3d Tubular intperpolation of a 2d fractal zoom?

[Mrz00m]

I wrote a 3d game that involves flying a spaceship in a tube, where the perspective naturally zooms towards infinity in the distance, so it is similar to a fractal zoom.

It would be nice to unwrap a mandelbrot zoom into square / cylinder array of textures that i can use to color the tube. perhaps it's possible?  For example, i record a ring of pixels around the centre of the zoom, about 1024 pixels in circumference, and i zoom the fractal through 4096 distances and add together all the circumference into a 1024 x 4096 pixel fractal texture? What is the maths to make a 2d fractal zoom into a list of textures? is it very easy?

[Pauldelbrot]

That'd be the Mercator map technique. Search https://www.google.ca/search?q=%22mercator+map%22+site%3Afractalforums.com