Technique · Geometry
Orbit sketches
Fine white lines on black: nested rings round dark cores that lean toward each other, lens-shaped field lines, a stream of dots and scattered stars.
Orbit sketches 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
- Iron filings spread on paper over a magnet line up along the field, which is how Faraday and generations of schoolchildren have seen magnetic field lines.
- Electrons in an atom do not circle the nucleus like planets: they are described by orbitals, regions where each is likely to be found, some shaped like spheres and some like dumbbells.
- The Sun is about 4.6 billion years old, and the planets still follow nearly circular, nearly co-planar orbits left from the disc of gas they formed in.
- In Niels Bohr's model of 1913 the electrons of an atom circle the nucleus on fixed orbits; modern quantum mechanics replaced the orbits with clouds of probability called orbitals, but the sketch of rings round a core has stayed the picture of an atom.
- Michael Faraday used iron filings sprinkled round a magnet in the 1830s to show his "lines of force", curved paths that loop from one pole to the other like the arcs here.
The mathematics
- A circle is fixed by three points: through two cores and a point at height b above their midpoint, its centre lies on the perpendicular bisector at the distance (b squared minus h squared) / 2b, where 2h is the gap between the cores; sweeping b gives the 18 field lines.
- In bipolar coordinates the circles through two points and the Apollonian circles round them form two families that cross at right angles; in the plane, the field lines of an electric dipole are the first family and its equipotentials the second.
- The radius of ring k of 30 follows r = core + (reach - core) (k / n) to the power 1.50, so with a power above 1 the rings crowd toward the core.
In art
- Wassily Kandinsky's Point and Line to Plane (1926) analyses a painting as points, lines and planes, and asks what each can express.
- Guilloche, the web of fine interlaced curves engraved on banknotes and watch dials, is drawn with the same machine-made circles and arcs.
More ways to use it
Related techniques
L-system · Space colonisation · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Curve families · Streamlines · Paint strokes