Philately Day: Fractal (Julia Set)
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The three segments of the fractal depicted on the stamp, the tab and the first day cover were processed on computer by Dr. Michael Larsen and Dr. Ayelet Lindenstrauss Larsen. The fractal segment on the stamp is marked by a box upon the fractal segment on the tab. This, in turn, is marked by a box upon the fractal segment on the first day cover. Issue: December 1997 Designer: Yitzhak Granot Stamp size: 25.7 x 40mm Plate #: 329 Sheet of 15 stamps Tabs :5 Printers: Government Printers Printing Method: Offset |
he Julia set depicted on the stamp is a fractal -- a shape of fractional dimension -- whose dimensions are between 1 and 2. The first fractal was defined in the 19th century by George Cantor. Felix Housdorff defined "fractional dimension" more precisely in 1918. The term "fractal" was coined in the 1960's by Benoit Mandelbrot, who emphasized the prevalence of fractal structures in nature. All three researchers, Cantor, Hausdorff and Mandelbrot, are of Jewish origin.The Julia set is named after Gaston Julia, a French mathematician who, working in the 1920's with Pierre Fatou, was the first to study such groups. When the formula Z-->Z2 +C (which appears on the stamp tab) is applied to any point on a plane, a new point F(z) is reached. The formula is applied again to the new point. And so on.
The color of each point on the stamp represents the growth rate of the series of dots that begins there.
The process of repeated application of the same formula is an example of a dynamical system.
The Julia Set, like many other fractals, has a trait of self-similarity: different parts of fractals resemble each other, albeit sometimes on a very small scale.
The complex structure of the picture on the stamp illustrates the sensitive dependence of the system on its initial conditions. Such sensitive dependence also appears in natural dynamic systems and can explain, for example, why it is difficult to make long-term weather forecasts.
Researching the Julia Set and other fractal forms which appear in dynamical systems is a rich and fascinating field of modern mathematics, revealing why Julia Sets are so complex and intricate, and why they are endowed with self-similarity. The source of their beauty, however, remains a mystery.
The Hebrew University of Jerusalem
