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I really like the simplicity.

Can you reverse the direction of one of the spirals?

Or maybe slow down one to half-speed?

(Maybe it would look better, maybe not.)

Very merry cleverness
This reminds me of when I first started programming in Turbo Pascal. I made a Christmas tree using graphic mode and trig functions. I also only used if-then statements so i ended up with about a thousand lines :) Looking at this more elegant tree reminds me of why I went into this career.
It seems awfully appropriate 'starring' this repository.
Very nice and not complicated at all -- good work!
Extra credit to anyone who can implement this in HTML/CSS without using the canvas element. Since CSS transformations are hardware accelerated, I bet it can be made to look as smooth as the reference GIF.
Several years ago I made a very silly simple Christmas tree in HTML/CSS, with <blink>ing lights and Unicode ornaments, and my friend made a way to place your own choice of "ornaments": http://unicodexmas.com/

Not as stylish, but in the spirit!

May I suggest t * sin( k * ln(t) ), for some constant k? That makes the path self similar about the (0, 0) point. Maybe you'd like that.
Oh god staring at this just motivates me to work. Thanks a lot for sharing, as well as all the commenters showing the different implementations of it.