Fourier TransformIn the first frames of the animation, a function

fis resolved into Fourier series: a linear combination of sines and cosines (in blue). The component frequencies of these sines and cosines spread across the frequency spectrum, are represented as peaks in the frequency domain (actually Dirac delta functions, shown in the last frames of the animation). The frequency domain representation of the function, f^ (f-hat), is the collection of these peaks at the frequencies that appear in this resolution of the function.Image (Animated gif): The Fourier transform takes an input function f (in red) in the “time domain” and converts it into a new function f-hat (in blue) in the “frequency domain”. In other words, the original function can be thought of as being “amplitude given time”, and the Fourier transform of the function is “amplitude given frequency”.

Shown here, a simple 6-component approximation of the square wave is decomposed (exactly, for simplicity) into 6 sine waves. These component frequencies show as very sharp peaks in the frequency domain of the function, shown as the blue graph. In practice, these peaks are never that sharp. That would require infinite precision.

Image (gif animation)byLucas Vieira Barbosa - http://1ucasvb.tumblr.com.See more: Replicate the Fourier transform time-frequency domains correspondence illustration using TikZ (at here).

bottom photo via http://steven-universe-confessions.tumblr.com/post/98637303817

What’s going on with the dramatic poses of Soos in his double exposure picture in the background? So mysterious!

- Does anyone know what shadow was shown before Bigfoot in the opening sequence? It shows right at the beginning of the forest scene. I swear I see a shadow but I don't recognize it. The middle one looks like a shuriken...
- Could it be an alien? or just some black effect?

A dinky little pascal’s cipher. I feel like I should humor this idea further and make a pretty colored version later, but it doesn’t look as cool as I anticipated, so we’ll see

Anyone else think that the shadow from the sandbags on the lower left corner of this screenshot looks like Bill Cipher (zoomed in on right above)? Or do I have Bill Cipher on the brain now? He’s everywhere!

Finally get the password to a computer on Gravity Falls and it is to Soos’ computer, not the infamous laptop. FIXINIT1 indeed.