Parametric Hand Turkey

This classic post from Alex Edelman originally appeared on Handshake 2.0 in 2008.

The quintessential childhood Thanksgiving arts-and-crafts project is the hand turkey, so I decided to make one. Unfortunately, a rigorous scientific education has enabled me to suck all the fun and child-like innocence out of any enterprise, so I ended up making a graph.

The graph in question is of a parametric equation. Whereas the graphs we are most familiar with give one variable as a function of another (y in terms of x, for instance), a parametric graph gives x and y in terms of another, or in our case, two other variables. I've parameterized in terms of r and t.

Equations and conditions that give us our parametric hand turkey

Equations and conditions that give us our parametric hand turkey

Equations and conditions that give us our parametric hand turkey

Equations and conditions that give us our parametric hand turkey

Wolfram Mathematica input statement that graphs the equations and conditions to create a parametric hand turkey

The parameterization, in terms of t, graphs the "shape" or "outline" of our mathematical hand turkey. It's a modification of a polar function that would normally give us a "rose" with nine petals. My fingers are not all the same size, though, so I tweaked the function with a square root of t to vary the petals a little bit. A few more changes gave me five "fingers."

A picture of the graph, as generated by Mathematica

 

Then, I multiplied by my second parameter, r. Since it ranges from 0 to 1, then for every possible value of r, the "t" function it is affecting will be drawn with a slightly different radius. When we put all these functions on top of each other, we get a continuous series of "outlines" which smoothly merge into a solid region.

Not entirely devoid of childlike aesthetic taste, I then used Mathematica to graph the function and, more importantly, apply a gradient of "Thanksgiving colors" to it.

All in all, though, you're still probably better off asking your kid to make a hand turkey.

***

If you're interested here's a high-resolution .pdf of the Mathematica notebook. It's big (8559K), and requires a little crunching from your computer, but the image it produces is gorgeous.

And for the sake of complete documentation, here's the original Mathematica notebook, in case readers of Handshake 2.0 use Mathematica.

Enjoy more Parametric Images by Alex Edelman.

Who's in FRONT? Christine Manhart
Doing mHealth Business with France

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