(these two pictures are the same thing (iterations towards the boundary of the mandelbrot set), only colored differently)
91*19
=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿n͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿o͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿=͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇͇̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿
Caustics are those lines that light traces at the bottom of your teacup.
So, the euler spiral! It’s the big one at the top. It’s traced out by the parametric equations written under it.
I thought something interesting would happen if I replaced the cosine and the sine with the derivatives of the parameterizations of various other curves, and then this happened.
That’s what I thought too, at first, (which is why I was surprised) but it turns out (after some thought) that it has more to do with the fact that the product of anything and 0 is 0 (Or, here, that the product of anything and the empty set is empty).
Foundationally, all you need is a functor from a Set-sized discrete category to Set, and then the fact that the empty set is initial and that the only function into it is the identity takes care of the rest, I think.
I don’t think the product of all non-empty sets is the empty set, but the only arguments I could think of against that use the axiom of choice, so maybe in some more exotic system…
Also, 100th post woohoo
It Could Be a Mothership - Zabutom
scibot9000 replied to your post: Could you tell us a little bit about…
oh man I JUST STARTED listening to that while browsing tumblr. that’s cool. you’re cool. what other kinds of music/artists do you like? (since apparently you dig chiptunes)
Well, recently I’ve been listening to a lot of the music on ubiktune. Most of their stuff is very good! In particular, I enjoyed Equilibrium a lot.
I also like this track. It was an nsf in some copy of the 2a03.org NES music archives.
In an earlier post you described your tool chain to produce gifs was (if I recall correctly) Haskell to LaTeX to ImageMagick. Have you tried anything with POVRay? I'm playing with POVRay and am wondering if I am wasting my time and should just go to LaTeX. Also, is Haskell your language of choice?from igetrashes
I don’t really know anything about POVRay, but I do know that the way I use LaTeX is Bad and Wrong and should not be imitated unless you already know how to use LaTeX and are too lazy to learn how to make things pretty with something more appropriate (like I was).
P.S. yes haskell is my favoriteCould you tell us a little bit about yourself? If you don't mind, that is.from Anonymous
FACTS:
- 2ⁿᵈ year undergrad Mathematics student at the EPFL in Switzerland
- Native speaker of French and English
- Likes non-human people and generalized minds
- Listening to the black box again now
- Really want to start reading Sheaves in Geometry and Logic.
- Poor impulse control, but most of my impulses are to stay at home and sleep, start reading another book on something mathematical or do internet things
- 10 Kg of pasta in kitchen
- …
- uh
- What do people want to know?
- Ask me questions.
