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The Mandelbrot set was discovered by Benoit Mandelbrot in 1980.

However, Gaston Julia lived from 1893 to 1978.

Does this mean Julia sets, in the popular form we know them today, were discovered before the famous Mandelbrot fractal?

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Yes, about 60 years before.

What is called "Julia set" was actually discovered by P. Fatou, his first publication on the subject is from 1917:

Sur les substitutions rationnelles, Comptes Rendus, 164, 806-808 (1917).

Julia's paper on the subject was published in 1918, but he was able to prove that he discovered it independently of Fatou.

It was called "irregular set" until, after the death of Fatou, Julia insisted that it must be called Julia set.

(Documented source: the book of Michele Audin, Fatou, Julia, Montel: The Great Prize of Mathematical Sciences of 1918, and Beyond, Springer 2011. )

Mandelbrot set was discovered by Brooks and Matelski in 1978 (but their paper was published in 1981):

The dynamics of 2-generator subgroups of PSL(2,C). Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), pp. 65–71, Ann. of Math. Stud., No. 97, Princeton Univ. Press, Princeton, NJ, 1981.

The contribution of Mandelbrot consists in production of high-tech computer pictures of it. His paper was published in 1980, it contains a good quality picture, but this first picture is not quite correct.

"The things are never named after their true discoverers" (Arnold).

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    $\begingroup$ Scan courtesy of BnF Gallica: P. Fatou, "Sur les substitutions rationnelles." Comptes rendus hebdomadaires des séances de l'Académie des sciences, Vol. 164, Jan. - Jun. 1917 (session of May 14, 1917), pp. 806-808 $\endgroup$
    – njuffa
    Dec 11, 2023 at 21:41
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    $\begingroup$ Here are the pictures of a Julia set (left) and Mandelbrot set (right) from the paper of Brooks and Matelski: math.purdue.edu/~eremenko/Pdf/brooks.pdf $\endgroup$ Dec 12, 2023 at 14:18
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    $\begingroup$ Ah, teletype graphics. I remember that from junior high school. $\endgroup$
    – Lee Mosher
    Dec 12, 2023 at 23:05
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    $\begingroup$ @LeeMosher there's more here: Grid spacing, iterations used in the 1978 first published rendering of the Mandelbrot set? which includes an answer by one of the paper's authors! $\endgroup$
    – uhoh
    Dec 14, 2023 at 5:03
  • $\begingroup$ @AlexandreEremenko ditto $\endgroup$
    – uhoh
    Dec 14, 2023 at 5:03

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