Heart Broken

Hi all, sorry for the lack of updates. Life has been really crazy.

Anyways, today’s math-art seem to be right up Randall Munroe’s alley. What do you do if you’re a math lover, and have had a terrible emotional roller coaster week?

Of course you go plot your love on a graph. Like me. ‘cept mine’s broken.

I plotted it quite quickly on a tool called PowerToy Calculator. It’s part of Windows XP Powertoys series applications from Microsoft, and it was a bitch getting it to work on Vista. Basically, you have to get Powecalc.exe from an XP computer and copy and paste it directly into Vista, then set compatibility to Windows XP SP2. But you’d appreciate the initial hassle, since you don’t have to boot up Mathematica to rapidly make functional graphs.

Because of the complexity of the graph (its not easy to get a heart shape), this picture is actually comprised of 4 different functions (or two functions if some functions are working). The two/four functions are:

f(x) = sqrt(2-(abs(x)-1)^2) and g(x)= acos(1-abs(x))-pi.

These are the two functions if the abs(x) [basically this means the absolute value of x; math notation: |x|] is working. Since its not properly functioning on my computer (yes I know this implies a CPU fault, and the universe will implode on itself blabla), I split each function up into two more, replacing each abs(x) with x and -x.

Also, if you got yourself Powetoys Calculator to play with, you’ll notice that the equation I gave above gives the full complete heart. To break the heart, simply make f(x) = sqrt(1-(abs(x)-1)^2). Stupidly, why would anyone want to break a heart? Oh well, some people just are heartbreakers. Idiots.

And I also added a 3rd function to make that crack in the heart. It’s just a arcsin-sin wave, also known as a triangle wave. The function is as thus:

j(x) = 0.5/pi*asin(sin(10*x))

Anyways, to combine them, I used Photoshop. I copied and pasted all the layers together, and used each layer with a Difference blend mode. The difference blend mode is also mathematical in nature. As I mentioned in the 76 Blowjobs post, each pixel has its numeric value. Difference is basically the absolute difference (i.e. |difference|) between the pixels of two layers. Nathan has a very good writeup on the math behind photoshop (and why Subtract is different from Difference)