Technique · Fields
Mirror smoke
Wisps of smoke curling into looped, mirror-symmetrical figures on a dark ground, grey-green with a warm beige core.
Mirror smoke is a field drawn for every pixel by the graphics chip. 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
- Smoke photographers shoot incense against black velvet with a fast flash and a long exposure, and many then mirror a patch of the result, which is the trick this piece uses.
- Rising smoke is laminar at first because the hot gas moves slowly; it speeds up as it climbs and hits the transition to turbulence, where the plume breaks into curls.
- Rorschach's inkblot test, published in 1921, uses the same trick of symmetry: a folded blot makes shapes the eye reads as figures.
- The figure-eight is a lemniscate, from the Latin for a ribbon; Jacob Bernoulli described the curve in 1694, and John Wallis introduced the sideways eight as the symbol of infinity in 1655.
- Smoke rising from incense stays smooth and layered for a few centimetres and then breaks into turbulence: the transition happens at a particular flow speed, which fluid dynamicists measure as a Reynolds number.
The mathematics
- The figure-eight is a lemniscate of Bernoulli, (x^2 + y^2)^2 = a^2 (y^2 - x^2), standing on its end; the picture estimates the distance to it as |f| / |grad f|, which is accurate close to the line and a good enough blur far from it.
- Mirror symmetry is one line of arithmetic: the horizontal position x is replaced by its absolute value, so a drawing on the right half appears on both.
- Each of four strands is displaced by three layers of noise at different scales (0.90 of turbulence); averaging the four gives a bundle that parts and rejoins, like smoke made of many filaments.
In art
- Photographers have treated smoke as a sculptural subject for a century, because a plume changes shape faster than the eye can follow and a fast flash holds it still.
- Symmetrical patterns have been used in religious art for millennia, in mandalas and rose windows, to suggest order and calm.
More ways to use it
Related techniques
Nebula and stars · Liquid · Droplets · Network · Terrain and maps · Neuron · Order to chaos · Fractal tree