Noise: a different flavour of wiggle

Because it’s so useful for adding pleasing randomness to anything, Wiggle has become a kind of gateway drug to expressions. But it has a much less famous sibling, noise. I’ve never really played with noise before, so I thought I’d investigate it further.

This is a test of noise vs wiggle. The blue circle has a straight-out-of-the-box wiggle(1, 500) applied to it (the parameters mean a frequency of 1 and amplitude of 500.

The yellow circle has noise applied to the X and Y according to this expression:

value + [noise(time), noise(time+12345)] * 500

According to the Adobe docs, noise can take a number or an array as its one parameter, but it always returns a number between -1 and 1. This is why I had to call it twice, once for each component of the position vector. noise always returns the same result for the same input, so to get it to change over time, I used time as the input.

The reason why I added 12345 to the time for the y component was that if I’d used noise(time) for both terms, they would have always been the same, meaning the layer would just move along a diagonal line. To create interesting movement I slipped the x and y components out of phase (more on that later).

The * 500 scales the movement up so that it fills the comp, and to move it to the center I added the layer’s original position to the expression adding the term value.

If you look at the difference between the noise layer and the wiggle layer you’ll see that wiggle wanders more, where noise keeps returning to the center. Here’s the path that each layer takes; first wiggle:

Then noise:

The reason for this daisy-shaped path can be seen from the graph of the position of the noise layer, and highlights an interesting and useful property of noise(). If you look at the graph of the expression something is immediately apparent: even though both components are varying smoothly and somewhat randomly, at the points where the time is an integer, i.e. every whole second, noise() returns zero, which means at that point both x and y come back to the origin.

This could be very useful for random behaviour that you want to loop. Since you know that the value will return zero at when the seed is an integer, you can make sure the seed you give it is an integer at the beginning and end of the loop.

In the above expression the y component is out of phase 12345 seconds, a whole number. What happens if I put it out of phase by half a second, as in the graph below?

The answer is this:

Now instead of a daisy-like pattern with a return to the center every second we get loops. The path looks like this:

So what happens if we animate the phase difference? That is, we move the offset of the time component from zero to an arbitrary number.

noise(time + (time * n))

In the video below, instead of applying the result to the movement of a layer, I applied it to the points in a path, because that’s a thing now. To create the path, I generated 6400 points and used noise to assign their x and y coordinates. I didn’t worry about the in-out handles because the number of points was high enough that it looks smooth just with straight lines.

let pt = [];

for (i = 0; i< 6400; i++){
	pt[i] = [thisComp.width,thisComp.height]/2 + [noise(i/100), noise(i/100 + time)]*500;
}
createPath(points = pt, inTangents = [], outTangents = [], isClosed = false)

It looks a bit Lorenz attractor-ish. Interestingly the figure appears to rotate in 3D, even though it’s completely 2D. You’ll also notice the way it comes back to the daisy-like figure at every second, because the two components are out of phase by a whole number. I wonder how long it would take to get back to the original figure?

A different flavour of wiggle

So that’s noise; a useful addition to the toolbox if you want a random fluctuation but you want it to be periodic. Good for buzzing flies, or looping asteroids, or stochastic daisies.

Next time I’m going to be looking at some of the undocumented text features built-in to expressions, and how they can be used for advanced project management.

Appendix: how I made the trails

Drawing lines and shapes programmatically in After Effects is harder than it should be. This is really basic stuff in something like Processing, but you have to jump through hoops in AE.

Here’s how I did the trails for the circles. It’s a bit of a brute-force approach, nothing too clever, but it does only use built-in effects (that’s generally how I roll).

• First I made a smaller copy of the circle layers, only a couple of pixels wide. I parented them to the originals, and put them on the bottom of the layer stack.
• Then I added an adjustment layer with the echo effect on it.
• I cranked up the number of echoes to an insane amount, 3200 in this case, and set the echo time to about 1/40 th of a frame, or -0.001. A bit of trial and error to get the sweet spot where the trails look smooth, but not too slow.
• to get the nice fade out I adjusted the decay. This setting sets how each echo fades out, so with so many echoes it needs to be close to 1 or the trail fades out too early. the value I ended up with was 0.9994 (In the UI it just show up as 1 until you click on the edit box).

For prettiness I also added another adjustment layer with a blur effect and some curves. This adds a little bit of a halo, and by affecting just the bright parts, makes the highlights pop. The transfer mode of this layer is Add, and its opacity is 60%

To create static shapes I could have used something like the expression in the third video, where I drive a shape layer with noise. But for the sake of a single image I did this:

• convert the position of the circles to keyframes (Animation Assistant>convert Expression to Keyframes)
• Select the keyframes by clicking on the position property.
• create a shape layer with an empty open path by clicking with the pen tool, and selecting the Contents>Shape 1>Path 1>Path property (you have to twirl down all the way
• With the Path property selected, paste the keyframes. They will get converted from movement to a shape (you can do this in reverse too, to make movement out of any shape, it’s quite useful).
• Adjust the properties of the stroke to suit.