You could definitely do this in 3DS Max. Just create a long tube, along with an extra spline down the middle to use as a camera path. Then bend the tube and spline using identical modifiers to the shape you want. I would create the animated material in After Effects, making sure that it's tileable on both x and y axes, as well as a seamless loop.
Then just apply the material to your tube in Max, so that it's animating the way you like it, and animate your camera along the path down the middle of the tube. I know nothing about Apophysis, other than it's a free fractal flame generator.