31 questions · 18 almanac · 2 findings

Chaos and Complex Systems

Nonlinear dynamics, emergent behavior, and complexity science.

Almanac A Rounded Decimal Breaks the Forecast
  • What rounding error led Edward Lorenz to discover sensitive dependence on initial conditions?
  • What does the 'butterfly effect' metaphor actually claim, and how careful was Lorenz about framing it?
  • What is the Lorenz attractor, and what does it represent in his three-variable convection model?
  • How did Lorenz's 1963 paper change what determinism can promise about long-term prediction?
Almanac A Legacy Built on Subtraction
  • How is the Sierpiński triangle constructed, and why does it enclose zero area despite infinite perimeter?
Almanac Order Feeding on Disorder
  • What is a dissipative structure, and how can a system organise itself while being driven far from equilibrium?
  • In what sense are a hurricane and a living cell both examples of the same underlying physical principle?
Almanac Four Medals, No Shared Ground
  • What did Jean-Christophe Yoccoz's work on linearizing maps near a fixed point contribute to dynamical systems theory?
Almanac The Physics the Playground Already Knew
  • What is a limit cycle attractor, and how does it describe hula hoop motion?
  • Why did children solve this physics problem empirically decades before scientists modeled it?
Almanac Weather Turns Out to Have a Signature
  • Why do disordered systems like spin glasses and flocking starlings obey the same probabilistic laws?
  • What connects the physics of disordered materials to feedbacks in the Earth's climate system?
Almanac When Waves Break, and When They Don't
  • What does it mean for a nonlinear wave equation's solution to 'blow up' in finite time?
  • How did Frank Merle's work clarify which initial conditions lead to blowup versus stable decomposition?
Finding Reaction-Diffusion Pattern in Shoot Apical Meristem of Plants
  • How does the WUS-CLV feedback system generate the overlapping molecular gradients that define distinct zones within the shoot apical meristem?
  • How can a reaction-diffusion model, building on Turing's 1952 framework, explain the spontaneous emergence of spatial pattern from an initially homogeneous meristem?
  • Why do the authors argue that reaction-diffusion dynamics are indispensable, rather than merely one possible explanation, for shoot apical meristem development?
Finding Turing-like mechanism in a stochastic reaction-diffusion model recreates three dimensional vascular patterning of plant stems
  • How does coupling a Turing-like reaction-diffusion instability with longitudinal efflux of a regulatory molecule generate three-dimensional vascular bundle patterns in plant stems?
  • How does introducing stochastic fluctuations into the reaction-diffusion framework affect the robustness of vascular pattern formation compared to deterministic Turing models?
  • How do changes in the diffusion rates of activator and substrate molecules alter the number and size of simulated vascular bundles?