Technique · Geometry
Filigree spirals
A dense tangle of spiral curls with trailing tails, drawn as glowing fibres on black and coloured in slow patches, like a flame fractal.
Filigree spirals 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
- Filigree is metalwork of fine twisted wire soldered into lacy scrolls; it has been made since ancient Mesopotamia and Greece and is still a craft in places from Portugal to India.
- The triple spiral carved at Newgrange in Ireland is about 5,000 years old, older than the pyramids of Giza.
- Many natural spirals come from uneven growth: a fern frond curls because the cells on its outer side grow faster than those on its inner side, and a snail's shell spirals because one side of its growing edge grows faster than the other; a galaxy's spiral arms have a different cause, waves of density moving through the disc.
- The Euler spiral, whose curvature grows in proportion to the distance along it, is used to ease railway track and roads from a straight line into a bend, and Marie Alfred Cornu drew it in 1874 to explain the diffraction of light.
- Flame fractals were invented by Scott Draves in 1992: millions of points are thrown through randomly chosen non-linear functions and each pixel is coloured by how often it was visited, which gives the soft, glowing filaments of this look.
- A fern frond unrolls from a tight coil called a fiddlehead or crozier, because the cells on the outer side grow faster than those on the inside.
The mathematics
- A coil whose radius shrinks steadily with each turn is close to an Archimedean spiral, r = a + b theta, in which neighbouring turns are always the same distance apart; here the coil makes 2.20 turns.
- Dart throwing accepts a random circle only if it is far enough from every circle already placed, and a grid of cells makes each test look at a handful of neighbours rather than all of them.
- Sizes drawn as a random number raised to a power greater than one favour small values, which is how many small curls and a few large ones come out of a uniform random generator.
- Each curl is drawn as 3 strands offset along the curve's normal by a width that narrows toward the centre, so the fibres part in the tail and gather in the coil.
In art
- Art Nouveau designers of the 1890s built ornament from whiplash curves, lines that swell and curl like growing stems.
- Victorian scrollwork and the flourishes of calligraphers both rely on spirals ending a stroke: the curl is the natural place for a hand to stop.
More ways to use it
Related techniques
L-system · Space colonisation · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Curve families · Streamlines · Paint strokes