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Author Topic: Did Julia know how a Julia set looked like?  (Read 1979 times)
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bib
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« on: November 19, 2011, 11:46:37 AM »

I have always been wondering if Julia and Fatou had an idea of what the graphical representation of their work would look like if properly drawn.

At that time, early 20th century, of course computers did not exist.

I just stumbled upon this page (in French) and it seems like some very early fractal drawings were made. In this case it's not a Julia set, but the image is really striking when you compare the one drawn by hand and the one by a computer.

http://images.math.cnrs.fr/Un-ensemble-limite.html

Any more ideas?
« Last Edit: November 19, 2011, 11:49:11 AM by bib » Logged

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bib
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« Reply #1 on: November 19, 2011, 11:53:21 AM »

The cover of a book with a drawing of a Julia set by Julia himself:

http://www.springerlink.com/content/978-3-642-00446-9#section=61103&page=1
« Last Edit: November 19, 2011, 01:22:17 PM by bib » Logged

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« Reply #2 on: November 19, 2011, 07:24:46 PM »

The cover of a book with a drawing of a Julia set by Julia himself:

http://www.springerlink.com/content/978-3-642-00446-9#section=61103&page=1

The sketch is even more primitive than I would have guessed; Julia didn't even use a French curve! Nevertheless, it is very recognizable. The alternating pattern of solid versus dashed curves struck me immediately. Julia's insight is amazing.
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« Reply #3 on: November 20, 2011, 02:24:01 PM »

Thanks Bib.

People tend not to know that Before Benoit named the field Fractal a lot of work was done in depicting these sets. The name for them was often not as appealing as the word fractal, and the notion of a function hides the iteration that is implicit. Of course a function is pure iteration, but we would not have singled out the boring repetition were it not for Benoit handing it over to  a computer programme.
There are other fractal investigators who explored this area geometrically, and Jakob Steiner is the main expert on the geometrical approach to space functions. He refused to go down the algebra route, and remained a synthetic geometer all his days. Albrecht Duerrer also deserves mention.

These forms were not called monsters for nothing!

Thanks for the links Bib.
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« Reply #4 on: November 20, 2011, 09:02:32 PM »

this is an interesting threat. i always thought julia  had no idea how his sets would look like. and the effort to get a short glance on these sets can't be rated high enough - his only resources were a slide rule and logarithmic tables. although julias ideas about the look of julia sets must have been quite rudimental.

There are other fractal investigators who explored this area geometrically, and Jakob Steiner is the main expert on the geometrical approach to space functions. He refused to go down the algebra route, and remained a synthetic geometer all his days.

to read steiner's name in conjunction with dynamic math (witch fractals are) wondered me a bit. i know steiner from constructive analysis (in fact static math). steiner is still daily task for millions of constructive engineers. steiner's theorem is essential for calculating the moment of inertia of any carrier section - mostly steel or ferroconcrete. but i see the world through the eyes of the architect - also a single-edge point of view.
thanks for broaden my horizon...  A Beer Cup
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« Reply #5 on: November 21, 2011, 10:06:29 AM »

Very interesting, thank you for the links bib!
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« Reply #6 on: November 21, 2011, 04:17:06 PM »

I have also seen an early sketch, by Julia if I remember correctly, which consisted of triangles.  Unfortunately it was in a book I loaned to a new potential fractaleer and she has yet to return it tongue stuck out
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bib
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« Reply #7 on: February 11, 2013, 11:38:20 AM »

Some interesting drawings and early Mandelbrot prints

Visionary Images: The Lost Fractals of Benoît Mandelbrot
http://www.wired.com/wiredscience/2013/01/mandelbrot-images/?pid=5938

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