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Its definition and name are due to Adrien Douady, in tribute to the mathematician Benoit Mandelbrot.[1] The set is connected to a Julia set, and related Julia sets produce similarly complex fractal shapes.

Mandelbrot set images may be created by sampling the complex numbers and testing, for each sample point {\displaystyle c} c, whether the sequence {\displaystyle f_{c}(0),f_{c}(f_{c}(0)),\dotsc } {\displaystyle f_{c}(0),f_{c}(f_{c}(0)),\dotsc } goes to infinity (in practice — whether it leaves some predetermined bounded neighborhood of 0 after a predetermined number of iterations).

Thanks so much for taking the time to educate me. Much appreciated.

I hope you took this as I intended, the original comment was a complimentary
one, or meant to be so, all the rest I shared because I found it to be mind
Boggling and interesting when I first read about it. I hoped you would
As well. Keep on steeming my friend @trudeehunter

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