Tuesday, February 15, 2011

"STRANDBEASTS"
by THEO JANSEN

THEO JANSEN Netherlands
Studies physics at Delft University of Technology

I can best explain how the leg works using a model I once made from a sheet of plywood. I often take this model to lectures to demonstrate the leg's action. In the middle of each beach animal is a kind of spine, more specifically a crankshaft. The remarkable thing about this spine is that it can rotate. In the model, my hand turns the crank of the crankshaft. This rotation is converted by 11 small rods into a walking movement drawn by a small pencil at the end of the leg. Let's call this pencil the toe.
Ideally, the pencil describes a kind of triangle with rounded corners and a horizontal base. Whenever the toe is on this base, it touches the ground and carries the animal. It describes a horizontal line, or rather the entire animal does, since the toe is carrying the animal. The same holds for a wheel; the axle also describes a horizontal straight line. The beach animal doesn't lurch. When the toe reaches the end of the base (at right), the leg is lifted whereupon it rapidly describes the other two sides of the triangle. During that time the animal is supported by the other legs which at this stage are on the ground. [The above curve is the ideal walking curve; a flat base with rounded corners] [Bijschrift?#] The curve this produces is dependent on the ratio between the lengths of the 11 small rods. Another ratio gives an entirely different curve, a figure 8 for example. Of course, I had no idea beforehand which ratio between the lengths I needed for the ideal walking movement. Which is why I developed a computer model to find this out for me.
But even for the computer the number of possible ratios between 11 rods was immense. Suppose every rod can have 10 different lengths, then there are 10,000,000,000,000 possible curves. If the computer were to go through all these possibilities systematically, it would be kept busy for 100,000 years. I didn't have this much time, which is why I opted for the evolutionary method.
Eleven holy numbers
Fifteen hundred legs with rods of random length were generated in the computer. It then assessed which of these approached the ideal walking curve. Out of the 1500, the computer selected the best 100. These were awarded the privilege of reproduction. Their rods were copied and combined into 1500 new legs. These 1500 new legs exhibited similarities with their parent legs and once again were assessed on their resemblance to the ideal curve. This process went through many generations during which the computer was on for weeks, months even, day and night. It finally resulted in eleven numbers denoting the ideal lengths of the required rods. The ultimate outcome of all this was the leg of Animaris Currens Vulgaris. This was the first beach animal to walk. And yet now and then Vulgaris was dead set against the idea of walking. A new computer evolution produced the legs of the generations that followed.
These, then, are the holy numbers: a = 38, b = 41.5, c = 39.3, d = 40.1, e = 55.8, f = 39.4, g = 36.7, h = 65.7, i = 49, j = 50, k = 61.9, l=7.8, m=15 . It is thanks to these numbers that the animals walk the way they do.