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The concept of a Fractal is a mathematical one and can be defined mathematically in a very accurate way. A less strict definition, which still describes very well the essential character of a Fractal, is:
Fractals are geometrical figures with as a characteristic property, that parts of the figure have (more or less) the same shape as the figure itself, but on a smaller scale.
One of the most fascinating fractals is the Mandelbrot fractal, shown in the upper picture .
The black shape in the middle, in the German language sometimes called das Apfelmännchen (apple man), is surrounded by a "luminous" border with a kind of antenna extending to the left.
In the middle picture this antenna is shown on an enlarged scale.
It can be seen clearly that on this antenna small "apple men" are located, and a further enlargement in the lower picture suggests, that there are many more. This is indeed the case, there are even infinitely many of these apple men, smaller and smaller.
Not only on this antenna copies of the apple man can be seen, they can be found everywhere in the "luminous" border region surrounding the central Mandelbrot fractal.
See the selection below. No 2 and 5 are located on the main antenna. From no 4
and 6 it can be seen that the copies are not always exactly similar to the main figure,
they are sometimes slightly distorted.
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