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Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 160
Posted:
Nov 24, 2012 3:51 PM


In article <90c3cfe3848148fa87c6059ad881f600@p17g2000vbn.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> 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_63 > 81_T2AdLEBT8HIT20&hl=de&sa=X&ei=Yb6GTiFDcvUsgao6ITPBg&sqi=2&ved=0CDMQ6AEwAQ#v > =onepage&q=Takayasu%3A%20%22Fractals%20in%20the%20physical%20sciences%22&f=fal > se > > Mandelbrot conjectures that radial crosssections 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
While nature is full of fractals (in which a pattern on one scale is repeated on apparently ever smaller scales) like the Cantor set construction, in nature the number of possible smaller scales on which such a pattern can repeat is always finite, unlike a purely mathematical Cantor set, whether fat or not! 



