Game of Life and musical harmony: two models of computation across scales
| Quand ? |
Le 18/09/2026, de 10:45 à 12:00 |
|---|---|
| Où ? | M7 101 |
| Participants |
Alexandre Guillet |
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Living organisms, jewels of evolution, are complex systems where myriad interacting processes perform forms of computation essential to survival, tightly coupled from molecules to ecosystems. The patchwork of physical descriptions, rather than a principled integrative framework, is no accident: models succeed by isolating subsystems with clearly identifiable times, lengths or energies, a strategy that fragments by construction where separation is limited and scaling ranges are narrow. Scales then appear less as constant parameters than as coordinates on a continuum, forming a landscape across which biological organization is distributed, inviting modelling as such.
We report two phenomenological models stepping in this direction.
First, a continuous Game of Life. Smoothing discrete survival rules into field dynamics coupling spatial resolution levels yields cell-like morphogenesis: unit patterns with a nucleus and shell move or divide by symmetry breaking. With finite resources, the system self-tunes to the edge of growth, the transition between dilute and dense regimes. A further extension allowing heritable parameter variation lets it evolve autonomously toward amoeboid- or keratocyte-like locomotion.
Second, Helmholtz's dissonance as a number-theoretic and thermodynamic structure of hearing. The fractal landscape over frequency ratios splits into the acoustics of a harmonic timbre, captured by Riemann's zeta function, and the neurocognitive effort of assessing justness as a maximum-entropy ensemble over rational approximations generated by the Euclidean algorithm. Its spectrum predicts the quasi-periods of musical scales from pentatonic to microtonal divisions of the octave.