[fern fractal is an example from www.dangries.com]
Judging by the avatar photos I see around Brilliant, there must be other people on here that share my fascination with with recursive self-similarity, so I thought I would show off this online fractal maker I just found.
What I like about this applet in particular is the extremely tasteful subdued tones that it plots my fractals in. I think it's the graphic design that really makes this fractal maker gratifying.
Read the instructions if you get lost. The easiest way to start out is to view the "examples" and start experimenting with how tweaking little things about the examples results in crazy changes.