pic: Happy Holidays!

Happy holidays everyone! And here’s some math!

The equation on the top of the image, when graphed creates the “Happy Holidays!” text as shown below, with a method similar to Wolfram Alpha’s shape curves or person curves. I created it last year with Mathematica using the code from here: http://mathematica.stackexchange.com/questions/17704/how-to-create-a-new-person-curve

The details of the math are beyond me (if anyone could explain it, that’d be awesome), but I believe it basically uses Fourier series-based formulas to reduce the curves of text into equations.

I don’t see any real Fourier here, just a parametric breakdown of x (first 9 lines) and y (next three lines) as a function of t (usually time). If it were a result of Fourier analysis, each term would have a linear increment of the multiplier for t.

Though I am reminded of the original “Duck Dodgers in the 24-1/2 Century” cartoon [Daffy Duck cast as Duck Dodgers, Porky Pig as Space Cadet].