Parametric functions

Just out of interest, here are the standard functions we are used to, but converting the second differential of the function to curvature instead. Or equivalently, converting gradient to path angle:

x

x^2

x^3

x^4

tan x

1/x

exp x

log x

x^x

normal dist

8.5 * normal dist

But one of the more interesting is probably the sine function, which looks quite different just by scaling up:

sin x

pi/2 sin x

2.11 sin x

2.405 sin x

2.66 sin x

pi sin x

4.7 sin x

5.24 sin x

The coefficient in the figure eight sine wave is more precisely the first zero of the Bessel function J_0. Credit to Greg Egan for pointing that out.