Date: Nov 24, 2012 3:49 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Matheology § 160
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]

http://books.google.de/books?id=NRYNAQAAIAAJ&pg=PA180&lpg=PA180&dq=Takayasu:+%22Fractals+in+the+physical+sciences%22&source=bl&ots=-_jQrSNVTs&sig=ttuEDGX_6381_T2AdLEBT8HIT20&hl=de&sa=X&ei=Yb6GT-iFDcvUsgao6ITPBg&sqi=2&ved=0CDMQ6AEwAQ#v=onepage&q=Takayasu%3A%20%22Fractals%20in%20the%20physical%20sciences%22&f=false

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.

http://classes.yale.edu/fractals/labs/paperfoldinglab/fatcantorset.html

http://www.youtube.com/watch?v=Ztgqa_5vumI

Regards, WM