The Lorenz attractor, drawn in ink
In 1961 Edward Lorenz re-ran a weather model with one number rounded off and got a very different forecast. In 1963 he published a system of three equations with the same sensitivity. With σ = 10, ρ = 28 and β = 8/3, their path never settles and never repeats, and it traces two wings, the picture most people now connect with the butterfly effect.
In Forgeplot, Lorenz is a Type inside the Strange Attractor generator. Sliders A, B and C shift σ, ρ and β, and at 0 they give Lorenz's exact numbers. Iterations runs from 50,000 to 400,000. Mark sets how the path reaches the paper: Dashes draws it as short dashes, 0.2 to 1.5 mm long, and Trail draws contour lines around where the path spends its time, with 1 to 6 Contour Levels. The page shows the x–z view.
The recipe
Enter these settings and the same drawing comes back, line for line.
- Generator
- Strange Attractor
- Seed
- 1
- Page
- AxiDraw V3 · A4, portrait
- Pens
- Black Fineliner
- Type
- Lorenz
- A, B, C
- 0 (they start elsewhere, so set all three)
- Iterations
- 50,000
- Mark
- Dashes
- Dash
- 0.6 mm
For the contour version, change Iterations to 400,000 and Mark to Trail.
Search Forgeplot on the App Store.
