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Dan Ebberts
Sacramento, California, USA
©2004 by Dan Ebberts and CreativeCow.net. All rights are reserved.
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Article Focus:
The After Effects expression language has a seldom-used random number generator that is really quite a gem. Dan Ebberts says “seldom-used” because he doesn't believe he's ever seen it used in a single expression he's seen posted on the internet. It’s not the easiest command to understand and the documentation is pretty sparse but once you get past that it’s very cool.
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Before we get into how to use it, let’s set up a scenario where we might want to use it (if we only knew that it existed). Suppose you had a grid of dots and you wanted to generate an undualting 3D motion like the dots were attached to a flag waving in the wind or were floating on water. One way to do this would be to set up a grid of dots and then have a comp-sized layer of Fractal Noise below and have each dot’s z position related to the luminace of the Fractal Noise patten directly below the dot. Let’s say we want brighter areas of the noise to move the dots closer to the camera and the darker areas to move the corresponding dots away from the camera. As we animate the “Evolution” parameter of the Fractal Noise we would expect the dots to undulate as the underlying luminance vlaues change. Note that what we’re looking for is not independent random motion for each dot. We want it to appear as if the dots are connected to an undulating surface. That means that the position of each dot is related to that of its neighbor.
OK this sounds like a cool project – let’s get started. There’s just one problem. As you may have discovered, there’s no way (without the help of a plugin) to access pixel luminance values from an expression. There are some nifty plugins that will let you do this “Anarchy Toolbox” from Digital Anarchy has “Color Sampler”, “Expression Effects” from Bresnev Shu has “Color Analysis Node”, and Useful Things from Profound Effects also gives you access to the pixel color and luminance values. Each of these wonderful plugins provides you a way to solve our design problem (and much, much more). But in this very specialized, particular case (where we want to use fractal noise to generate an undulating motion) we’re going to be able to pull this off with the tools provided within AE’s expression language.
The trick to all this is the “noise()” function. What this lets us do is create our own Perlin noise space (if you’re interested in the math, use Google to look up “Perlin noise” which is the basis of many fractal noise patterns). It gives us access to a 3D noise structure that extends in all directions. We can simulate moving through it in any direction. We won’t be able to see it like you can with Fractal Noise, but we’ll be able to see the affect it has on our dots. Picture it as a gigantic wispy fog bank that you can wander around in and take sample fog density readings wherever you are.
The noise() function accepts a single parameter that can have one, two, or three dimensions. It’s useful to visualize these as offsets in x, y, and z directions. If you supply a one-dimensional parameter the results of varying that parameter would be like moving along a straight line in our fractal noise environment. A two-dimensional parameter would be like moving around in a single plane of the noise space, and a three-dimensional parameter gives you access to the whole 3D space. The output is a number between 0 and 1 that is somewhat random, but has correlation to nearby points.
OK – so here’s the plan. We’ll set our dots up in a grid (actually, we’ll apply an expression that will allow our dots to position themselves in a grid - much less work). We’ll use each dot’s x and y position as the first two inputs to the noise() function. We’ll use the result of the noise() functin to calculate each dot’s z displacement based on the value of the noise field at that x/y location. We’ll use time as the third dimension of the input to noise() that will effectively move our plane throught the 3D fractal noise space. The result should be undulating dots.
So our position expression for each dot will be a combination of grid-positioning for x and y and a noise() component for z. Let’s tackle the grid part first. We’re going to set up a 10 x 10 grid of dots.
Start by creating a 640 x 480 comp several seconds in length. Then add a 30x30 solid layer. Make it 3D and set the quality to best. Make it a circle/dot by double clicking on the circular mask tool. Add this expression to the Position Property:
numRows = 10;
numCols = 10;
row = Math.floor((index - 1)/numCols);
col = (index - 1)%numCols;
x = col*width + width/2;
y = row*height + height/2;
xOffset = (this_comp.width - numCols*width)/2;
yOffset = (this_comp.height - numRows*height)/2;
[x,y,position[2]] + [xOffset,yOffset,0]
Now duplicate the “dot” layer 99 times. I do this by selecting the layer, hitting Ctrl+d 9 times, select all the dots and hit Ctrl+d nine more times. The dots should spread themselves out to fill in a 10x10 grid. Note that you can create any grid size you want by changing the “numRows” and “numCols” parameters and making the appropriate number of duplicates. If you want smaller dots, just start with a smaller solid – the expression will adjust.
At this point you might want to create a camera and position it so that you can see the grid on an angle so you’ll be able to clearly see motion in the z direction. I added a light for dramatic effect. Note – put the camera and light on the bottom of the layer stack, otherwise it will mess up the grid calculation, which relies on the layer index and expects layer 1 to be the first dot.
Now that we’ve demonstrated that we can, in fact, generate a self-populating 10x10 grid of dots without too much trouble, we’re ready to add in the undulating part of the expression. Delete 99 of the dot layers so we’ll only have to modify one expression – then we’ll recreate the duplicates.
Here’ the modified expression:
numRows = 10;
numCols = 10;
xyCompress = 200;
speedCompress = 1;
amplitude = 100;
row = Math.floor((index - 1)/numCols);
col = (index - 1)%numCols;
x = col*width + width/2;
y = row*height + height/2;
xOffset = (this_comp.width - numCols*width)/2;
yOffset = (this_comp.height - numRows*height)/2;
z = amplitude*noise([x/xyCompress,y/xyCompress,time/speedCompress]);
[x,y,z] + [xOffset,yOffset,0]
Let’s take a look at what’s different. You’ll notice that we’ve added three new parameters at the top of the expression. The first one, “xyCompress” that will define how closely correlated the z position of adjacent dots will be. The larger this number is, the more related adjacent positons will be. In other words, larger values of “xyCompress” will give you a smoother undulation, smaller values will give you more chaotic undulation. The next new parameter is “speedCompress”. This will determine how fast we move through our fractal noise field. In practical terms, the larger the value of “speedCompress” the slower the undulation. The last new parameter is “amplitude”. This simply scales the output of the noise() function (which is normally between 0 and 1) to the range of z movement (in pixels) that we want in our undulation. In this case, we’ll get values between 0 and 100 pixels.
Finally, the lst new line of code – where all the action takes place – is the call to noise(). We feed it the x and y position of our dot (scaled by “xyCompress”) and the current comp time (scaled by “speedCompress”) and get a z offset that we multiply by “amplitude”. Then all we have to do is replace “position[2]” from our first expression with “z” and we’re done.
Create the 99 duplicates again and preview. If you did everything correctly, you should be rewarded with a nice 10x10 grid of undulating dots.
Once you get your brain wrapped around noise(), you start to see where it can come in handy to have access to a 3D noise field within the environment of After Effects expressions. Think about it. Natural effects like wind flowing through a field of grass or lilypads on a pond. The possibilities are endless. That’s my hidden gem of the week. 8^>
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##Dan Ebberts
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