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You can run it with BigDecimals or whatever unlimited number type your language has just fine, and it will give a very similar looking image.
by kaba0 4y ago
You can run it with BigDecimals or whatever unlimited number type your language has just fine, and it will give a very similar looking image.
- Someone 4y agoThat doesn’t help in understanding why this thing is numerically quite stable. It only gives some confidence that it is.
- ataylor284_ 4y agoAll the visualizations of the mandelbrot set I've seen use a threshold of iterations that define the edge. I think that threshold is more significant than any instability due to floating point numbers. A more formal analysis of numerical stability comes down to whether the iterated function is considered well-conditioned. I don't have the math to state it formally, but my intuition is that the mandelbrot function is, in that a small change to the function input will have a small effect on the number of iterations except at the very edge where the threshold will define the boundary anyway.
- kaba0 4y agoYeah, I didn’t intend it as a formal proof, but it is an easy argument to make. I’m sure an error limit can be given, as it uses a quite basic arithmetics only.