The final stages of the Colorado River, as it flows into the Gulf of California, cover many kilometres, while the blood vessels in the kidney are just a few centimetres long, but the patterns they show are remarkably similar. The river delta is formed by simple physical forces. Gravity is pulling the water downhill, but obstacles such as stones sometimes get in the way, causing the flow to be diverted.
Because the surrounding land is almost flat, the pull of gravity is relatively weak, and so the resistance from stones and other obstacles has created a branching pattern, rather than a single torrent.
The branching of vessels in a kidney has evolved as an efficient way of transporting fluid evenly throughout the tissue. Kidneys have three sets of pipes. One takes the blood from an artery and spreads it around the kidney to be cleaned, and a reverse set then channels the clean blood into a vein to continue its journey around the body. A third, simpler set of tubes collects the urine - a solution of the impurities cleaned out of the blood - and transports it to the bladder.
Other natural structures, such as the branches of a tree, show this kind of pattern, as do some abstract concepts, such as evolutionary "trees" showing the relationships among different species of animals and plants.
The puzzle is to try and work out why such different aspects of nature can appear so similar, when we know that the delta is created by physical forces that we can observe operating in the present, that the branches of a tree are generated by biological growth over months or a few years, and the evolutionary tree of life developed over a much longer time scale.
To generate your own branching pattern, draw a straight line a centimetre long. Then toss a coin. If it lands head-side up, extend the line for another centimetre; if it lands tail-side up, split the line into two forks. Choose one branch and toss the coin again, repeating the process six or seven times, then come back and do the same for the other branch. Each time the line splits, choose one branch to continue the process, and return to finish the other branch later.
This simple method will produce a branching pattern that looks like the delta or kidney, with one noticeable difference. In both the river delta and the kidney, the thick branches at the start of the branching pattern tend to carry on for longer without splitting, while towards the tips, the degree of splitting is increased. Studying the changes in the rate of splitting - and why the resulting pattern differs from the simple branches you get by using a coin to decide whether a branch will split or not - can help geologists and biologists understand the real processes that have generated these fascinating natural patterns.
Peter Cotgreave is director of Save British Science