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! (more…)
All I have to say for myself is that it (see chapter 17) was too clever for me not to make a graph.
Also, Yudkowsky did actually use the product of two prime numbers. I checked: 181,429 factors to 397 * 457.
“Designers! I’m looking for logo/merch ideas for Symphony of Science. If you make something cool that I use you will be compensated somehow” — musicalscience
So, here’s an idea:
Also, ideas: SoS t-shirts (I’d wear one!) and posters.
And a math song!
Here’s some variations of the Mandelbrot Set I’ve been looking at. They aren’t terribly interesting from a mathematical perspective, but their pretty!
I’ve been producing some some printed copies of certain Free books.
3 MIT Guides to Lockpicking (pdf) and 1 _why's poigant guide to ruby (pdf)
I use psbook and psnup to make the books into pamphlets, print them, and bind them. The I give them out at hacklab.to!
For Christmas, I was handing out fractal Christmas Cards (they had images made in gnofract4d with the equation beneath… I gave my mom a handbound book with pictures of fractals made in sage in it since I didn’t get the latest revision of the math textbook done in time to get that). Thus, I made many fractals. At the end, I noticed something.
First I’ll make a (IMHO, reasonable) conjecture:
Now, it’s often interesting to look at julia sets when they fracture, thus they make good pictures. And it is easy to find the point of fracture on the positive real number line.
The 
So we want to find the maximum value of 
This is trivial to find: ![z|_{\frac{d}{dz}z-z^n=0}=\sqrt[n-1]{\frac{1}{n}}](http://s0.wp.com/latex.php?latex=z%7C_%7B%5Cfrac%7Bd%7D%7Bdz%7Dz-z%5En%3D0%7D%3D%5Csqrt%5Bn-1%5D%7B%5Cfrac%7B1%7D%7Bn%7D%7D&bg=ffffff&fg=333333&s=0 "z|_{\frac{d}{dz}z-z^n=0}=\sqrt[n-1]{\frac{1}{n}}")
![\sqrt[n-1]{\frac{1}{n}} -(\sqrt[n-1]{\frac{1}{n}})^n](http://s0.wp.com/latex.php?latex=%5Csqrt%5Bn-1%5D%7B%5Cfrac%7B1%7D%7Bn%7D%7D+-%28%5Csqrt%5Bn-1%5D%7B%5Cfrac%7B1%7D%7Bn%7D%7D%29%5En+&bg=ffffff&fg=333333&s=0 "\sqrt[n-1]{\frac{1}{n}} -(\sqrt[n-1]{\frac{1}{n}})^n")
