Students of human geography may be familiar with the German geographer Walter Christalle, who in 1933 published his Central Place theory (CPT). This theory basically involved the theoretical distribution of settlements given ideal conditions. He noticed that towns of a certain size were roughly equidistant, and around these towns were smaller towns. He proposed a model based on an isotropic* plane and a universal transport network*, assuming that the smaller towns would form hexagons* around the larger ones. These small towns would in turn have smaller villages in hexagons around them, and so on.
The popularity of a beach can be derived by applying Central Place Theory.
Picture a certain length of beach in summer, with a limited amount of sunbathing space. At dawn it's empty, and then slowly people arrive. It is human nature to try to sit as far apart as possible, so as not to be disturbed, but without having to do excessive walking. The first wave of early birds will therefore spread out to equidistant positions. Observations have shown that this typically results in people arranged in a straight line at ten metre intervals along the beach. The next wave of bathers, arriving after the first order bathers have taken their places, will place themselves between the first line but either higher or lower up the beach, forming the classic Christalle triangle/hexagon pattern. Subsequent waves will place themselves in the gaps, forming third and fourth level geometric shapes. Analysis of these shapes will determine the level of beach popularity over the course of a day or season.
It must be recognised that certain factors can skew the nice geometric shapes generated by the theory. Rocks, tides, topless girls, hunky lifeguards and noisy children will all have their effect. These can be noted and computer models used to correct for them.