Unstable Loops: Number Patterns in the Rikitake Dynamo

🌐 When Chaos Mimics the Earth’s Core

The Rikitake attractor is related to a model about how the Earth might flip its magnetic poles (I have heard it being discussed online that some 1000s of years ago the North and South poles were flipped and it will happen again). Unlike Lorentz or Rossler, it has sudden jumps and reversals—chaos with a lurch.

Looking at the geometry develop through time helps tune into the number sequences behind its strange heartbeat.

📘 The Equations

dx/dt = -b·x + y·z  
dy/dt = -b·y + x·(z - a)  
dz/dt = 1 - x·y

We’ll use: μ = 0.5, a = 3.

🔁 Code Simulation

let x = 0, y = 0.1, z = 0;
const a = 5, b = 2;
const dt = 0.005;

function step() {
  const dx = -b * x + z * y;
  const dy = -b * y + (z - a) * x;
  const dz = 1 - x * y;

  x += dx * dt;
  y += dy * dt;
  z += dz * dt;

  return { x, y, z };
}

🔂 The Number View

We plot the values step-by-step, just like in the previous posts.

🧮 X Values