Field Notesof Tia Bhardwaj · Form FN-2 · Rev. 10/26
№ P87CF2B6BF008 · WRITING · DYNAMICAL SYSTEMS · 1 MIN

(Sample) Why a deterministic system can still surprise you

Three equations, no randomness, and still no forecast a month out.

Contribution Learning notes: an explainer of a known result, Lorenz (1963)

OPENED 12 MAR 2026AMENDED 20 OCT 2026
Evidence levelE0E1E2E3E4E1 · Self-checkedE1 · Self-checked✗ errors found: none · how I rate ›
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Contribution: Learning notes
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Lorenz explorer
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text1
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In 1963 Edward Lorenz published a model of convection11Lorenz, “Deterministic Nonperiodic Flow”, Journal of the Atmospheric Sciences, 1963. with three variables and three parameters, σ=10\sigma = 10, ρ=28\rho = 28, β=8/3\beta = 8/3. Nothing in it is random.22No noise terms and no random seeds anywhere in the equations. Run it twice from the same start and you get the same path.33Same machine and compiler. On another, the paths part after about 40 time units. I rebuilt it in the Lorenz explorer to see where that stops being useful.44RK4, fixed step 0.01. Margin notes hang off their line; on a phone they fold in.

x˙=σ(y−x),y˙=x(ρ−z)−y,z˙=xy−βz\dot x = \sigma (y - x), \quad \dot y = x(\rho - z) - y, \quad \dot z = xy - \beta z
The Lorenz attractor drawn on the x–z plane: a single path looping around two lobes without ever repeating
One path, ten thousand steps. It never crosses itself and never settles.

That one number explains most of this file. It came out of the strange attractors rabbit hole from last year, and it’s why I started reading proofs slowly.

Where it broke

Every conjecture gets a broken E0 stamp. Every result links to the evidence behind its level.55See How I rate my work for what each level needs. A note on its own line sits level with its marker, so its line runs straight across.

Amendments

  1. 20 OCT 2026Wrote σ = 28 in paragraph one; it is ρ = 28. The conclusion holds.
  2. 12 MAR 2026File opened.