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Mandelbrot deep zoom theory and practice (2021)
Perturbation and rescaling for efficient rendering of fractal images.
This floatexp technique works for arbitrarily deep zooms, but the performance is terrible because it needs to handle every arithmetic operation in software (instead of them being a single CPU instruction). The Burning Ship fractal modifies the Mandelbrot set formula by taking absolute values of the real and imaginary parts before the complex squaring : It remains open how to choose the \(G\) for Pauldelbrot's glitch detection criterion, and how to robustly compute series approximation skipping: there is still no complete mathematical proof of correctness with rigourous error bounds, although the images do most often look plausible and different implementations do tend to agree.
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