Dendritic

Before I left on holiday, I read the recent post At One Remove about Hele-Shaw cells. The sculptor Richard Aumonier has a photograph of himself blowing air into a Hele-Shaw cell (glycerin between two sheets of perspex) and creating a snowflake-like pattern. The dendritic branching of the pattern appears to become exponentially more frequent the further in distance the spreading, unstable air front is from the central blow hole. It's an example of what specialists call 'viscous fingering'. Richard has used the technique to create a series of rather beautiful prints.

The word 'dendritic' comes from the ancient Greek word for 'tree'. Dendritic things branch in the same ways that trees branch. If you feel in need of some tree refreshment, have a look at Via Negative's recent Festival of the Trees. It includes a piece of my writing and is a great community blogging effort summoned together by Dave Bonta. Of course, with trees, both branches and roots are dendritic and form a symmetrical system linked by the trunk.

Many other natural phenomenon are also dendritic: The forking of lightening as it reaches from the clouds towards the ground; the gathering of stream tributaries in a river and the branching of its distributaries when it reaches the sea. The river system is symmetrical, one end of it gathering water, the other end dispersing it. Minerals may form dendritic crystal structures and in most metals, the process of solidification from a molten state occurs through the formation of dendritic structures. Rapidly cooling water forms dendritic ice crystals and snowflakes are tiny dendritic structures.

Sometimes one dendritic effect can be mistaken for another. Here is the view of one planetologist who thinks that recently identified sinuous channels on Mars are not the result of fluid movement but rather the evidence of huge lightening strikes which have produced soldered, branching structures on the planet surface. Such structures are formed on earth when lightning grounds itself in desert sand. The molten sand streaks may resemble the roots of a tree and are termed fulgurites.

While I was away on holiday, I noticed that the stones in the crazy paving around our rented holiday house had iron oxide (brown) and managanese oxide (black) dendritic structures, seeded off cracks in the thin limestone slabs. I imagine the slabs may be Lower Jurassic in age such as those from Solnhofen in Germany which show similar structures. The stones were probably sourced locally in the Dordogne region however. I took some photographs like the one at the top of the page which you can view here. These dendrites look like landscapes. I have the feeling that the manganese dendrites look slightly different from the iron dendrites, being slightly more spindly, chaotic and less formal. Perhaps they differ in form according to their crystal chemistry. One of the manganesse examples I photographed (the second photo) seems to show Mandelbrot type embayments.

Similar dendritic patterns can occur in agate, but are three-dimensional in character. The resulting rock is called moss agate (so named for its plant-like appearance) and also Mocha stone due to the fact the it was brought to Britain from traders departing from the port of this name in Yemen. Today, most of the Mocha stones are obtained from India, where they are found among the agate-pebbles resulting from the disintegration of the trap rocks of the Deccan.

Mocha stones gave their name to Mocha ware which is a style of pottery invented in Staffordshire in the 1780s. Mocha ware has slip decoration based on reproducing the natural dendritic mineral patterns of Mocha agates and dendritic limestones. The original recipe involves touching a water-based mixture of boiled tobacco and iron oxide onto the wet surface of the pot. The acidic "tea" reacts with the alkaline slip and the dendrites grow quickly from the point of contact. For more information and a lot of fascinating and beautiful nonlinear physics see here.

The site I've linked to says that: "The dendritic pattern of mocha ware is a result of a dynamic process in which the contact line between the two liquids, tea and slip, becomes unstable. The surface tension of the tea is less than that of the slip. The instability is probably driven by a combination of capillary and Marangoni (surface tension gradient) stresses, coupled somehow to the acid/base chemical reaction."

To return to where we started, I should imagine that when Richard Aumonier produced his Hele-Shaw cell prints, he reflected that the air he was blowing into the cell came from his own lungs which themselves have a branching structure very similar to that produced inside the cell. Perhaps that is how he came to arrange some of the prints as paired lung shapes.

The formation of dendrites seems to evolve from instabilities. They reflect gatherings, transport and dispersions of energy. Perhaps the universe, resulting from a cosmic instability, is itself dendritic.

Certainly, I think that most peoples' lives are dendritic. We begin from nothing, as a mass of little gathering streams: information, learnings coming from all over, pulling them into ourselves, gathering them around us, weaving them together. Such is nursery, school and university. All those subjects which we had to learn and yet now use so little of. Too bad. We take the 5% we do remember into ourselves to make us stronger.

The more streams we gather, the stronger we shall be as we surge onwards, become constant, find a plateau, a direction, a purpose. Then, everything we have learnt comes together and makes us good at what we do. We do not need to search around for clues. Every response comes powerfully from within us.

Then finally, we can't cope with it all. We start to give things up. One by one we let fall away skills, memories, good routines. We are aging, failing, coming apart. Freely, we give away advice, wisdom, all that we have learnt, all that we have carried with us along the way. Now it is a burden. Fragile, moss-like, we are dispersed, dissipated, dying away.