Mandelbrot Trajectory Infima

These renders below are the result of considering the "trajectories" of points inside the mandelbrot set when iterating $z \mapsto z^2 + c$. Specifically, looking at the closest point on such a trajectory to the origin $a(c) = \inf {\left|z_n\right|} = \inf {\left|P_c^n(0)\right|}$. As far as I can tell, this was first described / explored in a 1986 book "The Beauty of Fractals".

References

• Displaying the Internal Structure of the Mandelbrot Set
• The Beauty of Fractals, 1986, by Prof. Dr. Heinz-Otto Peitgen and Prof. Dr. Peter H. Richter.