-Api and simulated using native JavaScript (js/automata.js). The User-Interface is written in HTML and CSS (index.html) using onclick-event handlers to interact with the simulation (js/gui.js).
The synthesizer is web-based using HTML, CSS and JavaScript. To play notes the library Tone.js (js/tone.js)and their default synthesizer is used (js/synth.js). The simulation is visualized using the Canvas-Api and simulated using native JavaScript (js/automata.js). The User-Interface is written in HTML and CSS (index.html) using onclick-event handlers to interact with the simulation (js/gui.js).


[[File:finished.png|500px]]
 
 
[[File:finished.png|800px]]


The final synthesizer-ui  
The final synthesizer-ui  


===Further Reading:===
===Further Reading:===
====Elementary Cellular Automaton====
* http://mathworld.wolfram.com/ElementaryCellularAutomaton.html
* http://atlas.wolfram.com/01/01/rulelist.html
* https://plato.stanford.edu/entries/cellular-automata/supplement.html


Elementary Cellular Automaton:
====Pentatonic Scale====
http://mathworld.wolfram.com/ElementaryCellularAutomaton.html
* [[wikipedia:Pentatonic scale]]
http://atlas.wolfram.com/01/01/rulelist.html
* https://www.piano-keyboard-guide.com/pentatonic-scale.html
https://plato.stanford.edu/entries/cellular-automata/supplement.html
 
Pentatonic Scale:
https://en.wikipedia.org/wiki/Pentatonic_scale
https://www.piano-keyboard-guide.com/pentatonic-scale.html


Web Stuff:
====Web Stuff====
https://developer.mozilla.org/de/docs/Web/API/Web_Audio_API
* https://developer.mozilla.org/de/docs/Web/API/Web_Audio_API
https://developer.mozilla.org/de/docs/Web/HTML/Canvas
* https://developer.mozilla.org/de/docs/Web/HTML/Canvas
https://tonejs.github.io/
* https://tonejs.github.io/


===Downloads===
===Downloads===
[[:File:Just open index.html with a modern browser automata.zip]]
[[File:automata.zip]]
Just open index.html with a modern browser

Latest revision as of 15:26, 5 June 2019

<automata>

Context:

'Life is a simulation' or is it? The quest for finding a set of rules to simulate life in some shape or form has been around for ever. Whether it is in search for the free will or just to find out what makes things living. One mathematical approach got introduced to world in 1970 by the British mathematician John Horton Conway, the Game of Life. The so called Game of Life (or GoL in short) is a 'cellular automaton', a type of simulation that works on a regular grid of cells and in discrete time-steps. For every time-step a set of rules is enforced for every cell, determining it's state. In most cellular automaton there are only two states 'living' and 'dead'. Depending on the rules and other constrains of the simulation, complex patterns might occur and this project will try to take these patterns and represent them as notes in a 'cellular automaton synthesizer'.


Dim.png

cellular automaton in different dimensions

Concept:

For this project I will use a one-dimensional or so called elementary cellular automaton, represented as a line of 32 cells. In every time-step of the simulation the state of the cell (living or dead) is considered and than the state of the two neighboring cells, edge-cells will be wrapped around. Living cells will be represented as black and dead cells as white pixel. Rules are encoded by all of the possible combinations of the dead cell itself and its neighboring (2^3 = 8). To represent the rules, they are encoded in one-bit-array of length eight like the following graphic illustrates.


Rules.png

One rule-set and its representation


With theses 8-bits there are 256 possible combinations of rules that can be used for the simulation, these rules often form reoccurring patterns that will be important later.


All rules.png

Some elementary cellular automaton rules and their pattern


To interpret the simulation as music in every time-step the current line of the simulation is read and the different cells interpreted as notes in a musical scale. To minimize dissonance a anhemitonic pentatonic scale is used. Because there are only five notes per octave and no semitones in a pentatonic scale, they produce a simple harmonies that work well with random, pseudo-random and chaotic but structured input.


Scales.png

Different penatonic scales and the matching notes

Approach:

The synthesizer works like the following, the cellular automaton is simulated using the selected rule-set. The current state or line of the automaton is than read from left to right and the matching notes of the selected pentatonic scale played (low notes left, high notes right). To give the user more control over the sound, the notes are split up into eight channels of differing pitch.


Approach.png

One simulation step visualized


The synthesizer is web-based using HTML, CSS and JavaScript. To play notes the library Tone.js (js/tone.js)and their default synthesizer is used (js/synth.js). The simulation is visualized using the Canvas-Api and simulated using native JavaScript (js/automata.js). The User-Interface is written in HTML and CSS (index.html) using onclick-event handlers to interact with the simulation (js/gui.js).


Finished.png

The final synthesizer-ui


Further Reading:

Elementary Cellular Automaton

Pentatonic Scale

Web Stuff

Downloads

File:Automata.zip Just open index.html with a modern browser

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Last modified
This page was last edited on 5 June 2019, at 15:26.