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Topic: Matheology § 160
Replies: 1   Last Post: Nov 24, 2012 3:51 PM

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Posts: 18,076
Registered: 1/29/05
Matheology § 160
Posted: Nov 24, 2012 3:49 AM
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Matheology § 160

{{Another application of set theory?}} One of the remarkable
observations made by the Voyager 2 probe was of the extremely fine
structure of the Saturn ring system. [...] The Voyager 1 and 2
provided startling images that the rings themselves are composed of
thousands of thinner ringlets each of which has a clear boundary
separating it from its neighbours.
This structure of rings built of finer rings has some of the
properties of a Cantor set. The classical Cantor set is constructed by
taking a line one unit long, and erasing its central third. This
process is repeated on the remaining line segments, until only a
banded line of points remains. {{Materialized points are certainly not
available in the Saturn ring system.}}
[H. Takayasu: "Fractals in the physical sciences", Manchester
University Press (1990) p. 36]

Mandelbrot conjectures that radial cross-sections of Saturn's rings
are fat Cantor sets. For supporting evidence, click each picture for
an enlargement in a new window.

Regards, WM

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