Estimate the of fractal dimension of a black area in 2D and 3D (slices) images using the box-counting method. See Klinkenberg B. (1994) <doi:10.1007/BF02065874>.

Turn numeric,data.frame,matrix into fraction form.

The main function of this package allows numerical vector objects to
  be displayed with their values in vulgar fractional form.  This is convenient if
  patterns can then be more easily detected.  In some cases replacing the components
  of a numeric vector by a rational approximation can also be expected to remove
  some component of round-off error.  The main functions form a re-implementation
  of the functions 'fractions' and 'rational' of the MASS package, but using a
  radically improved programming strategy.

Provides functions for converting decimals to a
    matrix of numerators and denominators or a character vector of
    fractions.  Supports mixed or improper fractions, finding common
    denominators for vectors of fractions, limiting denominators to powers
    of ten, and limiting denominators to a maximum value.  Also includes
    helper functions for finding the least common multiple and greatest
    common divisor for a vector of integers.  Implemented using C++ for
    maximum speed.

A collection of user-friendly functions for assessing and visualizing fragility of individual studies (Walsh et al., 2014 <doi:10.1016/j.jclinepi.2013.10.019>; Lin, 2021 <doi:10.1111/jep.13428>), conventional pairwise meta-analyses (Atal et al., 2019 <doi:10.1016/j.jclinepi.2019.03.012>), and network meta-analyses of multiple treatments with binary outcomes (Xing et al., 2020 <doi:10.1016/j.jclinepi.2020.07.003>). The included functions are designed to: 1) calculate the fragility index (i.e., the minimal event status modifications that can alter the significance or non-significance of the original result) and fragility quotient (i.e., fragility index divided by sample size) at a specific significance level; 2) give the cases of event status modifications for altering the result's significance or non-significance and visualize these cases; 3) visualize the trend of statistical significance as event status is modified; 4) efficiently derive fragility indexes and fragility quotients at multiple significance levels, and visualize the relationship between these fragility measures against the significance levels; and 5) calculate fragility indexes and fragility quotients of multiple datasets (e.g., a collection of clinical trials or meta-analyses) and produce plots of their overall distributions. The outputs from these functions may inform the robustness of clinical results in terms of statistical significance and aid the interpretation of fragility measures. The usage of this package is detailed in Lin and Chu (2022 <doi:10.1371/journal.pone.0268754>).