🚀 go-pugleaf

David B. Greene wrote:
> 
> Anybody catch that recent PBS special, "Colors of Infinity," about the
> Mandelbrot Set and fractal geometry?  It was well hosted by Aurthur Clarke
> with a cameo appearance by Stephen Hawking.  Although the show was most
> interesting, I thought Clarke waxed overly eloquent about the Mandelbrot
> Set being the "Thumbprint of God" as though it opened up secrets of the
> universe so profound as to be mystical.
> 
> What I wonder is, can the Mandelbrot set really be called something that
> has always existed, as though it were part of the fabric of the universe,
> or is it a mere invention of mankind?  

The question makes no sense. Try:
Have numbers always existed or are they a mere invention of mankind?
For that matter, have complex numbers always existed upon which the
Mandelbrot set is based?
> 
> My own sense of coincidence was sparked (but I'm a sicko) when I realized
> that the dark part of the Madelbrot Set looked a lot like someone's
> derriere and if tipped ninety degrees (to properly orient the bum) it
> suddenly transformed into an image of a little Budda complete with pointy
> cap and hands to the side as though meditating in the lotus position.  This
> brings us full circle back to Clarke's idea in that remnants of the
> Mandelbrot Set can be found in the religious art of many cultures from
> Christian stained glass to Moslem mosaic tilings.  Even beyond that, to the
> collective unconscince of Carl Jung's psychology as mirrored in the artwork
> of one of his patients.  Clarke even speculates that the mind computes
> using fractals as when he closes his eyes and presses on his eyelids,
> patterns similar to Madelbrot patterns arise.  Similar patterns supposedly
> also arise from drug induced hallucinations as evidenced by the Paisly
> prints of the 60's.

The Mandelbrot set's shape is a direct consequence of the
"plane-twisting" behaviour of the complex fucntion f(z)=z^2. Anything
more than that, is just perceptual coincidence.One can choose to see a
"spaceship" if one tries hard enough.
>
> My own feeling is that all of this is just a little too mystical for a
> mathematical function.  It seems that humans try to find patterns where
> none exist. 

Correct.
That there exist tremendous amounts of information in the Mandelbrot set
is a fact. But then again, the REAL meaning behind the set is the fact
that it is a "map". Specifically, it is a map that describes which Julia
sets are connected and which are not. Maps, always carried in them
specific information. This is an example of a map which is too complex
for us to completely decifer, in the naive sense, because the number of
Julia sets is uncountable.

> Not that there are no patterns but that they don't rise to the
> level of the cosmic fingerprint of God.  One scientist, who has used
> fractal geometry to create a successful computer image compression company,
> stated that the ever increasing and, to casual observation, unpredictable
> patterns found in the fractals and the Mandelbrot Set answer the question
> of how an omniscient God created a universe with free will.

And I thought Barnsley was a serious scientist....

> 
> But hey, maybe the entire universe
> can be algorithmically compressed to a single equation.  Then, of course,
> you have found God.  OTOH, maybe the Mandelbrot Set is something much more
> prosaic.
> 
> Dave Greene

There are concessions to be made with everything. Barnsley's algorithms
are dependent upon many factors. Efficiency vs loss of data, is the most
important. He is able to compress data using very efficient algorithms
where the data are relatively canonical with inherent sub-patterns in
them. I have yet to see any Barnsley algorithm efficiently compressing
"almost" random data.
As a final remark, there are other agents which "convey" much more
information than fractal patterns. Try Bach's music. Many people have
made numerous efforts trying to exctract mathematical information from
his fugues,  yet his compositions consistently defy any such attempts.
Yet, it is plainly obvious that some of them are clearly "agents" of
some sort of information.  Hofstader in his books tried to touch upon
the subject, but with little success in my opinion.
Same can be said of DNA. But progress is being made everyday, and
someday will be able to decifer it completely. As for Bach's music, I
really doubt it.

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It is very simple: J.S.Bach
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