Posts Tagged ‘art’

Fractal Holiday/Solstice/Christmas Cards!

December 24, 2011

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.

Christopher Olah's fractal Christmas cards from 2011

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…)

Harry Potter and the Methods of Rationality Fanart

August 14, 2010

All I have to say for myself is that it (see chapter 17) was too clever for me not to make a graph.

Factoring by Time Travel

Also, Yudkowsky did actually use the product of two prime numbers.  I checked: 181,429 factors to 397 * 457.

Symphony of Science Logo Idea

August 10, 2010

“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:

Symphony of Science -- Posible logo

Also, ideas: SoS t-shirts (I’d wear one!) and posters.

And a math song!

Variations of the Mandelbrot Set

April 23, 2010

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!

(more…)

Pamphlet (zine?) Making

February 10, 2010

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!

Fractal Christmas Cards and More

January 4, 2010

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:

\forall n \in \mathbb{R}, n > 2; k \in \{x|x\in \mathbb{C}; \lim_{N\to\infty} (z\to z^n+x)^N(x) \neq \pm \infty\}

\implies

\{x|x\in \mathbb{C}; \lim_{N\to\infty} (z\to z^n+k)^N(x) \neq \pm \infty\} \in \{\text{connected}\}

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 (z\to z^n+x)-orbits of these points exhibit a rather simple behaviour: z converges to a value that satisfies z=z^n+x if it is possible.

So we want to find the maximum value of z-z^n (ie. M\cdot (z\to z-z^n)^{\to}(\mathbb{R}^+) where M is the supreumum).

This is trivial to find: z|_{\frac{d}{dz}z-z^n=0}=\sqrt[n-1]{\frac{1}{n}} and if we plug that into z-z^n we get \sqrt[n-1]{\frac{1}{n}} -(\sqrt[n-1]{\frac{1}{n}})^n


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