Two researchers at the Okinawa Institute of Science and Technology (OIST) in Japan have examined the physics behind dendritic painting, which involves mixing colourful inks with alcohol and applying the droplets to a surface coated with a layer of acrylic paint.

The process first involves diluting one part of acrylic paint to two or three parts of water and applying it to a non-absorbent surface with a brush.

The next step is to mix the alcohol and acrylic ink and apply a droplet of the mix to the surface layer while the acrylic paint is still wet.

The result is an intricate set of fractal patterns that can resemble snowflakes, thunderbolts or neurons.

OIST’s Chan San To and Eliot Fried examined the fluid dynamics at play when the liquids create these patterns (PNAS Nexus 3 pgae059).

The duo found that the surface tension as the droplet dries and the non-Newtonian nature of the fluids play an important role.

As the ink droplet mix expands it changes the viscosity of the surface layer by shearing it and this force is what creates the fractal patterns. The researchers found that a surface layer less than half a millimetre thick was best to create the fractal patterns.

They discovered that the physics of dendritic painting is similar to how a liquid travels in a porous medium such as soil.

“If you were to look at the mix of acrylic paint under the microscope, you would see a network of microscopic structures made of polymer molecules and pigments,” notes Fried. “The ink droplet tends to find its way through this underlying network, travelling through paths of least resistance, that leads to the dendritic pattern.”

For a video of the process, see here.