Centers of hyperbolic components in the Mandelbrot set, up to period 32, rounded to nearest 10^{-26}

The Mandelbrot set is the set of parameters c such that the sequence z_{n+1} = z_n^2 + c starting from z_0=0 remains bounded. Centers of hyperbolic components are the parameters c for which the sequence (z_n) is periodic. These centers are classified by their period, which is the smallest positive integer k such that z_k=0; the set of such parameters is denoted by Hyp(k). For a given integer n, the roots of the polynomial p_n(c) defined recursively by p_n(c) = p_{n-1}^2(c) + c where p_0(c)=0 is composed of hyperbolic centers of period k, for all divisors k of the integer n. In other terms, the set of roots of p_n is the union of Hyp(k) when k divides n. This data set contains a list of all hyperbolic centers Hyp(k) in the Mandelbrot set, up to period k=32, with non-negative imaginary part. Each file contains a list of roots, z=a+ib with a and b rounded to the nearest 10^{-26}, that is 85 bits of precision. The files are in CSV format, with one root per row, presented as the character chain "a, b". Note b is always non-negative. For periods 26 to 32, the CSV files are compressed using the BZ2 algorithm. This data results from a conversion to human-readable decimal form of a high-precision and certified database, as explained in the reference [arXiv:2402.06083]. This larger database extends all the way to period 41. Please contact the authors if you need access. For pre-periodic parameters, please refer to the dataset [https://doi.org/10.5281/zenodo.15527762]. Note: please be careful that some programs mishandle CSV files that contain floating point numbers whose precision exceed machine precision (which is definitly the case here). To avoid such unpleasantness, we suggest accessing the CSV files programmatically, as text-based files. To add data protection to your workflow, we recommend using a certified file format, as explained in [arXiv:2402.06083] and implemented in [https://github.com/fvigneron/Mandelbrot].