Hi Jim, If the scene were calculated closer and closer to point -0.75, the camera could zoom in on it proportionally and keeping the apparent width of the valley the same. What ever the computer, it could do this until it ran out of time to complete the next scene. Interestingly, this shows that while the distance to the singularity is finite, there are an infinite number of increments before getting there. If the scenes get slower and slower to calculate, presumably because the number of digits past the decimal point also approaches infinity, it can be thought in an abstract way as though the closer the scene gets to the singularity, that time is slowing down to the observer of the scene. Actually these statements are probably true of the whole fractal I suppose. I also am wondering if all the buds are pinched off in this manor. Roger
I have also often wondered what lies at the point -0.75 of the Mandelbrot set. What would we find there if we had a computer of infinite speed, which would give infinite magnification? I suspect that, at the -0.75 point, Seahorse Valley is kind of a singularity with a width of zero, which means that even infinite magnification would leave it with zero width. But a departure of an infinitesimal value in the imaginary direction would introduce an infinitesimal but real width, which an infinitely fast machine would calculate and magnify to any degree in an instant. Since infinitely fast machines will always exist only