Fade Over Time Node and Controlling Random Distributions with Curves

This week we have a look at the Fade Over Time node and also how we can control Random distributions with Curve Inputs
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[@artvfx1117]

Interesting stuff, and my feedback is nice beard

[@tomtawadros]

Audio's a bit low on this one but otherwise another good video. One thing I want to point out/correct is about using curves to control the distribution of random numbers. Around 10:15 you start showing how to do this, and you explain that the first example of a line gives the same result as no curve, meaning a uniform distribution. That's true and makes sense. The next example uses the template cubic curve that we use all the time in VFX with 0 on either end and 1 in the middle. You say that with this curve, you're much more likely to get values in the middle (where the curve peaks) as opposed to the ends. However, by this logic you would expect the line in the first example to produce many more values at the high end of the curve than at the low end. In the third example you then set the curve to 0 for most of the range, and explain that this will produce an output of 0 most of the time. This is of course true, but it contradicts the logic of the second example.
The curve that's used to define the distribution here is not the actual distribution of the results. It makes intuitive sense in the first and last examples as you explain, but I think the second one causes confusion because it looks like a bell curve and we (myself included) initially make the assumption that it actually represents the distribution. In reality the distribution of values for the second curve looks like a U, with many values around 0 and equally as many around 1. The distribution is bimodal. If you only want values to cluster around 1, then the ends of the curve need to drop sharply.
If you couldn't tell I've spent a good bit of time digging into this lol. I've wanted to learn how to redistribute random numbers in Niagara for a while now, and this video gave me some great insight and motivation to dig deeper. I haven't yet figured out how to visualize the actual distribution give an IO curve in Niagara, but I'll post here when I figure that out.

[@tharlevfx]

Yeah, you’re right - a normal distribution of results would be a sort of flattened S shape curve wouldn’t it?

[@tomtawadros]

@@tharlevfx Yeah something like that. Interestingly I'm finding that using sufficiently strong weighted tangents produces incorrect values when the index is high (near 1). The output values start dropping sharply to 0, which messes with the distribution of course.

[@johninglis2622]

What would you used this for an example?

[@tharlevfx]

@@johninglis2622 using curves to control randomness could be used for anything with a non linear random distribution. For example a lot of small particles and a few big ones could be spawned from the same emitter.
Fade over time is less frequently used since we tend to just animate parameters directly, but you could set up looping particles that changed their size this way, for example