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Fun fact: the Mandelbrot set (including its interior) is not known to be computable. A computable (compact) set is one where a program can compute arbitrarily
by rssoconnor 5y ago
Fun fact: the Mandelbrot set (including its interior) is not known to be computable. A computable (compact) set is one where a program can compute arbitrarily close approximations (in Hausdorff distance) by using a finite set of (rational) points.
Makes you wonder a little bit about the drawings you see rendered.
- ska 5y agoIt's not a practical problem. Renderings are all based on fixed resolution, so the approximation doesn't have to be arbitrarily close. Note this doesn't mean most of the renderers aren't wrong in subtle and not so subtle ways ways, but that you can do something reasonably careful with it and not need unbounded computation.