On 9/19/2012 8:39 AM, Bruno Marchal wrote:

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On 18 Sep 2012, at 18:02, meekerdb wrote:On 9/18/2012 8:13 AM, Bruno Marchal wrote:On 17 Sep 2012, at 22:25, meekerdb wrote:But did anybody think z' = z^2 + c was interesting before that?Yes. This was known by people like Fatou and Julia, in the early 1900.I knew they considered what are now called fractal sets, but not thatparticular one.I think Julia worked on the "Mandelbrot's Julia sets", notably. TheMandelbrot set is a classifier of the Julia sets. You can define theMandelbrot set by the the set of z such that z belongs to its Julia J(z).The point is that in math and physics such object are hard to miss,even if you need a computer to figure out what they looks like.Iterating analytical complex functions leads to the Mandelbrotfractal sets, or similar.The computer has made those objects famous, but the mathematiciansknow them both from logic (counterexamples to theorem in analysis,like finding a continuous function nowhere derivable), or fromdynamic system and iteration.If you iterate the trigonometric cosec function on the Gauss planeC, you can't miss the Mandelbrot set.But this iteration is a tedious and impractical *construction* whichin practice depends on computers.In practice, yes. But if I remember well, the point is that the M setsand alike are discovered, not fictitious human's construction. To seethem, we need a computer, but to see a circle you need a compass, or avery massive object, like the sun or the moon, ...In nature too as the following video does not illustrate too muchseriously :)http://www.youtube.com/watch?v=JGxbhdr3w2IIn such beautiful imagery it is generally overlooked that it is notthe Mandelbrot set you are looking at, but rather regions coloredaccording how close they are to the set (which cannot be seen at all).Hmm, the inside mandelbrot set has dimension 2, as you can extrapolatefrom the big spot, and then the filament ar made of little mandelbrotset. So you can always see something. You are correct, for thefilaments: usually we can see them, as the little Mandelbrot sets aretoo small. The coloring only makes them less thin and more easilyobservable, but you would see the same basic shape with a pure blackand white picture. for example, everywhere on the main (straight)antenna, there is a little mandelbrot set, so even black and whiteresolution will make a thin line (with always too big pixels, ofcourse). Of course, the line can become thinner and thinner, so withdeeper zoom, you will have "to darken the picture", and then light itup, etc. Of course this is true also for a circle, or a straight line,which are too thin to be seen, too, but we don't worry to draw themwith chalks or pens, which approximates them quite well.You can see that phenomenon here: http://www.youtube.com/watch?v=QXzgrtntRTY Bruno

Dear Bruno,

`Your remarks raise an interesting question: Could it be that both`

`the object and the means to generate (or perceive) it are of equal`

`importance ontologically?`

-- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.