Earth surface area is 5.1e14 m^2. A high-resolution display has resolution 200 dpi, or 0.000127 meters per pixel. We consider the task of generating a virtual world the size of earth at that resolution.
Earth surface area at that resolution would have 3.16e22 pixels. This is equivalent in area to a circle with radius 1.00e11 (10^11) pixels.
Fractal terrain generation (e.g., plasma fractal) is ideal for this kind of task: terrain can be computed on demand at the resolution and location needed, never having to precompute nor store. However, we will take a detour and consider the Mandelbrot set, a fractal different from the plasma fractal. The Mandelbrot set has a fixed size, which is useful to get a sense of the scale needed to generate 10^22 pixels. The Mandelbrot is contained within a circle of radius 2, so computing the Mandelbrot set with pixel spacing 2e-11 would yield 3.16e22 pixels. (Incidentally, this spacing is well within double precision's 15 significant digits of precision, so no need for arbitrary precision arithmetic.)
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