cusp˜ — energy-based synthesis through cusp catastrophe in Max/MSP
Resumo
This article presents cusp˜, an audio-rate external for Max/MSP that implements René Thom’s cusp catastrophe in real time as a nonlinear operator of energy transformation. Grounded in Gilbert Simondon’s theory of metastable ontogenesis and Ilya Prigogine’s irreversible thermodynamics, the object solves, sample by sample, the cubic equation x3 + αx + β = 0 via an internal cubic solver, exposing the multivalent region (∆ < 0) where hysteresis and bifurcation become compositional parameters. We describe the mathematical modeling of the quartic potential, the performative mapping of the parameters α, β, and width, and the branch memory logic that ensures sonic coherence across the hysteresis cycle. Three test presets demonstrate the correspondence between theoretical predictions, spectrograms, and α–state cycles, validating the device as an operator of sonic individuation. As a contribution, we provide (i) cross-platform open-source code, (ii) exemplary patches for real-time control of bifurcations, and (iii) a conceptual framework articulating catastrophe theory, musical energy, and contemporary sound design — offering the SBCM community a rigorous and reproducible tool for composing with energy gradients.
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