Actually, this particular corner of the Mandelbrot set (or the Julia set?) is called "The Phoenix". Wow, anyone else who is running Linux is strongly encouraged to find the XaoS program. Even on this ancient Pentium-100 machine, it is able to do a decent real-time zoom into the sets. In-set and out-set colourings are amply configurable. Just watching the tutorial is an adventure. Or set it on autopilot. Scotty, beam me up!
If you are still stuck in Windoze, well, there is probably something you can buy which might approximate it.
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