Some Julia sets are "large" and some are "small": can we tell which values of "c" lead to which? One way to try and get a sense of this experimentally is by just drawing a lot of Julia sets! Let's draw the Julia set for "c" right where "c" is in the complex plane

Something strange is going on at a couple points along the animation: near the center the fractal's roughly disk like (recall its a perfect disk at c=0), but if c strays too far in certain directions it bursts into a constellation of tiny dots and almost disappears

Indeed, we can associate every point c in the complex plane to a fractal in this way, by drawing the Julia set corresponding to z^2+c. Here's a quick animation moving through these (the red dot shows the associated point c)

And of course, showing a wormhole like object means we have got to fly through it! Here's the view of an intrepid astronaut who enters the connect sum tube to emerge over an island: can you make sense of what they see when looking back through the wormhole?