Articles

Scientific explorations of spirals and convergence phenomena in mathematics, physics, biology, astronomy, computer science and complex systems.

9 articles · Complex Systems

Complex Systems
Complex Systems
30–40 min

Convergence in Complex Systems: Resemblance, Constraint or Kinship?

Two systems can converge toward the same form because they share a constraint, without sharing a history or mechanism. An analytical grid separates analogy, homology and functional convergence.

Jun 1, 2026Read →
Complex Systems
Complex Systems
19–26 min

Reaction-Diffusion: How Uniformity Becomes Pattern

Two substances that react and diffuse at different speeds can destabilize a uniform state. Depending on parameters and geometry, spots, bands, fronts or spirals appear.

Jun 12, 2026Read →
Complex Systems
Complex Systems
20–27 min

Deterministic Chaos: The Lorenz Attractor Beyond the Butterfly

The Lorenz attractor has two lobes around which a trajectory winds irregularly. It is not two stable spirals, but a deterministic dynamic sensitive to initial conditions.

May 28, 2026Read →
Complex Systems
Complex Systems
24–32 min

Emergence: When the Whole Is Not Visible in the Parts

Emergence refers to the appearance of global properties that cannot be deduced from the properties of individual components. Starling murmurations, ant colonies and financial markets are examples.

Feb 6, 2026Read →
Complex Systems
Complex Systems
22–30 min

Long Economic Cycles: The Kondratiev Hypothesis

Kondratiev identified economic cycles of about 50 years in historical data. These waves of expansion and contraction correspond to major technological revolutions, but their existence remains debated.

Feb 2, 2026Read →
Complex Systems
Complex Systems
23–31 min

Epidemics and the SIR Model: Threshold, Peak and Extinction

The SIR model describes epidemic spread through three coupled differential equations. In phase space, the trajectory traces a curve converging toward an equilibrium point.

Jan 28, 2026Read →
Complex Systems
Complex Systems
22–30 min

Food Webs: How a Disturbance Travels Through an Ecosystem

A food web is a graph of predator-prey relationships. The disappearance of a keystone species can trigger a trophic cascade that propagates through the entire network.

Jan 24, 2026Read →
Complex Systems
Complex Systems
20–27 min

Feedback Loops: Stability, Runaway and Oscillation

Positive feedback amplifies perturbations; negative feedback dampens them. The dynamics of complex systems are governed by the interaction of these two types of loops.

Jan 20, 2026Read →
Complex Systems
Complex Systems
20–27 min

Stigmergy: Coordinating Without a Central Plan

Stigmergy is an indirect coordination mechanism where agents modify their environment. Ants build nests with complex structures without central coordination, each individual following simple local rules.

Jan 16, 2026Read →