Simple intro to dynamical systems and differential equations in Substance Designer
These are some quick sketches I've done in SD inspired by the simple and beautiful course on Dynamical Systems by David Feldman. This has been one of the simplest and most honest courses I ever watched: https://youtube.com/playlist?list=PLF0b3ThojznQwpDEClMZmHssMsuPnQxZT&si=GyuUAsbzyadz4Bvh
Differential equations, dynamical systems, iterated functions and feedback loops are of particular interest to me as I regard them as robust information generation systems, capable of rich expressivity, yet incredibly compressed.
coupled system of differential equations - solutions simply approximated by particle advection into the phase space.
the graph
simple iterated functions and deterministic chaos - butterfly effect and sensitivity dependence to initial conditions
simple Euler integrator for solution approximation
Newton's law of cooling
the graph
Lorenz equations
Roessler attractor
system of PDEs
solver
expected value
fixed point iteration
bifurcation diagram and transition to chaos
bifurcation diagram and transition to chaos
bifurcation diagram and transition to chaos
bifurcation diagram and transition to chaos
zoomed in - bifurcation diagram and transition to chaos
bifurcation diagram and transition to chaos
sensitive dependence on initial conditions
sensitive dependence on initial conditions
coupled system of differential equations
