Wednesday, November 24, 2010

Self-Generated Music By Cellular Automata

James Conway's Game Of Life Cellular Automata

Stephen Wolframs book: Explaining Life and The Universe with Cellular Automata

Note# If there is no sound when you click on the link and it's Play button, go to Download and email the Midi file to yourself as an attachment, then play it separately on your computer.
If you read Stephen Hawking's (and Leonard Mlodinow) latest book "The Grand Design", -New Answers To The Ultimate Questions Of Life [Bantam Press, 2010], in the last Chapter, he uses the example of Cellular Automata to explain how and why Life in this Universe could have come about-without the requirement for a God. It is an atheist's explanation and he makes no apology for it. Cellular Automata, are 2-dimensional grids of cells, with two states: occupied (represented by a colored cell) and unoccupied (represented by a blank cell]. Seeded with an initial pattern and then given certain rules for what happens next, the patterns on the grid evolve into unexpectedly wonderous states with a 'life' of their own. In 1970, James Conway created such a grid and called it The Game of Life with these simple rules: For each generation of the game, a cell's status in the next generation is determined by a set of rules. These simple rules are as follows:
If the cell is alive, then it stays alive if it has either 2 or 3 live neighbors
If the cell is dead, then it springs to life only in the case that it has 3 live neighbors. From this, enthusiasts began recording the multitudes of 'creatures' that evolved and their behavior. You can read more about Celllar Automata here: . Enthusiasts also witnessed the sheer diversity of paths traced by each generation and how infinitisimally small differences in initial conditions led to unimaginably different outcomes for future generations [a lesson in Life for us here?]
For this post, we talk about the work of that egoistic mathematician, Stephen Wolfram the creator of Mathematica the software which is something like Matlab. Stephen's voluminous book "A New Kind Of Science" was devoted entirely to the identification and classification of cellular automata, and he identified the four classes of cellular automata[see link above] with Class 4 being representative of Life. Class 4 cellular automata mimicked life in being always on the edge between Chaos and Order, the sole conditions for Life to thrive. Now, with the rules of cellular automata [CA] and some theory of music, Stephen has created Wofram tones: where the evolution of the CA is translated into sounds with patterns. And like real music, which is always a balance betwen random noise and basic structure with
complex variations and little surprises to tease our ears, the best results were obtained from Class 4 CA. Click on the links next to each CA that has been generated with Wolfram Tones and decide for yourself whether there is any musicality in the sequence and combination of sounds that were self-generated. In the image of the sound, you can see the Rule Number that created the music. I believe that although the un-tweaked examples above don't sound so good, with some time and patience the various parameters for generating the files can be tweaked to sound much more musical. But in fact I think the music generated by Peter Gannon's Band-In-A-Box [ see www. ] is much more 'musical and real'. The algorithms used by Peter are a big secret and I can't figure out how he does it though I believe it's a combination of neural networks, self-organizing map and genetic algorithms. As an example, the accompaniment to my guitar playing that you can hear in the virtual MP3 player on the top right corner of this Blog was generated by Band-In-A-Box.

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