The Julia Set Fractul Stamp

The colourful “Julia set” stamp issued in December 1997, depicts a fractal of dimensions 1-2. In mathematics, any class of complex geometric shapes that commonly exhibit the property of self-similarity, are called “fractal.” The three segments of the fractal on the stamp, processed by Dr. M. Larsen and Dr. A. Lindenstrauss Larsen using special computer software, are marked by a box on the tab. When the formula Z-<Z(2)+C, appearing on the tab, is applied to any point in a plane, a new point F(z) is reached, and so the formula in continued indefinitely. The colour of each point represents the growth rate of the series of dots that begins there.

This process of repeated application of the same formula presents a Dynamical system. The complex structure of the picture on the stamp shows the sensitive dependence of this system on its initial conditions. Such sensitive dependence also appears in natural dynamic systems and explains, for example why it is difficult to make long-term weather forecasts.

The “Julia Set” is named after Gaston Julia, a French mathematician who, with Pierre Fatou, was the first to study such groups, in the second decade of the 20th century. The stamp with an information sheet are enclosed in a plastic protection sheet.