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This is awesome, but reminds me of something I was recently wondering: why are there no infinite-zoom Mandelbrot viewers? They all stop at a certain level of zo

This is awesome, but reminds me of something I was recently wondering: why are there no infinite-zoom Mandelbrot viewers? They all stop at a certain level of zoom instead of generating the finer details. What's the limitation? I can't imagine you'd have to render the entire fractal in fine detail to zoom in on a specific piece.

shric 3y ago
Usually programs hit the limits of float32 or float64. A float64 has a around a 10 to the minus 16 precision to play with (53 bit significand) so you can hit the zoom limit with little effort. There are various techniques to go further (obviously one is just to use arbitrary precision arithmetic, another is for example perturbation theory[1]) And there are plenty of "infinite" (or at least some arbitrarily huge level) zoom viewers. You can find videos of zooms going into 10 to the power of thousands. The deeper you go the longer the calculations take. [1] https://en.m.wikipedia.org/wiki/Plotting_algorithms_for_the_Mandelbrot_set#Perturbation_theory_and_series_approximation https://en.m.wikipedia.org/wiki/Plotting_algorithms_for_the_...
- tetris11 3y ago
  Couldn't you seamlessly replace one number domain with another to keep the precision up? E.g. remap: 1e-7 to 9e-7, to numbers 1 to 9?
  - shric 3y ago
    Floating point already does that with separate mantissa and exponent bits. Regardless, you still have a limited number of bits for precision.
shric 3y ago
I'm replying again to you as I can't edit my previous reply. I forgot to mention that the iteration count in the linked site is set by default to only 200. That's the number of iterations of the formula (for the mandelbrot it's z=z*2+c where z and c are complex) is calculated to determine whether a given value of c (coordinate on the complex plane) diverges or not (the mandelbrot is the set of all values of c where it doesn't diverge. z starts at 0). Thus you can increase the iteration count, but again more calculations. All other things equal, more zoom leads to more precision and more iterations.

shric 3y ago

Usually programs hit the limits of float32 or float64. A float64 has a around a 10 to the minus 16 precision to play with (53 bit significand) so you can hit the zoom limit with little effort. There are various techniques to go further (obviously one is just to use arbitrary precision arithmetic, another is for example perturbation theory[1]) And there are plenty of "infinite" (or at least some arbitrarily huge level) zoom viewers. You can find videos of zooms going into 10 to the power of thousands. The deeper you go the longer the calculations take. [1] https://en.m.wikipedia.org/wiki/Plotting_algorithms_for_the_Mandelbrot_set#Perturbation_theory_and_series_approximation https://en.m.wikipedia.org/wiki/Plotting_algorithms_for_the_...

tetris11 3y ago
Couldn't you seamlessly replace one number domain with another to keep the precision up? E.g. remap: 1e-7 to 9e-7, to numbers 1 to 9?
- shric 3y ago
  Floating point already does that with separate mantissa and exponent bits. Regardless, you still have a limited number of bits for precision.

shric 3y ago

I'm replying again to you as I can't edit my previous reply. I forgot to mention that the iteration count in the linked site is set by default to only 200. That's the number of iterations of the formula (for the mandelbrot it's z=z*2+c where z and c are complex) is calculated to determine whether a given value of c (coordinate on the complex plane) diverges or not (the mandelbrot is the set of all values of c where it doesn't diverge. z starts at 0). Thus you can increase the iteration count, but again more calculations. All other things equal, more zoom leads to more precision and more iterations.