Technique · Geometry
Streamlines
Evenly spaced flow lines that fill the frame like a hand-drawn contour map of a fluid, with vortices.
Streamlines is drawn geometry, rebuilt as it changes. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- Leonardo da Vinci drew turbulent water in the early sixteenth century as curls within curls, and noted the pairs of vortices behind obstacles.
- Engravers describe the form of a surface with families of fine, parallel lines, and banknotes add guilloche, interlaced curves, to make forgery hard.
- The method is Jobard and Lefer's 1997 algorithm for evenly spaced streamlines, used to draw maps of wind and fluid flow.
- The streamlines of a steady flow can never cross, which is what makes the picture look so calm.
The mathematics
- Each new line starts one separation, about 0.015 of the frame, from an old one and stops within half that distance of another, which keeps the spacing between half and one separation everywhere.
- An ideal point vortex makes the fluid circle at a speed of strength / (2 pi r), so lines near each of the 3 centres loop tightly.
In art
- A single family of lines that never cross is how engravers describe the form of a surface.
- Weather maps and ocean charts draw wind as streamlines: art and science have used the same lines for the same reason.
More ways to use it
Related techniques
L-system · Space colonisation · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Curve families · Paint strokes · Stipple and Delaunay portrait