Animated line art

I'm hoping to create animation that is both a function of time and space, but, can't figure out if it is possible in UF 6. As an example, let's say that I have created a single layer that contains a single Beziar curve that is colored all white. I can apply a coloring algorithm that changes as a function of time (i.e. a function of frame number). When I apply the coloring function, it applies it spatially applies the coloring to the entire fractal. However, I'd like to make only a portion of the line to appear as a function of time (e.g. at frame 1 I'd like none of the curve to be visable and at frame number 20 I'd like only the 1st third of the Beziar curve frame to be fully visable).
I've tried several solutions, but, none really work that well. e.g. instead of one layer, I create several layers, and, then, try to make each new layer visable as a function of frame number. I doesn't appear that layer on/off can be animated.
Any ideas? Thanks. Bob

There are two possible approaches, depending on how you generate the "Beziar curve".

1. If your "Beziar curve" formula or coloring has parameters to show only part of the curve, you can animate those parameters to control how much of the curve is displayed over time.

2. Put your "Beziar curve" (or any other fractal) on one layer, and create a new layer with a white rectangle and a transparent background (the Clipping mapping is useful for this). Make the white rectangle cover the entire curve at frame 1, then animate the rectangle's center or position to move it right over time.

Thanks for the ideas. The second idea sounds promising. To implement the first idea, I'll need to hunt around for a formula or a coloring profile that allows control for only a portion of the curve to be displayed over time. I'll let you know how it works out.

You can animate the opacity of a layer by the way. But I think there are better ways to do what you want than by showing many layers one at a time.

Thx again for your ideas. I hadn't thought of animating the opacity of the layer. I've been successful at integrating the idea of movement along a predefined path using the "glass lens" transformation.

In my current fractal, there's only a single frame that contains a single Bezier line. But, it has the "twist" transformation applied to it, so it looks like a spiral. I'm trying to attach a short (3-second) video to show my current progress, to this post. Next step will be to hide portions of the curve as time changes. And then next step is to try to make it look 3-d. I'm having fun with this ....