Nature is cool. It is the Big Diminisher of Entropy. It organises. It optimizes. And in this optimisation, patterns emerge. The Golden Section, Fibonacci, optimal packing. Sometimes, the efficiency of nature grasps you, and you feel like blatantly breaking all laws of apathy and procrastination.

To me, it came with looking at a stupid pine cone bottom. Pine cones are fun, especially when you're a kid and go camping. Then they make for excellent fireworks when thrown in a camping fire, and make great ammo for pine cone figts. Recently, I picked up a pine cone laying on the ground somewhere, and wanted to figure out how and where the Fibonacci pattern of nature manifested itself here. I decided to create a Java applet that would mimick this optimal packing pattern. And behold. I swindled the source code for a Conway game of life applet out of the hands of a foolish yet trusting friend, and I totally mutilated the code until I came up with the applet below.

The controls are simple: you can start and stop growing seeds. As soon as the seed counter reaches its maximum, no extra seeds are created. You can also reset the applet by pressing the "clear" button.

Maybe a word on how this nature stuff works. When a plant leaves ("Why don't you make like a tree"), it does so in a way that all leaves catch maximum amounts of light and water. In order to be able to do so, it has to place its leaves and seeds according to an optimal packing scheme. When we look at seeds, they are usually more or less round. The best way to pack circles in a square, is in a hexagonal position: six other circles are positioned around each circle. That works perfecly for statically packing. But not for dynamically packed groups: whenever a seed has to be added to the existing pack of seeds, this never happens at the outside where there happens to be a free spot; instead, the pack of seeds grows from the inside, pushing other seeds further out. Hence, nature had to come up with a packing scheme more favourable for dynamic packing.

New cells form at the "apical meristem" of a plant. This is the growing point, where active cell division is taking place. In analogy, new seeds form at the centre of a seedhead. No matter how large the seedhead, they are uniformly packed, not crowding the centre and not too sparse at the edges. This can be achieved by adding each new seed under a different angle than the last one. This angle solely defines the efficiency of the packing. When each seed is placed 0,61803398874989484820458683436564 turns futher than the last one, optimal packing is achieved. We call the corresponding angle Phi (about 222,5 degrees). When you divide a Fibonacci number F_n by a Fibonacci number F_n-1, you will get an approximation for Phi. The greater n, the better the approximation.

Once a seed has its angle, this angle doesn't change. Of course, it does still get pushed outward by newer seeds. The proportion of this radial movement is the square root of the number of seeds that are younger than the seed in question. But go ahead and have a look for yourself. If you count the spirals near the centre, in both directions, they will both be Fibonacci numbers. Look closely and count the spirals curving to the left and to the right, you will see that both numbers of spirals are indeed always two consecutive numbers of the Fibonacci series. These spirals are patterns that the eye sees, curvier spirals appearing near the centre, flatter at the sides.