The parameter c=-2 belongs to the Mandelbrot set. For this parameter the critical point is pre-periodic (0 -> -2 -> 2 -> 2 -> ...), so it is bounded and the corresponding Julia set is connected (it is the interval [-2,2] on the real axis).
If the orbit gets outside of radius 2, you can show that it escapes to infinity, i.e. that the parameter is not in the Mandelbrot set.
Thanks for the nice lectures!
Your escape check in
VGA_Graphics/Mandelbrot_Set/mandelbrot_fixvfloat.cshould be|z|^2 > 4, and not https://github.com/vha3/Hunter-Adams-RP2040-Demos/blob/f5f85bafe148e3ee578c67afbdb08fc9f6d4ec0f/VGA_Graphics/Mandelbrot_Set/mandelbrot_fixvfloat.c#L101 https://github.com/vha3/Hunter-Adams-RP2040-Demos/blob/f5f85bafe148e3ee578c67afbdb08fc9f6d4ec0f/VGA_Graphics/Mandelbrot_Set/mandelbrot_fixvfloat.c#L188The parameter
c=-2belongs to the Mandelbrot set. For this parameter the critical point is pre-periodic (0 -> -2 -> 2 -> 2 -> ...), so it is bounded and the corresponding Julia set is connected (it is the interval [-2,2] on the real axis). If the orbit gets outside of radius 2, you can show that it escapes to infinity, i.e. that the parameter is not in the Mandelbrot set.