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Group Description

A club for sharing information on fractals (no matter how complex). Feel free to load your favourite fractal images in the photo albums.

The fractals group is in its 14th year.

A History of Fractals...in 1738 characters

Around 1670: German mathematician Gottfried Leibniz published his thoughts on recursive self-similarity, i.e. fractals.

Around 1832: Czech mathematician Bernhard Bolzano gave an example of a function that is continuous everywhere but nowhere differentiable. This example is regarded now as the first known fractal. The paper was first published in 1930, 98 years after it was written!

1854: German mathematician Bernhard Riemann highlighted the difference between continuity and differentiability.

1860: Swiss mathematician Charles Cellérier constructed the second known example of a fractal. The example was first published in 1890 (posthumously).

1872: German mathematician Karl Weierstrass published a function that is regarded today as the first published example of a fractal.

1875: English mathematician Henry John Stephen Smith published a description of a particular set of points lying on a single line segment, now known as a Cantor set.

1883: German mathematician Georg Cantor published remarkable and deep proerties of the Cantor set.

Early 20th Century: Swedish mathematician Helge von Koch, gave a geometric definition of a function similar to the Weierstrass function, now called the Koch curve. Polish mathematician Waclaw Sierpinski published a geometric construction of a curve now known as the Sierpinski triangle. Fractals in the complex plane were investigated by Henri Poincaré, Felix Klein, Pierre Fatou and Gaston Julia.

1975: French and American mathematician Benoît B. Mandelbrot coined the word "fractal" to denote an object whose Hausdorff–Besicovitch dimension is greater than its topological dimension. He illustrated this mathematical definition with striking computer-constructed visualizations...like that above.

Group Information

  • 203
  • Mathematics
  • Apr 4, 1999
  • English

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