## Details### CanyonDeepCanyonDeep will be a modestly deep zoom into the canyon part of the set (aka the Seahorse Valley), which we've previously explored a bit in Canyon1 and Canyon2. CanyonDeep will actually not be very deep itself in terms of its final frame magnification, and it will have a quite different plan from the previous two. Canyon1 and Canyon2 both zoomed into the cusp just a little bit, then moved off to one side and zoomed way deep down into some interesting structures. CanyonDeep will zoom way down into the cusp first, so deep that it will just look like a single-pixel wide line for a moment, then it will move off to one side and zoom in to something for a short span. Since this video will include a huge number of points very close to the boundary of the Mandelbrot set, this is a vastly more computationally demanding plan than the previous two Canyon animations. That is why I've been working hard to make sure that the software has everything I can think of to speed up the process. Last month we talked about improvements in the high-precision math and about using the rectangular decomposition method of rendering. I thought those would be enough, but I've had to dust off another old trick, and some people aren't going to like it. The problem with this project is that most of the test images I've made of reasonable endpoints are taking about 60-90 hours to render ... just a single frame! This is not because they're at super-deep magnifications, but rather because the iteration count has to be turned up so high to get an image. The average count number is in the tens of millions, which is a hundred to a thousand times higher most of the other videos I've made, even the ones that zoom to beyond 1e100. This is because the image is so close to the edge of the set, much closer than any other video I've tried to make. The solution -- the only solution I can see -- is to use frame interpolation to render this animation. ### Frame InterpolationThis technique has been around at least since 1988 and was described in Peitgen & Saupe, *The Science of Fractal Images*. Some commercial fractal programs do this, and many (but certainly not all!) of the existing fractal animations use this method. I've written a fair amount about this on the Technical-Animation page of HPDZ.NET, including a discussion of whether this is really "cheating" or not. |