I'm playing around with a couple of different fractals, and a recurring theme I'm seeing is the presence of baby Mandelbrots (small versions of the Mandelbrot set) in nearly all of these.
Here's one between -0.183346 + 0.36017685i and -0.18229 + 0.36072355i.
As you can see, it's got these cool structures around it. The equation used to generate this fractal is:
$$ z \to (z^2+2c)^4+c $$
So why does the Mandelbrot seem to appear here? And in other fractals generated with similar equations.