I clearly remember seeing a paper where the dynamic of the anti-conformal map $f(z)=\overline{z}^2+c$ was studied (the bar means complex conjugation). There was a picture of the analog of the Mandelbrot set, which looks very different from the usual one. Can someone help me to locate this paper ?

EDIT. Thanks to Benjamin Dickman. Another common name is Mandelbar, which escaped my memory. Once you know these two names, Tricorn and Mandelbar, the search becomes trivial.

EDIT 2. More information. Apparently this setting was introduced in the paper "On the structure of Mandelbar set by four authors, in Nonlinearity, 2 (1989), 541-553. I contacted one of the authors, and he told me the following story: someone wanted to draw a Mandelbrot set with a computer, but made a misprint in the program. The result looked interesting... Tricorn was discovered by Milnor (independently of this) in his experiments with a holomorphic (cubic) family.

EDIT 3. If someone is curious why I asked this, see the Comment in the end of this preprint: http://arxiv.org/abs/1507.01704

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    $\begingroup$ Higher-degree (unicritical) versions are sometimes called "multicorns". I believe Dierk Schleicher is among the people who has done some work on the topic (after Milnor). $\endgroup$ Jun 8 '15 at 8:11
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    $\begingroup$ Speaking of errors implementing the Mandelbrot fractal, you might like the Burning ship fractal, en.wikipedia.org/wiki/Burning_Ship_fractal $\endgroup$ Sep 2 '15 at 0:24
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    $\begingroup$ @Per Alexandersson: Thanks. They are funny. $\endgroup$ Sep 2 '15 at 1:55

Perhaps the key term is tricorn? See Inou's Self-similarity for the tricorn (arXiv pdf) and its references.

Sample excerpt:

enter image description here

  • $\begingroup$ @AlexandreEremenko You're welcome! I used antiholomorphic and Mandelbrot to find this particular paper; 'Mandelbar' is a pretty good word... $\endgroup$ Jun 6 '15 at 7:00

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