Field Notesof Tia Bhardwaj · Form FN-3 · Rev. 10/26
№ PDE73B79473C2 · WORK · TOOL · DYNAMICAL SYSTEMS

(Sample) Lorenz explorer

Drag two starting points a hair apart and watch them stop agreeing.

Contribution Reproduction of a known result: an interactive build of Lorenz (1963)

OPENED 02 APR 2026CORRECTED 09 APR 2026LAB NOTE 03 MAY 2026
Evidence levelE0E1E2E3E4E1 · Self-checkedE1 · Self-checked
  • ✓ available
  • ✓ functional
  • — reproduced
✗ errors found: none · how I rate ›
How to read this page ›

How sure is this file?

E1 · Self-checked
How well the file's main claim has been tested. E1 means I checked it myself. The scale runs from E0 (not tested) to E4 (checked by someone else). Select the stamp to see the evidence.
E0 · Untested
A dashed mark is an idea that hasn't been tested yet. Read it as speculation.
✗ · Error found
Something in this file was wrong. The file stays up, and the fix is listed under Amendments.
Contribution: Learning notes
What kind of work it is, from learning notes (explaining something known) up to an original result checked by others.

How I rate my work explains every level.

Inside the text

E1 ✓ Result
A boxed claim. The label says what kind it is: Result, Observation (something I saw), Derivation (worked out step by step), each with its own test level.
E0 ? Conjecture
A dashed pink box is a guess, not a finding.
Lorenz explorer
A link to another file. The code after it says where it goes: WR is a piece of writing, WK is a piece of work, R is an entry in the register.
text1
A footnote. The note sits in the right margin, joined to its line by a brown line. On a phone, notes appear under the paragraph.

Around the edges

Local portrait
A small map of files connected to this one. This file is in the middle. 1 shows files linked directly; 2 adds files one more step away. As a list shows the same links as text.
Referenced in
Other files that link to this one, with the sentence that links here.
In the register
Dated events around this file, such as the interest or rabbit hole it came from.
Amendments
Every correction, with its date. Nothing is deleted.

Using it

Mouse
Hover over a link to see a preview of the file it goes to.
Phone
Tap a link once to see the preview, then tap Open file (or the link again) to go there.
Tab Esc
Tab moves from link to link and shows each preview; Esc closes it. The first Tab offers to skip straight to the text or the side column.

For the whole site, including keyboard use and following new files, see How to use this site.

Receipts

I wanted to see sensitivity to initial conditions rather than read about it. The explorer integrates the Lorenz system from two starting points you place, and draws how far apart they get over time. The essay version is Why a deterministic system can still surprise you.

Two Lorenz paths that start 0.001 apart. For a while they trace the same loops, then they separate and wander independently.
Two paths, a hair apart at the start. Change the starting gap and press Restart: smaller gaps buy only a little more time.

What's established, observed, derived, and still a guess

  • ResultE1Equations and classic parameters, from Lorenz (1963)evidence ›
  • ObservationE1RK4 at dt = 0.01 stays on the attractor for 10⁵ steps in my runsevidence ›
  • DerivationE1Divergence-time estimate from the largest Lyapunov exponentevidence ›
  • ConjectureE0The two-point view helps people build intuition faster than a single trajectory.—

Reproduce it

  1. clone the repo at tag v1
  2. run notebook 01 (about 2 min on a laptop)
  3. pass if λ₁ is within 0.02 of 0.906 and the plots match fig. 2

Next level

E2 · Cold-replicated

Rebuild without notes, criteria fixed below. Due 30 Nov 2026.

Lab notebook

  1. 02 APR 2026Started. Euler drifts off the attractor within seconds; switched to RK4.
  2. 09 APR 2026CorrectionThe first plots used dt = 0.05. Regenerated all of them.
  3. 03 MAY 2026v1 shipped. Linked from the essay.