It’s that time of the year again: I’m making my fractal Holiday cards! I slacked last year and only made a few, but I’m back at it.

Previous years, I’d made up fractals for my cards. This year I just explored the Mandelbrot set and found cool looking regions. Since I obsessed over my choice of pictures, it took me a while to make them — I’ve made about twenty so far, and still need to make more!

It was time well spent, though, since picking the pictures gave me time to reflect on the variety one can find within the Mandelbrot set. While well aware of the mathematical elegance of the Mandelbrot Set, I’d started to forget about what one could find deep inside it… Yay, reminders!

(One thing I found really interesting is looking at “Julia sets” in the Mandelbort set. While very similar to the real Julia set they’re associated with, these disconnected Julia sets have become connected (since the Mandelbrot set is connected, they have to be). I figured that it would be binary trees based on their representation as Cantor sets, but it is clearly more intricate… Note to self: investigate this later!)

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Tags: art, fractals, math