Nobody tires of Mandelbrot Set images, especially the zoomed-in ones.
But there aren’t very many non-mathematicians who can explain them — though I hope my former Precalculus students can do so.
For everyone else, you really need to watch a 24-minute video by Ben Sparks, in which he not only shows a few of the infinitely many beautiful images found in the Mandelbrot Set but also explains the basics in clear English. Because the Mandelbrot Set is “the most complex object in mathematics,” you can’t expect everything to be explained in 24 minutes (nor in 24 hours nor even in 24 days), but the basics are all here, along with some relevant connections with Julia Sets. No, you won’t learn why the spiral shape here has seven arms (so it’s a heptapus, not an octopus), though you would learn that in certain Precalculus classes that I am intimately familiar with. But Sparks will teach you why some regions are black, some are blue, and some are other colors. More importantly, he explains the connection with iteration (which he takes enough time to explore thoroughly), though he just assumes that you know something about complex numbers — not the fact that i2 is –1 but the fact that they are representations of numbers in a 2-dimensional world. Go watch it!