Waves fractal Sharon

  • Issue: December 1997
  • Designer: Y. Granot
  • Stamp size: 25.7 x 40 mm
  • Plate no.: 329
  • Sheet of 15 stamp Tabs:5
  • Printers: Government Printers
  • Method of printing: Offset

The Julia set depicted on the stamp is a fractal whose dimensions are between 1 and 2, a fractal being a shape of fractional dimension.

The first fractal was defined in the 19th century by George Cantor, while Felix Housdorff defined "fractional dimension' more precisely in 1918. The term "fractal" was coined in the 60's by Benoit Mandelbrot, who emphasized the prevalence of fractal structures in nature.

The three researchers, Cantor, Hausdorff and Mandelbrot, are of Jewish origin.

The Julia Set Fractal

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. When the formula Z->Z2 +C (which appears on the stamp tab) is applied to any point in 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 complex structure of the picture on the stamp represents 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.

The Julia Set like many other fractals, has a trait of self-similarity: different parts of fractals resemble each other, sometimes on a very small scale. The research performed on the Julia Set, and other fractal forms which appear in dynamical systems, is a rich and fascinating field of modern mathematics. This research allows us to see why Julia Sets are so complex and intricate, and why they are endowed with self-similarity. But the source of their beauty remains a mystery.

The three segments of the fractal depicted on the stamp, the tab and the first day cover were processed by Dr. Michael Larsen and Dr. Ayelet Lindenstrauss Larsen using special computer software. 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.

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Philately day - fractal (Julia set)