Secant Animation 1
This newest animation is what I call a "tour" video -- it moves around the fractal, zooming in to certain areas, then zooming out and moving over to a new area, to give a sense of the entire structure. This kind of animation is enormously complicated to plan and requires careful storyboarding and lots of trial and error to get all the motion correct.
This kind of video is different from the style of SA2, which was a parameter roll type of animation (that is, the viewpoint stayed essentially fixed while the numerical values controlling the fractal shape changed). This is also different from most of the other animations I've made, which have mainly been deep-zooms that zoom into a specific point on the fractal without moving around at all.
It's number 1 because there's another related project that I started after this one. SA1 turned out to be much more difficult to render due to the elaborate motion paths that had to be carefully tuned, and it was also very difficult to colorize properly. SA2 was easier to make and also useful for some software testing issues, so it got published first.
The fractal is the result of applying the secant method for numerically solving equations to finding the zeros of the cosine function. More details can be found here.
The colorizing was done manually for the first time in this video. Overall, I am pleased, but there is one span around time 4:10 in the final video where the colors get kind of simplified and too monotone. This could have been changed, but the cost would have been that the ten seconds or so leading up to that point would have the color palette changing at an unacceptably fast and annoying pace.