We propose that the core mass function (CMF) can be driven by filament fragmentation. To model a star-forming system of filaments and fibers, we develop a fractal and turbulent tree with a fractal dimension of 2 and a Larson's law exponent (beta) of 0.5. The fragmentation driven by convergent flows along the splines of the fractal tree yields a Kroupa-IMF-like CMF that can be divided into three power-law segments with exponents alpha = -0.5, -1.5, and -2, respectively. The turnover masses of the derived CMF are approximately four times those of the Kroupa IMF, corresponding to a star formation efficiency of 0.25. Adopting beta = 1/3, which leads to fractional Brownian motion along the filament, may explain a steeper CMF at the high-mass end, with alpha = -3.33 close to that of the Salpeter IMF. We suggest that the fibers of the tree are basic building blocks of star formation, with similar properties across different clouds, establishing a common density threshold for star formation and leading to a universal CMF.