Over at **this math blog** I found **this**, and I found it totally adorable. In an *Aww, you wyke yer wittle chew toy, dontcha? Yes you dooooo* kind of way.

Basically, the idea is this. You take two functions and from and you plot as if were its x-axis. When you’re done you get some pretty sweet lookin’ plots.

Here are some of the ones I tried. The function is in black, and is in green, (where is the transformation discussed above). Note that using the same domains for and pretty much zooms out of the picture a lot of the time.

And here’s the **Scilab** code I used, if you’re interested:

function [r] = perpfunc(f,g,p) //f and g are functions

//p is a vector of x-values you want to plot

`//The function perpfunc plots g as if f was its x-axis.`

`deff('y=df(f,x)','y=derivative(f,x)');`

deff('y=T(x)','y=[x-g(x)*sin(atan(df(f,x))),f(x)+g(x)*cos(atan(df(f,x)))]');

`lengthp=length(p);`

b=ones(lengthp,2);

`for i = 1:lengthp`

b(i,:)=T(p(i));

end

`plot2d(b(:,1),b(:,2),style=3); fplot2d(h,f);`

`endfunction`

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