Archive for July, 2008

A Cute Lil Somethin’

Over at this math blog I found this, and I found it totally adorable. In an Aww, you wyke yer wittle chew toy, dontcha? Yes you dooooo kind of way.

Basically, the idea is this. You take two functions f and g from \mathbb{R} \rightarrow \mathbb{R} and you plot g as if f were its x-axis. When you’re done you get some pretty sweet lookin’ plots.

Here are some of the ones I tried. The function f is in black, and T(g) is in green, (where T is the transformation discussed above). Note that using the same domains for f and T pretty much zooms f out of the picture a lot of the time.

f(x)=\lfloor x \rfloor
g(x)=\lfloor x \rfloor

f(x)=\lfloor x \rfloor
g(x)={\lfloor x \rfloor}^2

f(x)=\cos x
g(x)=\lfloor x \rfloor

f(x)=x \cos x^2
g(x)=x^2

f(x)=0.5x^2
g(x)=x^3 \cos x

f(x)=\cos x
g(x)=\exp (\cos x^2 )

A fountain

And here’s the Scilab code I used, if you’re interested:


function [r] = perpfunc(f,g,p) //f and g are functions
//p is a vector of x-values you want to plot

//The function perpfunc plots g as if f was its x-axis.

deff('y=df(f,x)','y=derivative(f,x)');
deff('y=T(x)','y=[x-g(x)*sin(atan(df(f,x))),f(x)+g(x)*cos(atan(df(f,x)))]');

lengthp=length(p);
b=ones(lengthp,2);

for i = 1:lengthp
b(i,:)=T(p(i));
end

plot2d(b(:,1),b(:,2),style=3); fplot2d(h,f);

endfunction

Crackergate

I know the laws of the Blogoverse dictate that I’m supposed to feign unwillingness before kowtowing unabashedly to a popular controversy–citing, I dunno, journalistic integrity and civic duty? Sadly, I am no such hero. Because I just found this whole episode freakin’ funny. It provided many lulz, many in disbelief, most in hilarity.

Obligatory summary: Scienceblogger P.Z. Myers threatens a cracker. Turmoil ensues. Cracker gets poked with a nail. Epic anti-climax.

Survivors of the massacre

But this thing isn’t just crackers and circuses (see what I did there?). Yes, here’s where I pretentiously tell detractors of the kerfuffle that they don’t understand its subtleties. No, not really. But know that I’m thinking it. And feel scorned, won’t you please, in the process.

Seriously, though, (no not really) the only blameless people in this whole situation are those teasing P.Z. for claiming not to care about the cracker while devoting multiple posts to it. They haven’t yet figured out, poor souls, that web pages can be generated seamlessly via online user interfaces in mere minutes, and need not be coded painstakingly by hand in HTML anymore. And for that they deserve our collective pity. And a free Geocities account.

On a more important note, I get to leave work twenty minutes early today. Who’s jealous?

My Absence

Sorry about not making any posts in awhile. I found a place that gives me that green papery stuff in exchange for my participation in a chair-sitting competition. It goes like this. If I can sit in a chair for eight hours, tapping my fingers against lightly-springed buttons according to certain specified rules, I get to take home some of that green papery stuff. And then I get to trade it for foodstuffs, propellant for my vehicle, and many other luxuries.

OOH OOH OOH! And I have a whiteboard. A really big whiteboard. I puts maf on it. Hehehe…

Anyways, I’ve had to adjust my sleep schedule a bit, which is why the posts are lacking. I’ll get right back on that.