Simulating Noise Transition in Gradients

The current gradients have a "noise" transition option which is nice but you either turn it on or off - no control over how much noise, what the noise looks like, etc.. So I decided to try to simulate it using a noise function of my own and it turned out to be more complicated than I thought it would be. This is primarily due to the fact that there is no allowance for negative values in curves. What I needed was a linear curve with noise added to it. The noise needed to be damped at both ends to 0 and in the middle to be both positive and negative. In the end I centered the noise at 1/2, then took a max/min between the min and a straight line across at 1/2 to get the part of the noise greater than 1/2 and less. Subtracting out 1/2 from the max curve and subtracting the min curve from 1/2 gave me the portions above and below "0", multiplying them (for the damping) or adding them (for the linear case) finally got my final result. This seems like a lot of effort just to account for negative values in curves. Is there a better way?

In the attached file, I've grouped the damping portion separately from the addition portion. Probably would have been more efficient to put them together but I wanted to keep them separate for potential future use. Also, I should note that any function "centered" around 1/2 would work. Noise just happened to be the thing I was trying to simulate.

PosNeg Components.ffxml