S1. SPIRAL FRACTALS

The equiangular spiral occurs in many Julia sets as above, but its fractal characteristic is its natural self-similarity. We can see this in the sketch at left: each of the successive rectangles obtained by removing a square contains an exact but smaller image of the spiral. In theory this process can be carried out indefinitely (infinitely often). In fact, the unadorned continuous spiral is not generally classed as a fractal: some degree of discreteness is usually required. In applications to nature, we are only likely to get the first few steps of the spiral fractal. There is also likely to be some (small) variation in shape from the exact mathematical spiral.