I've spent a good portion of my life working on fractal software, trying basically every fractal rendering algorithm there is, reading everything I can about it

I've spent a good portion of my life working on fractal software, trying basically every fractal rendering algorithm there is, reading everything I can about it, managing fractal art communities and organising meetups... so I'm obviously very pro-fractals biased, and even so, I'm curious what makes you conjecture so strongly that 3-body stability islands would have anything to do with the Mandelbrot set. Why that one in particular, over the vast infinitude of possible fractal shapes?