Who Discovered The Mandelbrot Set?

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Offline 1Maniac

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« on: August 18, 2017, 06:40:47 AM »
Who Discovered the Mandelbrot Set?

https://www.scientificamerican.com/article/mandelbrot-set-1990-horgan/

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Offline Fraktalist

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« Reply #1 on: August 18, 2017, 08:08:54 AM »
Thanks 1maniac for that article.
We will some day make an episode for WTFract about this - the other discoveres deserve at least a bit of acknowledgement.
« Last Edit: September 01, 2017, 11:19:05 AM by Frank Fraktalist »

Offline claude

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« Reply #2 on: September 07, 2017, 04:58:05 PM »
Nice article!  I was intrigued by the penultimate paragraph, so searched the internet for the reference:

THE MATHEMATICAL INTELLIGENCER VOL. 12, NO. 2 9 1990 Springer-Veflag New York
https://link.springer.com/article/10.1007/BF03024000
https://page-one.live.cf.public.springer.com/pdf/preview/10.1007/BF03024000

The PDF preview contains this:
Quote
I would like to add a historical note to the topic of fractal geometry recently discussed in the Mathematical Intelligencer. In 1952 F. Riesz proposed the following problem for solution in the Hungarian mathematical journal Matematikai Lapok [Problem 54, Matematikai Lapok 3 (1952), 286]:

Given a complex number $a$, for what complex values of $z_1$ does the iteration $z_{n+1} = \frac{1}{2} (z_n + a)$ yield a convergent sequence?

If the proposer did not know the solution of a published problem, the editor noted it in a footnote.  Problem 54 has no such footnote. However, in 1956, shortly after the death of F. Riesz, the Matematikai Lapok published, among others, a Russian and a French translation of F. Riesz's problem [Matematikai Lapok 7 (1956), p. 125 (Russian), p. 147 (French)]. The French translation contains the footnote, "The author submitted the problem without knowing its solution.  Until now no solution has been received by the editor."

If we use the notations $z_n = 2x_n$, and $a = 4c$, we arrive at the equation $x_{n+1} = x_n^2 + c$ which recently has been extensively studied. See, for example, H.-O. Peitgen and P. H. Richter: The Beauty of Fractals, Springer-Verlag, Berlin, 1986, and B.Branner: "The Mandelbrot set," in Chaos and Fractals, R. L. Devaney and L. Keen, editors, Proceedings of Symposia in Applied Mathematics, Vol. 39, American Mathematical Society, 1989, 75-105.

If Professor F. Riesz were alive today, he would be very pleased to see these new results.

Lajos Talcs
Department of Mathematics and Statistics
Case Western Reserve University
Cleveland, OH 44106 USA

Offline taurus

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« Reply #3 on: October 26, 2020, 10:39:52 PM »
https://www.scientificamerican.com/article/mandelbrot-set-1990-horgan/

Just stubled upon this post and read the entire article. Very interesting. Less the question who documented what where first. I find it rather exciting to hear (or read), how many colleagues described Mandelbrot as not very accommodating or stingy in giving credit or influence. A typical loner who - somewhat bitterly - saw his own influence underestimated. One can even understand this, considering that he did not take up his first full professorship, until he was 75.
when life offers you a lemon, get some salt and tequila.

Offline Adam Majewski

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« Reply #4 on: October 27, 2020, 04:53:31 PM »
Should the article in wikipedia be updated ?


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