ODE's ode Pablo Riera Laboratorio de Inteligencia Artificial Aplicada, Instituto de Ciencias de la Computación, Universidad de Buenos Aires, CONICET, Argentina 4th Febraury, IMPA, Rio de Janeiro
Overview ● Background ● Dinamical Systems ○ ODEs, Maps ○ Vector fields, phase portrait ○ Non linear systems, bifurcations, chaos ● Playing with ODEs ● Live ODEing with LODE ○ Yaml interface ● Sound synthesis with ODEs ○ Supercollider Plugin ○ C++ shared libraries ● Demo
Background ● Generative music with spiking neural networks and EEG
Dynamical Systems ● Systems that describe the time dependence of a point in a space with a function ● Typical systems: ○ Continuous: Ordinary Differential Equations (ODE) ○ Discrete: Difference Equations (Maps)
Example: simple harmonic oscillator Dynamical Systems ● Vector fields ● Phase Portrait http://kevbase.com/phase/
Example: Logistic Map Dynamical Systems ● Iterated Maps ● Bifurcations
Playing with ODEs ● Temporal scale ● Chaos ● Noise ● External Inputs ● Delay
Live ODEing with LODE
Sound Synthesis with ODEs ● Numerical solutions of ODEs with Runge Kutta 4 method ● New Supercollider Extension Plugins ○ Oderk4 ○ Odemap ● Dynamic loading of shared libraries of equation definitions
Sound Synthesis with ODEs
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