• Yippee, my first animations in Mathematica!

Let a circle roll around a circle twice as big. The shape traced by a point on the outer circle is a cardioid. Now consider a third circle rolling around the second one as well (again half as big, and at the same speed); its trace is already less familiar. The more circles, the more fractal-ish the resulting curve will be. In the limit, the traced curve can be described with this parametric formula:

$\dpi{120} \begin{cases} x=\displaystyle\sum_{i=0}^\infty\dfrac{\cos(2^i\,\theta)}{2^i}\\[6mm] y=\displaystyle\sum_{i=0}^\infty\dfrac{\sin(2^i\,\theta)}{2^i} \end{cases}$

(Source of inspiration: http://www.mathrecreation.com/2013/12/brain-curve.html)

Deeply nifty.

So brain.

• A cartoon by David Borchart. For more cartoons from this week’s issue: http://nyr.kr/1dJy9v9

• Ugh.

(via think-progress)

• Also available as a print at INPRNT.

• Ice Balls Forming on the Shores of Lake Michigan.

They are a metaphor for something. Yet at minus 5 below zero we are unable to remember what it might be.

Birthday greetings of some sort?

Awesome awesome awesome,

• Albert Bierstadt - Cloudy Study, Moonlight (ca. 1860)

(via thenearsightedmonkey)

• Hastings and Seymour, 1886

Or more accurately, future Hastings and Seymour.

Source: City of Vancouver Archives #Str P202

• St. Louis (2013), 2013

digitally printed poster

Miss Elise Boudreau.

• We’re interviewing to replace Dustin (and by “we”, I mean me)… maybe I’ll just buy a puppy instead though.

No one can replace Dustin.

• # Sitting quietly in a chair in a crowded room eating cookies. Loving life. 2014 is the best.

• I WOKE UP LIKE THIS

Xena forevs.

(via katerpotater)

• Merry Christmas, Martin.

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