Technique · Simulations
Fluid ink
Dye released by wandering jets and swirled by an incompressible fluid solver: roll-ups, mushrooms and filaments of ink in water.
Fluid ink is a simulation that evolves step by step. 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 filled notebook pages around 1510 with drawings of swirling water, noting that turbulence forms spirals within spirals; he drew vortices with great care.
- Suminagashi, the Japanese art of floating ink on water and lifting the pattern onto paper, dates from at least the twelfth century; Turkish ebru marbling is its relative.
- An ink drop that is pushed into water rolls up into a vortex ring, which can travel a long way as a mushroom-shaped cap with a stem, a form every jet in this picture makes over and over.
- Jos Stam published the stable fluids method at the 1999 SIGGRAPH conference; because it traces each point backward along the flow, it cannot blow up however large the time step, which made fluids practical for games and films.
- Whether the equations of fluid motion always have smooth solutions in three dimensions is one of the seven Millennium Prize problems, with a million-dollar prize still unclaimed; this picture only solves them approximately, in two.
The mathematics
- The water is a grid of 360 by 180 velocities, with the dye on a grid twice as fine; each step the velocity is traced backward along itself, so no value can grow, then the divergence is removed by 16 Jacobi passes, each averaging a cell's pressure from its four neighbours.
- An incompressible fluid has zero divergence, the sum of the rates at which water leaves a cell through its four sides; any velocity field is the sum of a divergence-free part and the gradient of a pressure, so subtracting the pressure gradient leaves the flow that obeys the rule.
- Numerical blurring smooths out small whirls; vorticity confinement (strength 22.00) measures the local spin and adds a small force that pushes the water to keep it, a trick brought into computer graphics by Ronald Fedkiw, Jos Stam and Henrik Wann Jensen in 2001.
In art
- Ink in water is a favourite of photographers and video artists because every frame is unrepeatable; the picture here is different every time yet always unmistakably ink.
- Marbled papers and the endpapers of old books record the same swirls in permanent form, made by dragging combs through paint floating on a tray of thickened water.
More ways to use it
Related techniques
Reaction-diffusion · Cellular automata · Sandpile · Grain growth · Slime mould · Flocking boids · Attractor cloud · Elementary automaton