Wednesday, February 25, 2009

Sunday, February 22, 2009

Prose Poem: Morning Shift

Morning Shift

I like to think of her as the woman with the space ship, a classic style flying saucer loft with a kitchenette, great location above a bakery or independent cafĂ©, a bus stop nearby. Not red plastic or shiny chrome, but a subtle matte or twill – the fashionable fabric of the hour. Its landing gear is smooth as a designer heel and its port holes curtained with the priciest silk that can be bought on the intergalactic market.
  Her white hair whispers from beneath her jaunty beret, like a low resolution photograph of the milky way, and the wrinkles on her face are firm and definite from her travels, she wears them like diamonds. And she knows: the French don't set the fashion trends, she goes to the source, where the light reflecting off their purse-clasps will only be seen by earth long after it has gone out of style. And she knows: her scarf lies just so against the neckline of her coat and she can carry it off when the gravity changes and the sky is flaming orange. With pursed lips, having stared down the widely-feared armies of be-tentacled Europans, she condescends to wait in line to buy a fruit cup and a meat pastry, six dollars and eighty four cents.

Tuesday, February 17, 2009

Pretty Binary Functions

Following up my previous post about visualizing 3D binary, some prettiness from different two variable functions (at a much higher resolution). Note that the first level of the third function is the background of this blog. It used to be the first. I changed my mind.

   
  

First row left to right:
f(x,y)=(cos(x)+3)*(sin(y)+3) levels 1-4, 
f(x,y)=(cos(x/pi)+2)*(cos(x/pi)+2) levels 1-4, 
f(x,y)=(x^2)*(y^2) levels 7-8, 

Second row left to right:
f(x,y)=(log(x))*(log(y)) levels 1-2,
f(x,y)=(x^4)+(y^4) levels 6-9, 
f(x,y)=(x^2)+(y^2) levels 6-9

Monday, February 16, 2009

3D Binary Patterns

I've been doing multivariable function in math class, so I started thinking about graphing binary in 3D. I've been stacking 3D sets of binary words for ages now, but I'd never done anything more interesting than that. I'm not sure how mathematically rigorous this is, but it is pretty, and that is enough.

First, I drew out a few levels of f(x,y)=x+y on this scale, filling in the z-axis with the binary place value (a cube set on z=1 is in the 2^1=2 place value, so it has a value of 2).

Here is a diagram, rotated so that the pattern is easier to see:

This is not very informative, as all the information below the surface layer is hidden. To remedy this, I switched to considering each place value layer separately, as shown below for all the cubes at z=0 (or the place value 2^0=1)

In order to produce these digitally with my limited graphical abilities, I used a bird's eye view of each place value layer. I wrote a quick program to generate the patterns for my using the formula I worked out a while ago. Here is f(x,y)=x+y at z=1, 2, and 3:

Stripe-y, but not very interesting. 

f(x,y)=x*y, on the other hand, is just plane awesome. Shown here are the first 5 layers:
I don't know if this really qualifies as a fractal, but each decreasing level is a one quarter size approximation of the one that came before. If you try mentally stacking these views, it looks a bit like Cantor's comb, if it was a stool instead of a comb, and a bit more complicated.

The fact that binary produces fractally patterns (fractally is now a word) is not surprising. The most obvious binary pattern, just the numbers 1-31:

(isometric diagrams made with this)

Sunday, February 15, 2009

Background in Binary

The blog has a new pattern for the background. 

The formula I used to generate this pattern is...

f(x,y)=(cos(x)+3)*(sin(y)+3)

...where the results are rounded down to the nearest integer and converted to binary, and only the one's place is considered. The resulting pattern consists of these results with a 1 represented by a lighter dot, and a 0 by a darker dot.

Binary is pretty. Consider yourself warned.

Edit - change from this


to this:

Saturday, February 14, 2009

Happy Valentines Day?


This is all that I have to say on the matter. Interpret it how you will.

Friday, February 13, 2009

1378-1415, The Great Schism

In 1309, the pope visited Avignon, France, and, given the turbulence in Rome, decided to stay. Seven popes later, the papacy was still stationed in Avignon, and was suffering from the financial burdens of having to build a new infrastructure, as well as the symbolic burden of having abandoned Rome.

At the advice of Catherine of Sienna, the pope returned to Rome in order to restore the papacy to its former glory. Shortly after, as popes often do, he died. The next pope was elected with the consent of the French, but soon got on their bad side, and lost their support.

So the French elected their own pope in 1378. And for so for around 37 years, there were two popes (actually, there were even three at one point, ironically instated by the Council of Pisa in 1409, which was held in order to resolve the two-pope problem).

Basically, from 1378 to 1415, we had the glorious period of.... Pope Fight!

Tuesday, February 10, 2009

Buttons for Mouse's Neck Mark 1

I'm pretty sure there is a much better way of making something like this.

Sunday, February 8, 2009

Quilt

The quilt I made with guidence from my dear mother for college. It's massive and warm and comfy. 

New camera: success. 

Tuesday, February 3, 2009

Clockwork Necklace

I like to think this is more than the average clockwork necklace, what with it being in a case and terribly photographed. If I ever get hold of a camera I'll try and get a shot of the lovely detailing on the case and of the mechanism inside.

Sunday, February 1, 2009

Fairy Skulls, or the Medium of My Childhood

I have gotten back in touch with my childhood self through sculpey. 

I'm pretty happy with this second attempt:



Me first attempt was kind of, well, meh:


Now I just need to make them part of some kind of dazzling work of art...